def check_sums(array, k):
    potential_solutions = set()
    for num in array:
        if num in potential_solutions:
            return True
        potential_solutions.add(k - num)
    
    return False


assert not check_sums([], 17)
assert check_sums([10, 15, 3, 7], 17)
assert not check_sums([10, 15, 3, 4], 17)

def get_factors(array):
    cumulative_product = 1
    right_prod_array = list()
    for num in array:
        cumulative_product *= num
        right_prod_array.append(cumulative_product)

    cumulative_product = 1
    left_prod_array = list()
    for num in array[::-1]:
        cumulative_product *= num
        left_prod_array.append(cumulative_product)
    left_prod_array = left_prod_array[::-1]

    output_array = list()
    for i in range(len(array)):
        num = None
        if i == 0:
            num = left_prod_array[i + 1]
        elif i == len(array) - 1:
            num = right_prod_array[i - 1]
        else:
            num = right_prod_array[i - 1] * left_prod_array[i + 1]
        output_array.append(num)
    
    return output_array


assert get_factors([1, 2, 3, 4, 5]) == [120, 60, 40, 30, 24]
assert get_factors([3, 2, 1]) == [2, 3, 6]

import json

class Node:
    def __init__(self, data):
        self.data = data
        self.left = None
        self.right = None
    
    def __repr__(self):
        return str(self.data)

def serialize(root):
    if not root:
        return None

    serialized_tree_map = dict()
    serialized_left = serialize(root.left)
    serialized_right = serialize(root.right)

    serialized_tree_map['data'] = root.data
    if serialized_left:
        serialized_tree_map['left'] = serialized_left
    if serialized_right:
        serialized_tree_map['right'] = serialized_right

    return json.dumps(serialized_tree_map)


def deserialize(s):
    serialized_tree_map = json.loads(s)

    node = Node(serialized_tree_map['data'])
    if 'left' in serialized_tree_map:
        node.left = deserialize(serialized_tree_map['left'])
    if 'right' in serialized_tree_map:
        node.right = deserialize(serialized_tree_map['right'])

    return node


node_a = Node('a')
node_b = Node('b')
node_c = Node('c')
node_d = Node('d')
node_e = Node('e')
node_f = Node('f')
node_g = Node('g')
node_a.left = node_b
node_a.right = node_c
node_b.left = node_d
node_b.right = node_e
node_c.left = node_f
node_c.right = node_g

serialized_a = serialize(node_a)
print(serialized_a)

deserialized_a = deserialize(serialized_a)
assert str(deserialized_a) == "a"

def get_positive_subset(array):
    i = 0
    j = len(array) - 1

    while i < j:
        if array[i] > 0 and array[j] <= 0:
            array[i], array[j] = array[j], array[i]
            i += 1
            j -= 1
        elif array[i] > 0:
            j -= 1
        else:
            i += 1

    # print("i: {}, j: {}".format(i, j))
    # print("partitioned_array:", array)
    pivot = i if array[i] > 0 else i + 1
    return array[pivot:]


def get_missing_number(array):
    if not array:
        return 1

    array = get_positive_subset(array)
    array_len = len(array)
    # print("array: {}".format(array))

    if not array:
        return 1

    if max(array) == len(array):
        return max(array) + 1

    for num in array:
        current_num = abs(num)
        if (current_num - 1) < array_len:
            array[current_num - 1] *= -1
    # print("mutated_array: {}".format(array))

    for i, num in enumerate(array):
        if num > 0:
            return i + 1


assert get_missing_number([3, 4, -1, 1]) == 2
assert get_missing_number([1, 2, 0]) == 3
assert get_missing_number([1, 2, 5]) == 3
assert get_missing_number([1]) == 2
assert get_missing_number([-1, -2]) == 1
assert get_missing_number([]) == 1

def cons(a, b):
    return lambda f: f(a, b)

def car(f):
    z = lambda x, y: x
    return f(z)

def cdr(f):
    z = lambda x, y: y
    return f(z)


assert car(cons(3, 4)) == 3
assert cdr(cons(3, 4)) == 4

class Node:
    def __init__(self, data):
        self.data = data
        self.both = id(data)

    def __repr__(self):
        return str(self.data)

a = Node("a")
b = Node("b")
c = Node("c")
d = Node("d")
e = Node("e")

# id_map simulates object pointer values
id_map = dict()
id_map[id("a")] = a
id_map[id("b")] = b
id_map[id("c")] = c
id_map[id("d")] = d
id_map[id("e")] = e


class LinkedList:

    def __init__(self, node):
        self.head = node
        self.tail = node
        self.head.both = 0
        self.tail.both = 0

    def add(self, element):
        self.tail.both ^= id(element.data)
        element.both = id(self.tail.data)
        self.tail = element

    def get(self, index):
        prev_node_address = 0
        result_node = self.head
        for i in range(index):
            next_node_address = prev_node_address ^ result_node.both
            prev_node_address = id(result_node.data)
            result_node = id_map[next_node_address]
        return result_node.data


llist = LinkedList(c)
llist.add(d)
llist.add(e)
llist.add(a)

assert llist.get(0) == "c"
assert llist.get(1) == "d"
assert llist.get(2) == "e"
assert llist.get(3) == "a"

def is_char(code):
    return 0 if code > 26 or code < 1 else 1

def get_message_count(code):
    code_str = str(code)
    if len(code_str) == 1:
        count = 1
    elif len(code_str) == 2:
        count = 1 + is_char(code)
    else:
        count = get_message_count(int(code_str[1:]))
        if is_char(int(code_str[:2])):
            count += get_message_count(int(code_str[2:]))

    return count


assert get_message_count(81) == 1
assert get_message_count(11) == 2
assert get_message_count(111) == 3
assert get_message_count(1111) == 5
assert get_message_count(1311) == 4

   0
  / \
 1   0
    / \
   1   0
  / \
 1   1

class Node:
    def __init__(self, data):
        self.data = data
        self.left = None
        self.right = None
    
    def __repr__(self):
        return str(self.data)

def count_unival_trees(root):
    if not root:
        return 0
    elif not root.left and not root.right:
        return 1
    elif not root.left and root.data == root.right.data:
        return 1 + count_unival_trees(root.right)
    elif not root.right and root.data == root.left.data:
        return 1 + count_unival_trees(root.left)
    
    child_counts = count_unival_trees(root.left) + count_unival_trees(root.right)
    current_node_count = 0
    if root.data == root.left.data and root.data == root.left.data:
        current_node_count = 1

    return current_node_count + child_counts


node_a = Node('0')
node_b = Node('1')
node_c = Node('0')
node_d = Node('1')
node_e = Node('0')
node_f = Node('1')
node_g = Node('1')
node_a.left = node_b
node_a.right = node_c
node_c.left = node_d
node_c.right = node_e
node_d.left = node_f
node_d.right = node_g

assert count_unival_trees(None) == 0
assert count_unival_trees(node_a) == 5
assert count_unival_trees(node_c) == 4
assert count_unival_trees(node_g) == 1
assert count_unival_trees(node_d) == 3

import sys

def get_largest_non_adj_sum(array):
    previous, largest = 0, 0
    for amount in array:
        print("amount: {}; previous: {}; largest: {}".format(amount, previous, largest))
        previous, largest = largest, max(largest, previous + amount)
        print("new_previous: {}; new_largest: {}".format(previous, largest))
    return largest

print(get_largest_non_adj_sum([2, 4, 6, 8]))
print(get_largest_non_adj_sum([5, 1, 1, 5]))

from time import sleep

def sample_function():
    print("hello")

def schedule_function(f, delay_in_ms):
    delay_in_s = delay_in_ms / 1000
    sleep(delay_in_s)
    f()

schedule_function(sample_function, 10000)

def add_to_trie(s, trie):
    if not s:
        return trie

    character = s[0]
    if character not in trie:
        trie[character] = dict()
    
    trie[character] = add_to_trie(s[1:], trie[character])

    return trie

def get_dictionary_trie(dictionary):
    trie = dict()
    for word in dictionary:
        trie = add_to_trie(word, trie)

    return trie

def get_possible_completions(trie):
    possible_completions = list()
    for character in trie:
        if trie[character]:
            child_completions = get_possible_completions(trie[character])
            for child_completion in child_completions:
                possible_completions.append(character + child_completion)
        else:
            possible_completions.append(character)
        
    return possible_completions

def get_autocomplete_suggestions(s, dictionary):
    trie = get_dictionary_trie(dictionary)

    current_trie = trie
    for character in s:
        if character not in current_trie:
            return []
        current_trie = current_trie[character]

    completions = get_possible_completions(current_trie)
    completions = [s + x for x in completions]

    return completions 

assert get_autocomplete_suggestions("de", ["dog", "deer", "deal"]) == ["deer", "deal"]
assert get_autocomplete_suggestions("ca", ["cat", "car", "cer"]) == ["cat", "car"]
assert get_autocomplete_suggestions("ae", ["cat", "car", "cer"]) == []
assert get_autocomplete_suggestions("ae", []) == []

1, 1, 1, 1
2, 1, 1
1, 2, 1
1, 1, 2
2, 2

def get_step_combos(num_steps, step_sizes):
    combos = list()
    
    if num_steps < min(step_sizes):
        return combos
    
    for step_size in step_sizes:
        if num_steps == step_size:
            combos.append([step_size])
        elif num_steps > step_size:
            child_combos = get_step_combos(num_steps - step_size, step_sizes)
            for child_combo in child_combos:
                combos.append([step_size] + child_combo)
    return combos


assert get_step_combos(4, [1, 2]) == \
    [[1, 1, 1, 1], [1, 1, 2], [1, 2, 1], [2, 1, 1], [2, 2]]
assert get_step_combos(4, [1, 2, 3]) == \
    [[1, 1, 1, 1], [1, 1, 2], [1, 2, 1], [1, 3], [2, 1, 1], [2, 2], [3, 1]]

def get_longest_sub_with_k_dist(s, k):
    if not s:
        return ""
    elif len(s) <= k:
        return s
    elif k == 1:
        return s[0]

    distinct_char_count = 0
    seen_chars = set()
    candidate = None
    remaining_string = None

    # to keep track of where the second character occurred
    first_char = s[0]
    second_char_index = 0
    while s[second_char_index] == first_char:
        second_char_index += 1

    candidate = s
    for index, char in enumerate(s):
        if char not in seen_chars:
            seen_chars.add(char)
            distinct_char_count += 1

        if distinct_char_count > k:
            candidate = s[:index]
            remaining_string = s[second_char_index:]
            break
            
    longest_remaining = get_longest_sub_with_k_dist(remaining_string, k)
    
    longest_substring = None
    if len(candidate) < len(longest_remaining):
        longest_substring = longest_remaining
    else:
        longest_substring = candidate
    return longest_substring


assert get_longest_sub_with_k_dist("abcba", 2) == "bcb"
assert get_longest_sub_with_k_dist("abccbba", 2) == "bccbb"
assert get_longest_sub_with_k_dist("abcbbbabbcbbadd", 2) == "bbbabb"
assert get_longest_sub_with_k_dist("abcbbbaaaaaaaaaabbcbbadd", 1) == "a"
assert get_longest_sub_with_k_dist("abccbba", 3) == "abccbba"

from random import random
radius = 2


def estimate_pi(num_random_tests):
    pi_counter = 0
    rsquared = radius ** 2
    for _ in range(num_random_tests):
        x_rand = random() * radius
        y_rand = random() * radius
        if (x_rand ** 2) + (y_rand ** 2) < rsquared:
            pi_counter += 1

    return 4 * pi_counter / num_random_tests


assert round(estimate_pi(100000000), 3) == 3.141

from random import random

count_so_far = 0
result = None


def pick_random_element(x):
    global count_so_far, result
    count_so_far += 1

    print(count_so_far)

    if count_so_far == 1:
        result = x
    else:
        random_value = int(count_so_far * random())
        if random_value == count_so_far - 1:
            result = x

    return result


sample_stream = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
for index, element in enumerate(sample_stream):
    random_element = pick_random_element(element)
    print("Random element of the first {} is {}".format(index + 1, random_element))

class OrderLog:
    def __init__(self, size):
        self.log = list()
        self.size = size

    def __repr__(self):
        return str(self.log)

    def record(self, order_id):
        self.log.append(order_id)
        if len(self.log) > self.size:
            self.log = self.log[1:]

    def get_last(self, i):
        return self.log[-i]


log = OrderLog(5)
log.record(1)
log.record(2)
assert log.log == [1, 2]
log.record(3)
log.record(4)
log.record(5)
assert log.log == [1, 2, 3, 4, 5]
log.record(6)
log.record(7)
log.record(8)
assert log.log == [4, 5, 6, 7, 8]
assert log.get_last(4) == 5
assert log.get_last(1) == 8

dir
    subdir1
    subdir2
        file.ext

dir
    subdir1
        file1.ext
        subsubdir1
    subdir2
        subsubdir2
            file2.ext

class Node:
    def __init__(self, name, pathtype):
        self.name = name
        self.type = pathtype
        self.children = list()
        self.length = len(name)
        self.max_child_length = 0

    def __repr__(self):
        return "(name={}, type={}, len={}, max_child_len={})".format(
            self.name, self.type, self.length, self.max_child_length)


def create_graph(node_list):
    if not node_list:
        return None

    parent_node = node_list[0][1]
    level = node_list[0][0]

    for index, (node_level, _) in enumerate(node_list[1:]):
        if node_level <= level:
            break
        if node_level == level + 1:
            child_node = create_graph(node_list[index + 1:])
            parent_node.children.append(child_node)
            if child_node.children or child_node.type == 'file':
                if child_node.max_child_length + child_node.length > parent_node.max_child_length:
                    parent_node.max_child_length = child_node.max_child_length + child_node.length

    # print("current_parent: {}".format(parent_node))
    # print("it's children: {}".format(parent_node.children))

    return parent_node


def get_path_type(name):
    return 'file' if '.' in name else 'directory'


def get_longest_path(s):
    if not s:
        return 0

    individual_lines = s.split('\n')
    split_lines = [x.split('\t') for x in individual_lines]
    annotated_lines = [
        (len(x) - 1, Node(name=x[-1], pathtype=get_path_type(x[-1])))
        for x in split_lines]

    graph = create_graph(annotated_lines)

    return graph.max_child_length + graph.length if graph.max_child_length > 0 else 0


assert get_longest_path("dir\n\tsubdir1\n\tsubdir2") == 0
assert get_longest_path("dir\n\tsubdir1\n\tsubdir2\n\t\tfile.ext") == 18
assert get_longest_path(
    "dir\n\tsubdir1\n\t\tfile1.ext\n\t\tsubsubdir1\n\tsubdir2\n\t\t" +
    "subsubdir2\n\t\t\tfile2.ext") == 29

10 = max(10, 5, 2)
7 = max(5, 2, 7)
8 = max(2, 7, 8)
8 = max(7, 8, 7)

from collections import deque


def get_sliding_max(a, k):

    window_max_elements = list()

    if not a:
        return None
    if len(a) <= k:
        return max(a)

    dq = deque()

    for i in range(k):
        while dq and a[dq[-1]] < a[i]:
            dq.pop()
        dq.append(i)
    window_max_elements.append(a[dq[0]])

    for i in range(k, len(a)):
        while dq and dq[0] <= i - k:
            dq.popleft()

        while dq and a[dq[-1]] < a[i]:
            dq.pop()
        dq.append(i)

        window_max_elements.append(a[dq[0]])

    return window_max_elements


assert get_sliding_max([10, 5, 2, 7, 8, 7], 3) == [10, 7, 8, 8]
assert get_sliding_max([5, 2, 1], 2) == [5, 2]

import sys


def get_minimum_painting_cost(cost_matrix, num_houses, num_colors):
    if not cost_matrix:
        return 0

    prev_house_min = 0
    prev_house_min_index = -1
    prev_house_second_min = 0

    for i in range(num_houses):
        curr_house_min = sys.maxsize
        curr_house_second_min = sys.maxsize
        curr_house_min_index = 0

        for j in range(num_colors):
            if prev_house_min_index == j:
                cost_matrix[i][j] += prev_house_second_min
            else:
                cost_matrix[i][j] += prev_house_min

            if curr_house_min > cost_matrix[i][j]:
                curr_house_second_min = curr_house_min
                curr_house_min = cost_matrix[i][j]
                curr_house_min_index = j
            elif curr_house_second_min > cost_matrix[i][j]:
                curr_house_second_min = cost_matrix[i][j]

        prev_house_min = curr_house_min
        prev_house_second_min = curr_house_second_min
        prev_house_min_index = curr_house_min_index

    return min(cost_matrix[num_houses - 1])


cost_matrix = \
    [[7, 3, 8, 6, 1, 2],
     [5, 6, 7, 2, 4, 3],
     [10, 1, 4, 9, 7, 6]]
assert get_minimum_painting_cost(cost_matrix,
                                 len(cost_matrix), len(cost_matrix[0])) == 4

cost_matrix = \
    [[7, 3, 8, 6, 1, 2],
     [5, 6, 7, 2, 4, 3],
     [10, 1, 4, 9, 7, 6],
     [10, 1, 4, 9, 7, 6]]
assert get_minimum_painting_cost(cost_matrix,
                                 len(cost_matrix), len(cost_matrix[0])) == 8

class Node:
    def __init__(self, x):
        self.val = x
        self.next = None

    def __str__(self):
        string = "["
        node = self
        while node:
            string += "{} ->".format(node.val)
            node = node.next
        string += "None]"
        return string


def get_nodes(values):
    next_node = None
    for value in values[::-1]:
        node = Node(value)
        node.next = next_node
        next_node = node

    return next_node


def get_list(head):
    node = head
    nodes = list()
    while node:
        nodes.append(node.val)
        node = node.next
    return nodes


def get_intersection_node(list_a, list_b):

    def get_list_length(linked_list):
        length = 0
        node = linked_list
        while node:
            length += 1
            node = node.next

        return length

    len_a, len_b = get_list_length(list_a), get_list_length(list_b)
    min_len = min(len_a, len_b)

    for _ in range(len_a - min_len):
        list_a = list_a.next
    for _ in range(len_b - min_len):
        list_b = list_b.next

    node_a = list_a
    node_b = list_b
    for _ in range(min_len):
        if node_a.val == node_b.val:
            return node_a
        node_a = node_a.next
        node_b = node_b.next

    return None


assert not get_intersection_node(
    get_nodes([]), get_nodes([]))
assert get_intersection_node(
    get_nodes([0, 3, 7, 8, 10]), get_nodes([99, 1, 8, 10])).val == 8
assert get_intersection_node(
    get_nodes([7, 8, 10]), get_nodes([99, 1, 8, 10])).val == 8

def get_num_classrooms(timing_tuples):
    if not timing_tuples:
        return 0

    start_times = dict()
    end_times = dict()
    for start, end in timing_tuples:
        if start not in start_times:
            start_times[start] = 0
        start_times[start] += 1

        if end not in end_times:
            end_times[end] = 0
        end_times[end] += 1

    global_start, global_end = min(start_times), max(end_times)

    max_class_count = 0
    current_class_count = 0
    for i in range(global_start, global_end):
        if i in start_times:
            current_class_count += start_times[i]
            if current_class_count > max_class_count:
                max_class_count = current_class_count
        if i in end_times:
            current_class_count -= end_times[i]

    return max_class_count


assert get_num_classrooms([]) == 0
assert get_num_classrooms([(30, 75), (0, 50), (60, 150)]) == 2
assert get_num_classrooms([(30, 75), (0, 50), (10, 60), (60, 150)]) == 3
assert get_num_classrooms([(60, 150)]) == 1
assert get_num_classrooms([(60, 150), (150, 170)]) == 2
assert get_num_classrooms([(60, 150), (60, 150), (150, 170)]) == 3

def get_sentence_split(s, words):
    if not s or not words:
        return []

    word_set = set(words)
    sentence_words = list()
    for i in range(len(s)):
        if s[0:i + 1] in word_set:
            sentence_words.append(s[0:i + 1])
            word_set.remove(s[0:i + 1])
            sentence_words += get_sentence_split(s[i + 1:], word_set)
            break

    return sentence_words


assert get_sentence_split("thequickbrownfox", ['quick', 'brown', 'the', 'fox']) == [
    'the', 'quick', 'brown', 'fox']
assert get_sentence_split("bedbathandbeyond", [
                          'bed', 'bath', 'bedbath', 'and', 'beyond']) == ['bed', 'bath', 'and', 'beyond']

[[f, f, f, f],
 [t, t, f, t],
 [f, f, f, f],
 [f, f, f, f]]

from copy import deepcopy


def add_to_cache(coordinate, cache):
    new_cache = deepcopy(cache)
    new_cache.add("{}-{}".format(coordinate[0], coordinate[1]))
    return new_cache


def is_visited(coordinate, cache):
    return "{}-{}".format(coordinate[0], coordinate[1]) in cache


def find_path(matrix, rows, cols, start, end, cache):
    if start == end:
        return 0

    cache = add_to_cache(start, cache)

    def explore_neighbour(coordinate):
        if not is_visited(coordinate, cache) and \
                matrix[coordinate[0]][coordinate[1]] != "t":
            path_length = find_path(matrix, rows, cols, coordinate, end, cache)
            if path_length != None:
                path_lengths.append(path_length)

    path_lengths = list()
    if start[0] != 0:
        coordinate = (start[0] - 1, start[1])
        explore_neighbour(coordinate)
    if start[0] != rows - 1:
        coordinate = (start[0] + 1, start[1])
        explore_neighbour(coordinate)
    if start[1] != 0:
        coordinate = (start[0], start[1] - 1)
        explore_neighbour(coordinate)
    if start[1] != cols - 1:
        coordinate = (start[0], start[1] + 1)
        explore_neighbour(coordinate)

    return min(path_lengths) + 1 if path_lengths else None


matrix = [["f", "f", "f", "f"],
          ["t", "t", "f", "t"],
          ["f", "f", "f", "f"],
          ["f", "f", "f", "f"]]
assert find_path(matrix, len(matrix), len(
    matrix[0]), (0, 0), (0, 0), set()) == 0
assert find_path(matrix, len(matrix), len(
    matrix[0]), (1, 0), (0, 0), set()) == 1
assert find_path(matrix, len(matrix), len(
    matrix[0]), (3, 0), (0, 0), set()) == 7
assert find_path(matrix, len(matrix), len(
    matrix[0]), (3, 0), (0, 3), set()) == 6

matrix = [["f", "f", "f", "f"],
          ["t", "t", "t", "f"],
          ["f", "f", "f", "f"],
          ["f", "f", "f", "f"]]
assert find_path(matrix, len(matrix), len(
    matrix[0]), (0, 0), (0, 0), set()) == 0
assert find_path(matrix, len(matrix), len(
    matrix[0]), (1, 0), (0, 0), set()) == 1
assert find_path(matrix, len(matrix), len(
    matrix[0]), (3, 0), (0, 0), set()) == 9
assert find_path(matrix, len(matrix), len(
    matrix[0]), (3, 0), (0, 3), set()) == 6
assert find_path(matrix, len(matrix), len(
    matrix[0]), (2, 0), (3, 3), set()) == 4

def is_parent_locked(node):
    if not node.parent:
        return False
    elif node.parent.locked:
        return True
    return is_parent_locked(node.parent)


def update_parent(node, enable_locks):
    increment = 1 if enable_locks else -1
    if node.parent:
        node.parent.locked_descendants += increment
        update_parent(node.parent, enable_locks)


class Node:
    def __init__(self, val, parent):
        self.val = val
        self.parent = parent
        self.left = None
        self.right = None
        self.locked = False
        self.locked_descendants = 0

    def __str__(self):
        return "val={}; locked={}; locked_descendants={}".format(
            self.val, self.locked, self.locked_descendants)

    def lock(self):
        if is_parent_locked(self) or self.locked_descendants:
            return False
        else:
            self.locked = True
            update_parent(node=self, enable_locks=True)
            return True

    def unlock(self):
        if is_parent_locked(self) or self.locked_descendants:
            return False
        else:
            self.locked = False
            update_parent(node=self, enable_locks=False)
            return True

    def is_locked(self):
        return self.locked


a = Node("a", None)
b = Node("b", a)
c = Node("c", a)
d = Node("d", b)
e = Node("e", b)
f = Node("f", c)
g = Node("g", c)

assert b.lock()
assert b.is_locked()
assert c.lock()
assert b.unlock()
assert not b.is_locked()
assert d.lock()

assert not g.lock()
assert c.unlock()
assert g.lock()

assert f.lock()
assert e.lock()
assert a.locked_descendants == 4
assert b.locked_descendants == 2
assert c.locked_descendants == 2

def is_match(regex, string):

    # if no pattern and no text, return True
    if not regex:
        return not string

    # first character will not be a Kleene star
    first_match = bool(string) and regex[0] in {string[0], '.'}

    if len(regex) >= 2 and regex[1] == '*':
        # regex[0] consumes no characters or
        # regex[0] consumes one character
        return is_match(regex[2:], string) or \
            (first_match and is_match(regex, string[1:]))
    else:
        # regex[0] consumes one character
        return first_match and is_match(regex[1:], string[1:])


assert is_match("ra.", "ray")
assert not is_match("ra.", "raymond")
assert is_match(".*at", "chat")
assert not is_match(".*at", "chats")

class Node:
    def __init__(self, x):
        self.val = x
        self.next = None

    def __str__(self):
        string = "["
        node = self
        while node:
            string += "{} ->".format(node.val)
            node = node.next
        string += "None]"
        return string


def get_nodes(values):
    next_node = None
    for value in values[::-1]:
        node = Node(value)
        node.next = next_node
        next_node = node

    return next_node


def get_list(head):
    node = head
    nodes = list()
    while node:
        nodes.append(node.val)
        node = node.next
    return nodes


def remove_kth_last(head, k):
    if not head or not k:
        return head

    dummy = Node(None)
    dummy.next = head
    runner = head

    for _ in range(k):
        runner = runner.next

    current_node = dummy
    while runner:
        runner = runner.next
        current_node = current_node.next

    current_node.next = current_node.next.next

    return dummy.next


assert get_list(remove_kth_last(
    get_nodes([]), 1)) == []
assert get_list(remove_kth_last(
    get_nodes([0, 3, 7, 8, 10]), 2)) == [0, 3, 7, 10]
assert get_list(remove_kth_last(
    get_nodes([7, 8, 10]), 3)) == [8, 10]
assert get_list(remove_kth_last(
    get_nodes([7, 8, 10]), 1)) == [7, 8]

brace_map = {
    ")": "(",
    "}": "{",
    "]": "["
}


def is_balanced(s):
    stack = list()
    for char in s:
        if stack and char in brace_map and stack[-1] == brace_map[char]:
            stack.pop()
        else:
            stack.append(char)
    return not stack


assert is_balanced("")
assert is_balanced("{}")
assert is_balanced("([])")
assert is_balanced("([])[]({})")
assert not is_balanced("(")
assert not is_balanced("]")
assert not is_balanced("((()")
assert not is_balanced("([)]")

def justify_text(words, max_line_length):
    lines = list()

    cumulative_length = -1
    current_words = list()
    line_lengths = list()
    for word in words:
        if cumulative_length + (len(word) + 1) > max_line_length:
            lines.append(current_words)
            line_lengths.append(cumulative_length)
            cumulative_length = -1
            current_words = list()
        cumulative_length += (len(word) + 1)
        current_words.append(word)
        # print(current_words)
        # print(cumulative_length)
    if current_words:
        lines.append(current_words)
        line_lengths.append(cumulative_length)

    # print(lines)
    # print(line_lengths)

    justified_lines = list()
    for words, length in zip(lines, line_lengths):
        spaces_to_add = max_line_length - length
        guaranteed_spaces = 1 + (spaces_to_add // (len(words) - 1))
        bonus_space_recipients = spaces_to_add % (len(words) - 1)
        # print("spaces_to_add: {}".format(spaces_to_add))
        line = ""
        for (index, word) in enumerate(words[:-1]):
            line += word
            line += guaranteed_spaces * " "
            if index < bonus_space_recipients:
                line += " "
        line += words[-1]
        # print(line)
        justified_lines.append(line)

    # print(justified_lines)
    return justified_lines


assert justify_text(["the", "quick", "brown", "fox", "jumps",
                     "over", "the", "lazy", "dog"], 16) == \
    ['the  quick brown', 'fox  jumps  over', 'the   lazy   dog']
assert justify_text(["the", "quick", "brown", "fox", "jumps", "over"], 16) == \
    ['the  quick brown', 'fox  jumps  over']
assert justify_text(["the", "quick"], 16) == ['the        quick']

def encode_string(s):
    encoded_chars = list()

    count = 0
    prev_char = None
    for char in s:
        if char == prev_char or not prev_char:
            count += 1
        else:
            encoded_chars.append(str(count))
            encoded_chars.append(prev_char)
            count = 1
        prev_char = char

    if count:
        encoded_chars.append(str(count))
        encoded_chars.append(prev_char)

    return "".join(encoded_chars)


def decode_string(s):

    decoded_chars = list()
    index = 0

    while index < len(s):
        decoded_chars.append(int(s[index]) * s[index + 1])
        index += 2

    return "".join(decoded_chars)


assert encode_string("") == ""
assert encode_string("AAA") == "3A"
assert encode_string("AAAABBBCCDAA") == "4A3B2C1D2A"

assert decode_string("") == ""
assert decode_string("3A") == "AAA"
assert decode_string("4A3B2C1D2A") == "AAAABBBCCDAA"

def calculate_trapped_water(walls):
    if len(walls) < 3:
        return 0

    total_water_volume = 0

    left = 0
    right = len(walls) - 1
    left_max = 0
    right_max = 0

    while left <= right:
        if walls[left] < walls[right]:
            if walls[left] > left_max:
                left_max = walls[left]
            else:
                total_water_volume += left_max - walls[left]
            left += 1
        else:
            if walls[right] > right_max:
                right_max = walls[right]
            else:
                total_water_volume += right_max - walls[right]
            right -= 1

    return total_water_volume


assert calculate_trapped_water([1]) == 0
assert calculate_trapped_water([2, 1]) == 0
assert calculate_trapped_water([2, 1, 2]) == 1
assert calculate_trapped_water([4, 1, 2]) == 1
assert calculate_trapped_water([4, 1, 2, 3]) == 3
assert calculate_trapped_water([3, 0, 1, 3, 0, 5]) == 8
assert calculate_trapped_water([10, 9, 1, 1, 6]) == 10

def get_edit_distance(s1, s2):
    if s1 == s2:
        return 0
    elif not s1:
        return len(s2)
    elif not s2:
        return len(s1)

    if s1[0] == s2[0]:
        return get_edit_distance(s1[1:], s2[1:])

    return 1 + min(
        get_edit_distance(s1[1:], s2),      # deletion from s1
        get_edit_distance(s1, s2[1:]),      # addition to s1
        get_edit_distance(s1[1:], s2[1:]))  # modification to s1


assert get_edit_distance("", "") == 0
assert get_edit_distance("a", "b") == 1
assert get_edit_distance("abc", "") == 3
assert get_edit_distance("abc", "abc") == 0
assert get_edit_distance("kitten", "sitting") == 3

from math import log


def arbitrage(table):
    transformed_graph = [[-log(edge) for edge in row] for row in table]

    # Pick any source vertex -- we can run Bellman-Ford from any vertex and
    # get the right result
    source = 0
    n = len(transformed_graph)
    min_dist = [float('inf')] * n

    min_dist[source] = 0

    # Relax edges |V - 1| times
    for _ in range(n - 1):
        for v in range(n):
            for w in range(n):
                if min_dist[w] > min_dist[v] + transformed_graph[v][w]:
                    min_dist[w] = min_dist[v] + transformed_graph[v][w]

    # If we can still relax edges, then we have a negative cycle
    for v in range(n):
        for w in range(n):
            if min_dist[w] > min_dist[v] + transformed_graph[v][w]:
                return True

    return False


assert arbitrage([[1, 2], [2, 1]])
assert not arbitrage([[1, 1], [1, 1]])

2
1.5
2
3.5
2
2
2

import heapq as hq


def get_running_medians(arr):
    if not arr:
        return None

    min_heap = list()
    max_heap = list()
    medians = list()

    for x in arr:
        hq.heappush(min_heap, x)
        if len(min_heap) > len(max_heap) + 1:
            smallest_large_element = hq.heappop(min_heap)
            hq.heappush(max_heap, -smallest_large_element)

        if len(min_heap) == len(max_heap):
            median = (min_heap[0] - max_heap[0]) / 2
        else:
            median = min_heap[0]
        medians.append(median)

    return medians


assert not get_running_medians(None)
assert not get_running_medians([])
assert get_running_medians([2, 5]) == [2, 3.5]
assert get_running_medians([3, 3, 3, 3]) == [3, 3, 3, 3]
assert get_running_medians([2, 1, 5, 7, 2, 0, 5]) == [2, 1.5, 2, 3.5, 2, 2, 2]

def is_palindrome(s):
    return s[::-1] == s


def get_nearest_palindrome(s):

    if is_palindrome(s):
        return s

    if s[0] == s[-1]:
        return s[0] + get_nearest_palindrome(s[1:-1]) + s[-1]
    else:
        pal_1 = s[0] + get_nearest_palindrome(s[1:]) + s[0]
        pal_2 = s[-1] + get_nearest_palindrome(s[:-1]) + s[-1]

        if len(pal_1) > len(pal_2):
            return pal_2
        elif len(pal_1) < len(pal_2):
            return pal_1
        return pal_1 if pal_1 < pal_2 else pal_2


assert get_nearest_palindrome("racecar") == "racecar"
assert get_nearest_palindrome("google") == "elgoogle"
assert get_nearest_palindrome("egoogle") == "elgoogle"
assert get_nearest_palindrome("elgoog") == "elgoogle"
assert get_nearest_palindrome("race") == "ecarace"

def swap_indices(arr, i, j):
    tmp = arr[i]
    arr[i] = arr[j]
    arr[j] = tmp


def pull_elements_to_front(arr, start_index, end_index, letter):
    i = start_index
    j = end_index
    last_letter_index = -1

    while i < j:
        if arr[i] == letter:
            last_letter_index = i
            i += 1
        elif arr[j] != letter:
            j -= 1
        else:
            last_letter_index = i
            swap_indices(arr, i, j)

    return last_letter_index


def reorder_array(arr):
    last_index = pull_elements_to_front(arr, 0, len(arr) - 1, "R")
    pull_elements_to_front(arr, last_index + 1, len(arr) - 1, "G")

    return arr


assert reorder_array(['G', 'R']) == ['R', 'G']
assert reorder_array(['G', 'B', 'R']) == ['R', 'G', 'B']
assert reorder_array(['B', 'G', 'R']) == ['R', 'G', 'B']
assert reorder_array(['G', 'B', 'R', 'R', 'B', 'R', 'G']) == [
    'R', 'R', 'R', 'G', 'G', 'B', 'B']

class Node:
    def __init__(self, data):
        self.data = data
        self.left = None
        self.right = None

    def __repr__(self):
        return str(self.data)


def find_largest_and_parent(node):
    parent = None
    while node.right:
        parent = node
        node = node.right

    return node, parent


def find_second_largest(root):
    if not root:
        return None

    second_largest = None
    if root.left and not root.right:
        second_largest, _ = find_largest_and_parent(root.left)
    else:
        _, second_largest = find_largest_and_parent(root)
    print("second_largest", second_largest)

    return second_largest


def test_0():
    node_a = Node(5)

    assert not find_second_largest(node_a)


def test_1():
    node_a = Node(5)
    node_b = Node(3)
    node_c = Node(8)
    node_d = Node(2)
    node_e = Node(4)
    node_f = Node(7)
    node_g = Node(9)
    node_a.left = node_b
    node_a.right = node_c
    node_b.left = node_d
    node_b.right = node_e
    node_c.left = node_f
    node_c.right = node_g

    assert find_second_largest(node_a).data == 8


def test_2():
    node_a = Node(5)
    node_b = Node(3)
    node_d = Node(2)
    node_e = Node(4)
    node_a.left = node_b
    node_b.left = node_d
    node_b.right = node_e

    assert find_second_largest(node_a).data == 4


test_0()
test_1()
test_2()

def get_power_set(numbers):
    if len(numbers) == 0:
        return [set([])]

    power_set = list()

    current_number = numbers[0]
    child_power_set = get_power_set(numbers[1:])
    power_set.extend(child_power_set)

    for child_set in child_power_set:
        new_set = child_set.copy()
        new_set.add(current_number)
        power_set.append(new_set)

    return power_set


assert get_power_set([]) == [set()]
assert get_power_set([1]) == [set(), {1}]
assert get_power_set([1, 2]) == [set(), {2}, {1}, {1, 2}]
assert get_power_set([1, 2, 3]) == [
    set(), {3}, {2}, {2, 3}, {1}, {1, 3}, {1, 2}, {1, 2, 3}]
assert get_power_set([1, 2, 3, 4]) == [
    set(), {4}, {3}, {3, 4}, {2}, {2, 4}, {2, 3}, {2, 3, 4}, {1}, {1, 4},
    {1, 3}, {1, 3, 4}, {1, 2}, {1, 2, 4}, {1, 2, 3}, {1, 2, 3, 4}]

def is_valid(board, row):
    if row in board:
        return False

    column = len(board)
    for occupied_column, occupied_row in enumerate(board):
        if abs(occupied_row - row) == abs(occupied_column - column):
            return False

    return True


def get_queen_configurations(board, n):
    if n == len(board):
        return 1

    count = 0
    for row in range(n):
        if is_valid(board, row):
            count += get_queen_configurations(board + [row], n)

    return count


assert not is_valid([0, 2], 0)
assert not is_valid([0, 2], 2)
assert is_valid([0, 8], 3)
assert not is_valid([1, 3], 2)
assert is_valid([], 1)

assert get_queen_configurations([], 2) == 0
assert get_queen_configurations([], 4) == 2
assert get_queen_configurations([], 5) == 10
assert get_queen_configurations([], 8) == 92

import sys


class Coordinate():
    def __init__(self, x, y):
        self.x = x
        self.y = y

    def __hash__(self):
        return hash((self.x, self.y))

    def __eq__(self, other):
        return (self.x, self.y) == (other.x, other.y)

    def __ne__(self, other):
        return not(self == other)

    def __repr__(self):
        return "C(x={};y={})".format(self.x, self.y)

    def get_adjacent_coordinates(self):
        adjacent_coordinates = list()
        adjacent_coordinates.append(Coordinate(self.x, self.y - 1))
        adjacent_coordinates.append(Coordinate(self.x, self.y + 1))
        adjacent_coordinates.append(Coordinate(self.x - 1, self.y))
        adjacent_coordinates.append(Coordinate(self.x - 1, self.y - 1))
        adjacent_coordinates.append(Coordinate(self.x - 1, self.y + 1))
        adjacent_coordinates.append(Coordinate(self.x + 1, self.y))
        adjacent_coordinates.append(Coordinate(self.x + 1, self.y - 1))
        adjacent_coordinates.append(Coordinate(self.x + 1, self.y + 1))
        return adjacent_coordinates


def get_live_coordinates(all_live_coordinates, coordinates_to_check):
    count = 0
    for coordinate in coordinates_to_check:
        if coordinate in all_live_coordinates:
            count += 1

    return count


def update_liveness_neighbourhood(liveness_neighbourhood, adjacent_coordinates):
    for coordinate in adjacent_coordinates:
        if coordinate not in liveness_neighbourhood:
            liveness_neighbourhood[coordinate] = 0
        liveness_neighbourhood[coordinate] += 1


def play_iteration(board):
    coordinate_set = set(board)
    dead_coordinates = set()
    liveness_neighbourhood = dict()

    for coordinate in board:
        adjacent_coordinates = coordinate.get_adjacent_coordinates()
        live_adjacent_coordinate_count = get_live_coordinates(
            coordinate_set, adjacent_coordinates)
        update_liveness_neighbourhood(
            liveness_neighbourhood, adjacent_coordinates)

        if live_adjacent_coordinate_count < 2 or live_adjacent_coordinate_count > 3:
            dead_coordinates.add(coordinate)

    for coordinate in liveness_neighbourhood:
        if liveness_neighbourhood[coordinate] == 3:
            coordinate_set.add(coordinate)

    new_coordinate_set = coordinate_set - dead_coordinates

    return list(new_coordinate_set)


def print_board(coordinates):
    min_x, min_y, max_x, max_y = sys.maxsize, sys.maxsize, -sys.maxsize, -sys.maxsize

    if not coordinates:
        print(".")
        return

    for coordinate in coordinates:
        if coordinate.x < min_x:
            min_x = coordinate.x
        if coordinate.x > max_x:
            max_x = coordinate.x
        if coordinate.y < min_y:
            min_y = coordinate.y
        if coordinate.y > max_y:
            max_y = coordinate.y

    board = []
    for _ in range(max_x - min_x + 1):
        board.append(["."] * (max_y - min_y + 1))

    for coordinate in coordinates:
        board[coordinate.x - min_x][coordinate.y - min_y] = "*"

    for row in board:
        print(" ".join(row))


def play_game(initial_board, steps):
    print("\nPlaying Game of Life with the intial board:")
    print_board(initial_board)
    current_board = initial_board
    for step in range(steps):
        current_board = play_iteration(current_board)
        print("Iteration: {}".format(step))
        print_board(current_board)


# board is a list of Coordinates
board_0 = [
    Coordinate(0, 0), Coordinate(1, 0), Coordinate(1, 1), Coordinate(1, 5)]
play_game(board_0, 3)


board_1 = [
    Coordinate(0, 0), Coordinate(1, 0), Coordinate(1, 1), Coordinate(1, 5),
    Coordinate(2, 5), Coordinate(2, 6)]
play_game(board_1, 4)


board_2 = [
    Coordinate(0, 0), Coordinate(1, 0), Coordinate(1, 1),
    Coordinate(2, 5), Coordinate(2, 6), Coordinate(3, 9),
    Coordinate(4, 8), Coordinate(5, 10)]
play_game(board_2, 4)

WORD_SIZE = 32


def get_non_duplicated_number(arr):
    non_duplicate = 0

    for i in range(0, WORD_SIZE):
        sum_i_position_bits = 0
        x = 1 << i
        for j in range(len(arr)):
            if arr[j] & x:
                sum_i_position_bits += 1

        if sum_i_position_bits % 3:
            non_duplicate |= x

    return non_duplicate


assert get_non_duplicated_number([6, 1, 3, 3, 3, 6, 6]) == 1
assert get_non_duplicated_number([13, 19, 13, 13]) == 19

def get_itinerary(flights, starting_point, current_itinerary):
    # print("flights", flights)
    # print("starting_point", starting_point)
    # print("current_itinerary", current_itinerary)

    if not flights:
        return current_itinerary + [starting_point]

    updated_itinerary = None
    for index, (city_1, city_2) in enumerate(flights):
        if starting_point == city_1:
            child_itinerary = get_itinerary(
                flights[:index] + flights[index + 1:], city_2, current_itinerary + [city_1])
            if child_itinerary:
                if not updated_itinerary or "".join(child_itinerary) < "".join(updated_itinerary):
                    updated_itinerary = child_itinerary

    # print(updated_itinerary)

    return updated_itinerary


assert get_itinerary([('SFO', 'HKO'), ('YYZ', 'SFO'), ('YUL', 'YYZ'),
                      ('HKO', 'ORD')], "YUL", []) == ['YUL', 'YYZ', 'SFO', 'HKO', 'ORD']
assert not get_itinerary([('SFO', 'COM'), ('COM', 'YYZ')], "YUL", [])
assert get_itinerary([('A', 'B'), ('A', 'C'), ('B', 'C'), ('C', 'A')], "A", []) == [
    'A', 'B', 'C', 'A', 'C']

def get_subset_for_sum(arr, k):

    if len(arr) == 0:
        return None

    if arr[0] == k:
        return [arr[0]]

    with_first = get_subset_for_sum(arr[1:], k - arr[0])
    if with_first:
        return [arr[0]] + with_first
    else:
        return get_subset_for_sum(arr[1:], k)


assert not get_subset_for_sum([], 1)
assert get_subset_for_sum([12, 1, 61, 5, 9, 2], 24) == [12, 1, 9, 2]
assert get_subset_for_sum([12, 1, 61, 5, 9, 2], 61) == [61]
assert get_subset_for_sum([12, 1, 61, 5, -108, 2], -106) == [-108, 2]

class Stack:
    def __init__(self):
        self.stack = []
        self.max_stack = []

    def push(self, val):
        self.stack.append(val)
        if not self.max_stack or val > self.stack[self.max_stack[-1]]:
            self.max_stack.append(len(self.stack) - 1)

    def pop(self):
        if not self.stack:
            return None
        if len(self.stack) - 1 == self.max_stack[-1]:
            self.max_stack.pop()

        return self.stack.pop()

    def max(self):
        if not self.stack:
            return None
        return self.stack[self.max_stack[-1]]


s = Stack()
s.push(1)
s.push(3)
s.push(2)
s.push(5)
assert s.max() == 5
s.pop()
assert s.max() == 3
s.pop()
assert s.max() == 3
s.pop()
assert s.max() == 1
s.pop()
assert not s.max()

s = Stack()
s.push(10)
s.push(3)
s.push(2)
s.push(5)
assert s.max() == 10
s.pop()
assert s.max() == 10
s.pop()
assert s.max() == 10
s.pop()
assert s.max() == 10
s.pop()
assert not s.max()

def merge(a_with_inv, b_with_inv):
    i, k = 0, 0
    merged = list()
    a, a_inv = a_with_inv
    b, b_inv = b_with_inv
    inversions = a_inv + b_inv

    while i < len(a) and k < len(b):
        if a[i] < b[k]:
            merged.append(a[i])
            i += 1
        else:
            merged.append(b[k])
            inversions += len(a[i:])
            k += 1

    while i < len(a):
        merged.append(a[i])
        i += 1
    while k < len(b):
        merged.append(b[k])
        k += 1

    return merged, inversions


def merge_sort(arr):
    if not arr or len(arr) == 1:
        return arr, 0

    mid = len(arr) // 2
    merged_array, inversions = merge(
        merge_sort(arr[:mid]), merge_sort(arr[mid:]))

    return merged_array, inversions


def count_inversions(arr):
    _, inversions = merge_sort(arr)
    return inversions


assert count_inversions([1, 2, 3, 4, 5]) == 0
assert count_inversions([2, 1, 3, 4, 5]) == 1
assert count_inversions([2, 4, 1, 3, 5]) == 3
assert count_inversions([2, 6, 1, 3, 7]) == 3
assert count_inversions([5, 4, 3, 2, 1]) == 10

from random import randint


def rand5():
    return randint(1, 5)


def rand7():
    i = 5*rand5() + rand5() - 5  # uniformly samples between 1-25
    if i < 22:
        return i % 7 + 1
    return rand7()


num_experiments = 100000
result_dict = dict()
for _ in range(num_experiments):
    number = rand7()
    if number not in result_dict:
        result_dict[number] = 0
    result_dict[number] += 1

desired_probability = 1 / 7
for number in result_dict:
    result_dict[number] = result_dict[number] / num_experiments
    assert round(desired_probability, 2) == round(result_dict[number], 2)

def is_palindrome(s1):
    return s1 == s1[::-1]


def get_longest_palindrome_substring(s):
    if not s or is_palindrome(s):
        return s

    s1 = get_longest_palindrome_substring(s[1:])
    s2 = get_longest_palindrome_substring(s[:-1])

    return s1 if len(s1) >= len(s2) else s2


assert get_longest_palindrome_substring("aabcdcb") == "bcdcb"
assert get_longest_palindrome_substring("bananas") == "anana"

import sys


def get_stock_profit(prices):
    if not prices or len(prices) < 2:
        return

    min_price = prices[0]
    max_diff = -sys.maxsize
    for price in prices[1:]:
        if price - min_price > max_diff:
            max_diff = price - min_price
        if price < min_price:
            min_price = price

    return max_diff


assert get_stock_profit([9]) == None
assert get_stock_profit([9, 11, 8, 5, 7, 10]) == 5
assert get_stock_profit([1, 2, 3, 4, 5]) == 4
assert get_stock_profit([1, 1, 1, 1, 1]) == 0
assert get_stock_profit([1, 1, 1, 2, 1]) == 1
assert get_stock_profit([5, 4]) == -1

[a, b, d, e, c, f, g]

[d, b, e, a, f, c, g]

    a
   / \
  b   c
 / \ / \
d  e f  g

class Node:
    def __init__(self, val):
        self.val = val
        self.left = None
        self.right = None


def get_tree(preorder, inorder):
    if not preorder or not inorder:
        return None

    root_char = preorder[0]
    if len(preorder) == 1:
        return Node(root_char)

    root_node = Node(root_char)
    for i, char in enumerate(inorder):
        if char == root_char:
            root_node.left = get_tree(
                preorder=preorder[1:i+1], inorder=inorder[:i])
            root_node.right = get_tree(
                preorder=preorder[i+1:], inorder=inorder[i+1:])

    return root_node


tree = get_tree(preorder=['a', 'b', 'd', 'e', 'c', 'f', 'g'],
                inorder=['d', 'b', 'e', 'a', 'f', 'c', 'g'])
assert tree.val == 'a'
assert tree.left.val == 'b'
assert tree.left.left.val == 'd'
assert tree.left.right.val == 'e'
assert tree.right.val == 'c'
assert tree.right.left.val == 'f'
assert tree.right.right.val == 'g'

tree = get_tree(preorder=['a', 'b', 'd', 'e', 'c', 'g'],
                inorder=['d', 'b', 'e', 'a', 'c', 'g'])
assert tree.val == 'a'
assert tree.left.val == 'b'
assert tree.left.left.val == 'd'
assert tree.left.right.val == 'e'
assert tree.right.val == 'c'
assert tree.right.right.val == 'g'

def get_max_subarray(arr):
    if not arr or max(arr) < 0:
        return 0

    current_max_sum = arr[0]
    overall_max_sum = arr[0]

    for num in arr[1:]:
        current_max_sum = max(num, current_max_sum + num)
        overall_max_sum = max(overall_max_sum, current_max_sum)

    return overall_max_sum


assert get_max_subarray([34, -50, 42, 14, -5, 86]) == 137
assert get_max_subarray([-5, -1, -8, -9]) == 0
assert get_max_subarray([44, -5, 42, 14, -150, 86]) == 95

    *
   / \
  +    +
 / \  / \
3  2  4  5

class Node:
    def __init__(self, val):
        self.val = val
        self.left = None
        self.right = None


def solve_graph(root):
    if root.val.isnumeric():
        return float(root.val)

    return eval("{} {} {}".format(solve_graph(root.left), root.val, solve_graph(root.right)))


d = Node("3")
e = Node("2")
f = Node("4")
g = Node("5")

b = Node("+")
b.left = d
b.right = e

c = Node("+")
c.left = f
c.right = g

a = Node("*")
a.left = b
a.right = c


assert solve_graph(a) == 45
assert solve_graph(c) == 9
assert solve_graph(b) == 5
assert solve_graph(d) == 3

from random import randint

NUM_CARDS = 52


def get_random_number(k):
    return randint(0, k)


def shuffle_card_deck():
    cards = [x for x in range(NUM_CARDS)]

    for old_pos in cards:
        new_pos = old_pos + get_random_number(NUM_CARDS - old_pos - 1)
        temp = cards[new_pos]
        cards[new_pos] = cards[old_pos]
        cards[old_pos] = temp

    return cards


for _ in range(10):
    assert all(x in shuffle_card_deck() for x in range(NUM_CARDS))

class Node:
    def __init__(self, key, value):
        self.key = key
        self.value = value
        self.prev = None
        self.next = None


class LRU:
    def __init__(self, cache_limit):
        self.cache_limit = cache_limit
        self.cache_contents = dict()
        self.head = Node(None, None)
        self.tail = Node(None, None)
        self.head.next = self.tail
        self.tail.prev = self.head

    def _remove(self, node):
        prev_node = node.prev
        next_node = node.next
        prev_node.next = next_node
        next_node.prev = prev_node

    def _add(self, node):
        prev_node = self.tail.prev
        node.next = self.tail
        node.prev = prev_node
        prev_node.next = node
        self.tail.prev = node

    def set_value(self, key, value):
        if key in self.cache_contents:
            node = self.cache_contents[key]
            self._remove(node)
        node = Node(key, value)
        self._add(node)
        self.cache_contents[key] = node
        if len(self.cache_contents) > self.cache_limit:
            node_to_delete = self.head.next
            self._remove(node_to_delete)
            del self.cache_contents[node_to_delete.key]

    def get_value(self, key):
        if key in self.cache_contents:
            node = self.cache_contents[key]
            self._remove(node)
            self._add(node)
            return node.value

        return None


lru = LRU(cache_limit=3)

assert not lru.get_value("a")
lru.set_value("a", 1)
assert lru.get_value("a") == 1
lru.set_value("b", 2)
lru.set_value("c", 3)
lru.set_value("d", 4)
lru.set_value("e", 5)
lru.set_value("a", 1)
assert lru.get_value("a") == 1
assert not lru.get_value("b")
assert lru.get_value("e") == 5
assert not lru.get_value("c")

class Queue:
    def __init__(self):
        self.main_stack = list()
        self.aux_stack = list()

    def __repr__(self):
        return str(self.main_stack)

    def enqueue(self, val):
        self.main_stack.append(val)

    def dequeue(self):
        if not self.main_stack:
            return None

        while self.main_stack:
            self.aux_stack.append(self.main_stack.pop())
        val = self.aux_stack.pop()
        while self.aux_stack:
            self.main_stack.append(self.aux_stack.pop())
        return val


q = Queue()
q.enqueue(1)
assert q.main_stack == [1]
q.enqueue(2)
assert q.main_stack == [1, 2]
q.enqueue(3)
assert q.main_stack == [1, 2, 3]
val = q.dequeue()
assert val == 1
assert q.main_stack == [2, 3]
val = q.dequeue()
assert val == 2
assert q.main_stack == [3]

BOARD_DIM = 9
GRID_DIM = 3


def get_grid_details(x, y):
    grid_row = x - (x % GRID_DIM)
    grid_col = y - (y % GRID_DIM)
    return grid_row, grid_col


def solveSudokuHelper(board, row_elements, col_elements, grid_elements):

    for i in range(BOARD_DIM):
        for k in range(BOARD_DIM):
            if board[i][k] == ".":
                grid_row, grid_col = get_grid_details(i, k)
                grid_key = "{}-{}".format(grid_row, grid_col)
                for m in range(1, BOARD_DIM + 1):
                    if str(m) not in row_elements[i] and \
                            str(m) not in col_elements[k] and \
                            str(m) not in grid_elements[grid_key]:
                        board[i][k] = str(m)
                        row_elements[i].add(str(m))
                        col_elements[k].add(str(m))
                        grid_elements[grid_key].add(str(m))
                        if solveSudokuHelper(
                                board, row_elements, col_elements, grid_elements):
                            return True
                        else:
                            board[i][k] = "."
                            row_elements[i].remove(str(m))
                            col_elements[k].remove(str(m))
                            grid_elements[grid_key].remove(str(m))
                return False
    return True


def solveSudoku(board):
    """
    :type board: List[List[str]]
    :rtype: void Do not return anything, modify board in-place instead.
    """
    row_elements = dict()
    col_elements = dict()
    grid_elements = dict()

    for i in range(BOARD_DIM):
        row_elements[i] = set()
        col_elements[i] = set()

    for i in range(BOARD_DIM):
        for k in range(BOARD_DIM):
            if not i % GRID_DIM and not k % GRID_DIM:
                grid_elements["{}-{}".format(i, k)] = set()

    for i in range(BOARD_DIM):
        for k in range(BOARD_DIM):
            if board[i][k].isnumeric():
                row_elements[i].add(board[i][k])
                col_elements[k].add(board[i][k])

                grid_row, grid_col = get_grid_details(i, k)
                grid_elements[
                    "{}-{}".format(grid_row, grid_col)].add(board[i][k])

    solveSudokuHelper(board, row_elements,
                      col_elements, grid_elements)


sudoku_board_1 = [
    ["5", "3", ".", ".", "7", ".", ".", ".", "."],
    ["6", ".", ".", "1", "9", "5", ".", ".", "."],
    [".", "9", "8", ".", ".", ".", ".", "6", "."],
    ["8", ".", ".", ".", "6", ".", ".", ".", "3"],
    ["4", ".", ".", "8", ".", "3", ".", ".", "1"],
    ["7", ".", ".", ".", "2", ".", ".", ".", "6"],
    [".", "6", ".", ".", ".", ".", "2", "8", "."],
    [".", ".", ".", "4", "1", "9", ".", ".", "5"],
    [".", ".", ".", ".", "8", ".", ".", "7", "9"]
]
solveSudoku(sudoku_board_1)
print(sudoku_board_1)

import hashlib


class UrlShortener:

    def __init__(self):
        self.short_to_url_map = dict()
        self.m = hashlib.sha256
        self.prefix = "http://urlsho.rt/"

    def shorten(self, url):
        sha_signature = self.m(url.encode()).hexdigest()
        short_hash = sha_signature[:6]
        self.short_to_url_map[short_hash] = url
        return self.prefix + short_hash

    def restore(self, short):
        short_hash = short.replace(self.prefix, "")
        return self.short_to_url_map[short_hash]


url_0 = "https://www.tutorialspoint.com/python/string_replace.htm"
us = UrlShortener()
short_0 = us.shorten(url_0)
assert us.restore(short_0) == url_0
short_1 = us.shorten(url_0)
assert us.restore(short_1) == url_0

def can_color_graph(adjacency_matrix, k):
    max_adjacencies = 0
    for row in adjacency_matrix:
        max_adjacencies = max(max_adjacencies, sum(row))

    return k > max_adjacencies


adjacency_matrix_1 = [
    [0, 1, 1, 1],
    [1, 0, 1, 1],
    [1, 1, 0, 1],
    [1, 1, 1, 0],
]
assert can_color_graph(adjacency_matrix_1, 4)
assert not can_color_graph(adjacency_matrix_1, 3)

adjacency_matrix_2 = [
    [0, 0, 0, 0],
    [0, 0, 0, 0],
    [0, 0, 0, 0],
    [0, 0, 0, 0],
]
assert can_color_graph(adjacency_matrix_2, 4)
assert can_color_graph(adjacency_matrix_2, 1)

adjacency_matrix_3 = [
    [0, 1, 1, 0],
    [1, 0, 0, 1],
    [1, 0, 0, 1],
    [0, 1, 1, 0],
]
assert can_color_graph(adjacency_matrix_3, 4)
assert can_color_graph(adjacency_matrix_3, 3)
assert not can_color_graph(adjacency_matrix_3, 2)

def break_test(sentence, k):
    words = sentence.split()

    broken_text = list()
    char_counter = -1
    current_words = list()
    index = 0
    while index < len(words):
        word = words[index]

        if len(word) > k:
            return None

        if char_counter + len(word) + 1 <= k:
            char_counter += len(word) + 1
            current_words.append(word)
            index += 1
        else:
            broken_text.append(" ".join(current_words))
            char_counter = -1
            current_words = list()

    broken_text.extend(current_words)
    return broken_text


assert not break_test("encyclopedia", 8)
assert break_test("the quick brown fox jumps over the lazy dog", 10) == [
    "the quick", "brown fox", "jumps over", "the lazy", "dog"]

def find_element(arr, element, start, end):

    if start == end:
        return

    mid = start + ((end - start) // 2)

    if arr[mid] == element:
        return mid
    elif arr[mid] > element:
        if arr[start] >= element:
            return find_element(arr, element, start, mid)
        else:
            return find_element(arr, element, mid, end)
    elif arr[mid] < element:
        if arr[start] <= element:
            return find_element(arr, element, start, mid)
        else:
            return find_element(arr, element, mid, end)


def find_element_main(arr, element):
    element_pos = find_element(arr, element, 0, len(arr))
    return element_pos


assert find_element_main([13, 18, 25, 2, 8, 10], 2) == 3
assert find_element_main([13, 18, 25, 2, 8, 10], 8) == 4
assert find_element_main([25, 2, 8, 10, 13, 18], 8) == 2
assert find_element_main([8, 10, 13, 18, 25, 2], 8) == 0

import hashlib

m = hashlib.md5


class MerkleNode:
    def __init__(self):
        self.parent = None
        self.node_hash = None


class MerkleDirectory(MerkleNode):
    def __init__(self):
        MerkleNode.__init__(self)
        self.children = list()
        self.is_dir = True

    def recalculate_hash(self):
        if self.children:
            collated_hash = ""
            for child in self.children:
                collated_hash += child.node_hash
            self.node_hash = m(collated_hash.encode()).hexdigest()


class MerkleFile(MerkleNode):
    def __init__(self):
        MerkleNode.__init__(self)
        self.node_contents = None
        self.is_dir = False

    def update_contents(self, new_contents):
        self.node_hash = m(new_contents.encode()).hexdigest()
        self.node_contents = new_contents
        if self.parent:
            self.parent.recalculate_hash()

    def add_to_directory(self, dir_node):
        self.parent = dir_node
        dir_node.children.append(self)

        while dir_node:
            dir_node.recalculate_hash()
            dir_node = dir_node.parent


a_1 = MerkleFile()
b_1 = MerkleDirectory()
a_1.update_contents("abc")
a_1.add_to_directory(b_1)
a_1.update_contents("abcd")

a_2 = MerkleFile()
b_2 = MerkleDirectory()
a_2.update_contents("abc")
a_2.add_to_directory(b_2)

# Use a tree comparison algorithm to find differences and sync them

def partition_helper(mset, start, end, outer_sum, inner_sum):
    if start >= end:
        return False
    if outer_sum == inner_sum:
        return True

    return \
        partition_helper(mset, start + 1, end, outer_sum + mset[start],
                         inner_sum - mset[start]) or \
        partition_helper(mset, start, end - 1, outer_sum + mset[end],
                         inner_sum - mset[end])


def can_partition(mset):
    if not mset:
        return True

    if sum(mset) % 2 == 1:
        return False

    mset.sort()

    return partition_helper(mset, 0, len(mset) - 1, 0, sum(mset))


assert can_partition([15, 5, 20, 10, 35, 15, 10])
assert not can_partition([15, 5, 20, 10, 35])
assert can_partition([1, 2, 3, 4, 9, 1])
assert can_partition([1, 1, 1, 1, 1, 1, 6])

def pow(x, y):
    if not x:
        return 0
    elif not y:
        return 1

    y_abs = abs(y)

    current_pow = 1
    prev_result, prev_pow = 0, 0
    result = x
    while current_pow <= y_abs:
        prev_result = result
        prev_pow = current_pow
        result *= result
        current_pow *= 2

    prev_result *= pow(x, y_abs - prev_pow)

    return 1/prev_result if y != y_abs else prev_result


assert pow(2, 2) == 4
assert pow(2, 10) == 1024
assert pow(2, 1) == 2
assert pow(3, 3) == 27
assert pow(10, 3) == 1000
assert pow(2, -3) == 0.125
assert pow(10, -2) == 0.01
assert pow(5, 0) == 1
assert pow(0, 2) == 0

def matrix_traversal_helper(row_count, col_count, curr_row, curr_col):

    if curr_row == row_count - 1 and curr_col == col_count - 1:
        return 1

    count = 0
    if curr_row < row_count - 1:
        count += matrix_traversal_helper(row_count, col_count,
                                         curr_row + 1, curr_col)
    if curr_col < col_count - 1:
        count += matrix_traversal_helper(row_count, col_count,
                                         curr_row, curr_col + 1)

    return count


def get_matrix_traversals(row_count, col_count):
    if not row_count or not col_count:
        return None
    count = matrix_traversal_helper(row_count, col_count, 0, 0)
    return count


assert not get_matrix_traversals(1, 0)
assert get_matrix_traversals(1, 1) == 1
assert get_matrix_traversals(2, 2) == 2
assert get_matrix_traversals(5, 5) == 70

[['F', 'A', 'C', 'I'],
 ['O', 'B', 'Q', 'P'],
 ['A', 'N', 'O', 'B'],
 ['M', 'A', 'S', 'S']]

def get_row_word(matrix, word_len, rows, x, y):
    row_chars = list()
    for i in range(word_len):
        row_chars.append(matrix[x + i][y])

    return "".join(row_chars)


def get_col_word(matrix, word_len, cols, x, y):
    return "".join(matrix[x][y:y + word_len])


def word_checker(matrix, word, word_len, rows, cols, x, y):

    if x >= rows or y >= cols:
        return False

    row_word, col_word = None, None
    if x + word_len <= rows and y < cols:
        row_word = get_row_word(matrix, word_len, rows, x, y)
    if y + word_len <= cols and x < rows:
        col_word = get_col_word(matrix, word_len, cols, x, y)

    if row_word == word or col_word == word:
        return True

    check_1 = word_checker(matrix, word, word_len, rows, cols, x + 1, y) \
        if col_word else None
    check_2 = word_checker(matrix, word, word_len, rows, cols, x, y + 1) \
        if row_word else None

    return check_1 or check_2


def word_exists(matrix, word):
    rows = len(matrix)
    cols = len(matrix[0])
    word_len = len(word)

    return word_checker(matrix, word, word_len, rows, cols, 0, 0)


matrix = [['F', 'A', 'C', 'I'],
          ['O', 'B', 'Q', 'P'],
          ['A', 'N', 'O', 'B'],
          ['M', 'A', 'S', 'S']]

assert not word_exists(matrix, "FOAMS")
assert word_exists(matrix, "FOAM")
assert word_exists(matrix, "MASS")
assert not word_exists(matrix, "FORM")

import random


class Position:
    def __init__(self, x, y):
        self.x = x
        self.y = y

    def __hash__(self):
        return hash((self.x, self.y))

    def __eq__(self, other):
        return self.x == other.x and self.y == other.y

    def __repr__(self):
        return "Position=[x={},y={}]".format(self.x, self.y)


def get_potential_knight_moves(start, size, visited):
    moves = list()
    moves.append(Position(start.x + 1, start.y + 2))
    moves.append(Position(start.x + 1, start.y - 2))
    moves.append(Position(start.x - 1, start.y + 2))
    moves.append(Position(start.x - 1, start.y - 2))
    moves.append(Position(start.x + 2, start.y + 1))
    moves.append(Position(start.x + 2, start.y - 1))
    moves.append(Position(start.x - 2, start.y + 1))
    moves.append(Position(start.x - 2, start.y - 1))

    valid_moves = [pos for pos in moves if
                   pos.x >= 0 and pos.x < size and
                   pos.y >= 0 and pos.y < size and
                   pos not in visited]

    return valid_moves


def run_knights_tour(start, size, visited):
    if len(visited) == size * size:
        return 1

    moves = get_potential_knight_moves(start, size, visited)

    count = 0
    for move in moves:
        tmp_visted = visited.copy()
        tmp_visted.add(move)
        count += run_knights_tour(move, size, tmp_visted)

    return count


def count_knights_tours(size):
    count = 0
    for i in range(size):
        for j in range(size):
            start = Position(i, j)
            count += run_knights_tour(start, size, set([start]))

    return count


assert count_knights_tours(1) == 1
assert count_knights_tours(2) == 0
assert count_knights_tours(3) == 0
assert count_knights_tours(4) == 0
assert count_knights_tours(5) == 1728

[[1,  2,  3,  4,  5],
 [6,  7,  8,  9,  10],
 [11, 12, 13, 14, 15],
 [16, 17, 18, 19, 20]]

1, 2, 3, 4, 5, 10, 15, 20, 19, 18, 17, 16, 11, 6, 7, 8, 9, 14, 13, 12

def get_spiral(matrix, srow, scol, erow, ecol):
    numbers = list()
    for i in range(scol, ecol + 1):
        numbers.append(matrix[srow][i])

    for i in range(srow + 1, erow + 1):
        numbers.append(matrix[i][ecol])

    if srow < erow:
        for i in range(ecol - 1, srow - 1, -1):
            numbers.append(matrix[erow][i])

    if scol < ecol:
        for i in range(erow - 1, srow, -1):
            numbers.append(matrix[i][scol])

    return numbers


def spiral_helper(matrix):
    srow, scol, erow, ecol = 0, 0, len(matrix) - 1, len(matrix[0]) - 1
    clockwise_numbers = list()
    while srow < erow or scol < ecol:
        clockwise_numbers.extend(get_spiral(matrix, srow, scol, erow, ecol))
        if srow < erow:
            srow += 1
            erow -= 1
        if scol < ecol:
            scol += 1
            ecol -= 1

    return clockwise_numbers


matrix_0 = [[1,  2,  3,  4,  5],
            [6,  7,  8,  9,  10],
            [11, 12, 13, 14, 15],
            [16, 17, 18, 19, 20]]
assert spiral_helper(matrix_0) == [
    1, 2, 3, 4, 5, 10, 15, 20, 19, 18, 17, 16, 11, 6, 7, 8, 9, 14, 13, 12]

matrix_1 = [[1,  2,  3],
            [6,  7,  8],
            [11, 12, 13],
            [16, 17, 18]]
assert spiral_helper(matrix_1) == [
    1, 2, 3, 8, 13, 18, 17, 16, 11, 6, 7, 12]

matrix_2 = [[1, 4], [2, 5], [3, 6]]
assert spiral_helper(matrix_2) == [1, 4, 5, 6, 3, 2]

matrix_3 = [[1, 2, 3]]
assert spiral_helper(matrix_3) == [1, 2, 3]

matrix_4 = [[1], [2], [3]]
assert spiral_helper(matrix_4) == [1, 2, 3]

# assume HEADS = 1 and TAILS = 0 or vice-versa

from random import random


def get_biased_flip():
    rand = random()
    return 0 if rand < 0.7 else 1


num_experiments = 1000000
results_biased = {1: 0, 0: 0}
results_unbiased = {1: 0, 0: 0}
for i in range(num_experiments):
    flip = get_biased_flip()
    results_biased[flip] += 1
    flip = not flip if i % 2 == 0 else flip
    results_unbiased[flip] += 1

for key in results_biased:
    results_biased[key] /= num_experiments
    results_biased[key] = round(results_biased[key], 2)
for key in results_unbiased:
    results_unbiased[key] /= num_experiments
    results_unbiased[key] = round(results_unbiased[key], 2)

assert results_biased[0] == 0.7
assert results_biased[1] == 0.3
assert results_unbiased[0] == 0.5
assert results_unbiased[1] == 0.5

class DuplicateException(Exception):
    pass


class NotFoundException(Exception):
    pass


class Node(object):
    """Node containing data, pointers to previous and next node."""

    def __init__(self, data):
        self.data = data
        self.prev = None
        self.next = None


class DoublyLinkedList(object):
    def __init__(self):
        self.head = None
        self.tail = None
        # Number of nodes in list.
        self.count = 0

    def add_node(self, cls, data):
        """Add node instance of class cls."""

        return self.insert_node(cls, data, self.tail, None)

    def insert_node(self, cls, data, prev, next):
        """Insert node instance of class cls."""

        node = cls(data)
        node.prev = prev
        node.next = next
        if prev:
            prev.next = node
        if next:
            next.prev = node
        if not self.head or next is self.head:
            self.head = node
        if not self.tail or prev is self.tail:
            self.tail = node
        self.count += 1
        return node

    def remove_node(self, node):
        if node is self.tail:
            self.tail = node.prev
        else:
            node.next.prev = node.prev
        if node is self.head:
            self.head = node.next
        else:
            node.prev.next = node.next
        self.count -= 1

    def remove_node_by_data(self, data):
        """Remove node which data is equal to data."""

        node = self.head
        while node:
            if node.data == data:
                self.remove_node(node)
                break
            node = node.next

    def get_nodes_data(self):
        """Return list nodes data as a list."""

        data = []
        node = self.head
        while node:
            data.append(node.data)
            node = node.next
        return data


class FreqNode(DoublyLinkedList, Node):
    """Frequency node.

    Frequency node contains a linked list of item nodes with same frequency.
    """

    def __init__(self, data):
        DoublyLinkedList.__init__(self)
        Node.__init__(self, data)

    def add_item_node(self, data):
        node = self.add_node(ItemNode, data)
        node.parent = self
        return node

    def insert_item_node(self, data, prev, next):
        node = self.insert_node(ItemNode, data, prev, next)
        node.parent = self
        return node

    def remove_item_node(self, node):
        self.remove_node(node)

    def remove_item_node_by_data(self, data):
        self.remove_node_by_data(data)


class ItemNode(Node):
    def __init__(self, data):
        Node.__init__(self, data)
        self.parent = None


class LfuItem(object):
    def __init__(self, data, parent, node):
        self.data = data
        self.parent = parent
        self.node = node


class Cache(DoublyLinkedList):
    def __init__(self):
        DoublyLinkedList.__init__(self)
        self.items = dict()

    def insert_freq_node(self, data, prev, next):
        return self.insert_node(FreqNode, data, prev, next)

    def remove_freq_node(self, node):
        self.remove_node(node)

    def access(self, key):
        try:
            tmp = self.items[key]
        except KeyError:
            raise NotFoundException('Key not found')

        freq_node = tmp.parent
        next_freq_node = freq_node.next

        if not next_freq_node or next_freq_node.data != freq_node.data + 1:
            next_freq_node = self.insert_freq_node(
                freq_node.data + 1, freq_node, next_freq_node)
        item_node = next_freq_node.add_item_node(key)
        tmp.parent = next_freq_node

        freq_node.remove_item_node(tmp.node)
        if freq_node.count == 0:
            self.remove_freq_node(freq_node)

        tmp.node = item_node
        return tmp.data

    def insert(self, key, value):
        if key in self.items:
            raise DuplicateException('Key exists')
        freq_node = self.head
        if not freq_node or freq_node.data != 1:
            freq_node = self.insert_freq_node(1, None, freq_node)

        item_node = freq_node.add_item_node(key)
        self.items[key] = LfuItem(value, freq_node, item_node)

    def get_lfu(self):
        if not len(self.items):
            raise NotFoundException('Items list is empty.')
        return self.head.head.data, self.items[self.head.head.data].data

    def delete_lfu(self):
        """Remove the first item node from the first frequency node.

        Remove the LFU item from the dictionary.
        """
        if not self.head:
            raise NotFoundException('No frequency nodes found')
        freq_node = self.head
        item_node = freq_node.head
        del self.items[item_node.data]
        freq_node.remove_item_node(item_node)
        if freq_node.count == 0:
            self.remove_freq_node(freq_node)

    def __repr__(self):
        """Display access frequency list and items.

        Using the representation:
        freq1: [item, item, ...]
        freq2: [item, item]
        ...
        """
        s = ''
        freq_node = self.head
        while freq_node:
            s += '%s: %s\n' % (freq_node.data, freq_node.get_nodes_data())
            freq_node = freq_node.next
        return s


cache = Cache()
cache.insert('k1', 'v1')
cache.insert('k2', 'v2')
cache.insert('k3', 'v3')
print(cache)
assert cache.access('k2') == 'v2'
print(cache)
cache.get_lfu() == ('k1', 'v1')
cache.delete_lfu()
print(cache)

(0, 0)
(1, 2)
(2, 2)
(4, 0)

[b 0 0 0 0]
[0 0 b 0 0]
[0 0 b 0 0]
[0 0 0 0 0]
[b 0 0 0 0]

def add_new_bishop(location, attack_positions, board_size):
    # count how many times existing bishops can attack
    count = 0
    if location in attack_positions:
        count += 1

    # add new attack positions for future bishops
    new_attack_positions = list()

    i, j = location
    while i > 0 and j > 0:
        i -= 1
        j -= 1
        new_attack_positions.append((i, j))
    i, j = location
    while i > 0 and j < board_size - 1:
        i -= 1
        j += 1
        new_attack_positions.append((i, j))
    i, j = location
    while i < board_size - 1 and j > 0:
        i += 1
        j -= 1
        new_attack_positions.append((i, j))
    i, j = location
    while i < board_size - 1 and j < board_size - 1:
        i += 1
        j += 1
        new_attack_positions.append((i, j))

    attack_positions.extend(new_attack_positions)

    return count, attack_positions


def get_attack_vectors(bishop_locations, board_size):
    attack_positions = list()
    total_count = 0
    for location in bishop_locations:
        count, attack_positions = add_new_bishop(
            location, attack_positions, board_size)
        total_count += count

    return total_count


assert get_attack_vectors([(0, 0), (1, 2), (2, 2), (4, 0)], 5) == 2
assert get_attack_vectors([(0, 0), (1, 2), (2, 2)], 5) == 1

import sys


def get_pairwise_products(arr):
    pairwise_products = list()
    for i in range(len(arr)):
        for j in range(len(arr)):
            if i != j:
                pairwise_products.append([set([i, j]), arr[i] * arr[j]])

    return pairwise_products


def get_largest_product(arr):
    pairwise_products = get_pairwise_products(arr)
    max_triple = -1 * sys.maxsize
    for i in range(len(arr)):
        for prev_indices, product in pairwise_products:
            if i not in prev_indices:
                triple_prod = arr[i] * product
                if triple_prod > max_triple:
                    max_triple = triple_prod

    return max_triple


assert get_largest_product([-10, -10, 5, 2]) == 500
assert get_largest_product([-10, 10, 5, 2]) == 100

def get_perfect_number(n):
    tmp_sum = 0
    for char in str(n):
        tmp_sum += int(char)

    return (n * 10) + (10 - tmp_sum)


assert get_perfect_number(1) == 19
assert get_perfect_number(2) == 28
assert get_perfect_number(3) == 37
assert get_perfect_number(10) == 109
assert get_perfect_number(11) == 118
assert get_perfect_number(19) == 190

from random import randint


def rand5():
    return randint(1, 5)


def rand7():
    i = 5*rand5() + rand5() - 5  # uniformly samples between 1-25
    if i < 22:
        return i % 7 + 1
    return rand7()


num_experiments = 100000
result_dict = dict()
for _ in range(num_experiments):
    number = rand7()
    if number not in result_dict:
        result_dict[number] = 0
    result_dict[number] += 1

desired_probability = 1 / 7
for number in result_dict:
    result_dict[number] = result_dict[number] / num_experiments
    assert round(desired_probability, 2) == round(result_dict[number], 2)

ABACA
[(0, 1),
 (0, 2),
 (2, 3),
 (3, 4)]

A
[(0, 0)]

class GraphPath:
    def __init__(self, nodes=set(), letter_counts=dict()):
        self.nodes = nodes
        self.letter_counts = letter_counts

    def __repr__(self):
        return "nodes={}, letters={}".format(self.nodes, self.letter_counts)


def get_max_value_string(graph_path, node, adjacency_map):
    if node in graph_path.nodes:
        return [graph_path]

    new_nodes = graph_path.nodes.copy()
    new_nodes.add(node)
    new_letter_counts = graph_path.letter_counts.copy()
    if node[0] not in new_letter_counts:
        new_letter_counts[node[0]] = 0
    new_letter_counts[node[0]] += 1

    new_graph_path = GraphPath(new_nodes, new_letter_counts)

    if node not in adjacency_map:
        return [new_graph_path]

    paths = list()
    for child_node in adjacency_map[node]:
        new_paths = get_max_value_string(
            new_graph_path, child_node, adjacency_map)
        paths.extend(new_paths)

    return paths


def get_max_value_string_helper(graph_string, edge_list):

    letter_counts = dict()
    nodes = list()
    for char in graph_string:
        if char not in letter_counts:
            letter_counts[char] = 0
        else:
            letter_counts[char] += 1
        nodes.append("{}{}".format(char, letter_counts[char]))

    adjacency_map = dict()
    for start, end in edge_list:
        if nodes[start] not in adjacency_map:
            adjacency_map[nodes[start]] = set()
        if nodes[start] != nodes[end]:
            adjacency_map[nodes[start]].add(nodes[end])

    paths = list()
    graph_path = GraphPath()
    for node in adjacency_map:
        new_paths = get_max_value_string(graph_path, node, adjacency_map)
        paths.extend(new_paths)

    max_value = 0
    for path in paths:
        max_path_value = max(path.letter_counts.values())
        if max_path_value > max_value:
            max_value = max_path_value

    return max_value if max_value > 0 else None


assert get_max_value_string_helper(
    "ABACA", [(0, 1), (0, 2), (2, 3), (3, 4)]) == 3
assert not get_max_value_string_helper("A", [(0, 0)])

class Node:
    def __init__(self, x):
        self.val = x
        self.next = None

    def __str__(self):
        string = "["
        node = self
        while node:
            string += "{} ->".format(node.val)
            node = node.next
        string += "None]"
        return string


def get_nodes(values):
    next_node = None
    for value in values[::-1]:
        node = Node(value)
        node.next = next_node
        next_node = node

    return next_node


def get_list(head):
    node = head
    nodes = list()
    while node:
        nodes.append(node.val)
        node = node.next
    return nodes

def reverse_list(head, new_head):
    if not head:
        return new_head

    old_head = head.next
    head.next = new_head

    return reverse_list(old_head, head)


assert not get_list(reverse_list(get_nodes([]), None))
assert get_list(reverse_list(get_nodes([1]), None)) == [1]
assert get_list(reverse_list(get_nodes([1, 2]), None)) == [2, 1]
assert get_list(reverse_list(get_nodes([1, 2, 3]), None)) == [3, 2, 1]

def get_mult_count(n, x):
    if n == 1:
        return n

    tuples = list()
    for i in range(1, (x + 1) // 2):
        if not x % i:
            tuples.append((i, x // i))

    return len(tuples)


assert get_mult_count(1, 1) == 1
assert get_mult_count(6, 12) == 4
assert get_mult_count(2, 4) == 1
assert get_mult_count(3, 6) == 2

cache = None


def get_subseq(arr, start):
    if start == len(arr):
        return 0

    current = arr[start]
    max_inc = 1
    for index in range(start + 1, len(arr)):
        if arr[index] >= current:
            if index in cache:
                count = cache[index]
            else:
                count = get_subseq(arr, index) + 1
                cache[index] = count
            if count > max_inc:
                max_inc = count

    return max_inc


def get_subseq_helper(arr):
    global cache
    cache = dict()
    return get_subseq(arr, 0)


assert get_subseq_helper([]) == 0
assert get_subseq_helper([0, 1]) == 2
assert get_subseq_helper([0, 2, 1]) == 2
assert get_subseq_helper([0, 1, 2]) == 3
assert get_subseq_helper([2, 1, 0]) == 1
assert get_subseq_helper(
    [0, 8, 4, 12, 2, 10, 6, 14, 1, 9, 5, 13, 3, 11, 7, 15]) == 6

cba
daf
ghi

ca
df
gi

abcdef

zyx
wvu
tsr

def get_col_rem_count(matrix):
    if not matrix:
        return 0

    rows = len(matrix)
    if rows == 1:
        return 0

    cols = len(matrix[0])

    col_drop_count = 0
    for i in range(cols):
        for k in range(1, rows):
            if matrix[k][i] < matrix[k-1][i]:
                col_drop_count += 1
                break

    return col_drop_count


assert get_col_rem_count(["cba", "daf", "ghi"]) == 1
assert get_col_rem_count(["abcdef"]) == 0
assert get_col_rem_count(["zyx", "wvu", "tsr"]) == 3

def merge_overlaps(intervals):
    interval_starts, interval_ends = set(), set()
    for start, end in intervals:
        interval_starts.add(start)
        interval_ends.add(end)

    min_start = min(interval_starts)
    max_end = max(interval_ends)
    current_active = 0
    instant_statuses = list([current_active])
    merged = list()
    for i in range(min_start, max_end + 1):
        if i in interval_ends:
            current_active -= 1
        if i in interval_starts:
            current_active += 1
        instant_statuses.append(current_active)

    start, end = None, None
    for i in range(len(instant_statuses)):
        if instant_statuses[i] and not instant_statuses[i-1]:
            start = i
        if not instant_statuses[i] and instant_statuses[i-1]:
            end = i
            merged.append((start, end))
            start, end = None, None
    return merged


assert merge_overlaps([(1, 3), (5, 8), (4, 10), (20, 25)]) == [
    (1, 3), (4, 10), (20, 25)]
assert merge_overlaps([(1, 3), (5, 8), (4, 10), (20, 25), (6, 12)]) == [
    (1, 3), (4, 12), (20, 25)]

import sys
from heapq import heappush, heappop


class Node:
    def __init__(self, x):
        self.val = x
        self.next = None

    def __str__(self):
        string = "["
        node = self
        while node:
            string += "{} ->".format(node.val)
            node = node.next
        string += "None]"
        return string


def get_nodes(values):
    next_node = None
    for value in values[::-1]:
        node = Node(value)
        node.next = next_node
        next_node = node

    return next_node


def get_list(head):
    node = head
    nodes = list()
    while node:
        nodes.append(node.val)
        node = node.next
    return nodes


def merge_lists(all_lists):
    merged_head = Node(None)
    merged_tail = merged_head
    candidates = list()
    counter = 0
    for llist in all_lists:
        heappush(candidates, (llist.val, counter, llist))
        counter += 1

    while candidates:
        _, _, new_node = heappop(candidates)

        if new_node.next:
            heappush(candidates, (new_node.next.val, counter, new_node.next))
            counter += 1

        merged_tail.next = new_node
        merged_tail = new_node

    return merged_head.next


assert get_list(merge_lists([get_nodes([1, 4, 6]),
                             get_nodes([1, 3, 7])])) == [1, 1, 3, 4, 6, 7]
assert get_list(merge_lists([get_nodes([1, 4, 6]),
                             get_nodes([2, 3, 9]),
                             get_nodes([1, 3, 7])])) == [1, 1, 2, 3, 3, 4, 6, 7, 9]

def can_edit(arr):
    decr_pairs = 0
    for i in range(1, len(arr)):
        if arr[i] < arr[i - 1]:
            decr_pairs += 1

    return decr_pairs <= 1


assert can_edit([10, 5, 7])
assert not can_edit([10, 5, 1])
assert can_edit([1, 10, 5, 7])

    a
   / \
  b   c
 /
d

class Node:

    def __init__(self, val):
        self.val = val
        self.left = None
        self.right = None

    def __repr__(self):
        return str(self.val)


def find_deepest_node(root, depth):
    if not root.left and not root.right:
        return (root, depth)

    left_depth = depth
    right_depth = depth
    if root.left:
        left_deepest, left_depth = find_deepest_node(root.left, depth + 1)
    if root.right:
        right_deepest, right_depth = find_deepest_node(root.right, depth + 1)

    return (left_deepest, left_depth) if left_depth > right_depth \
        else (right_deepest, right_depth)


def find_deepest_node_helper(root):
    return find_deepest_node(root, 0)[0]


a = Node('a')
b = Node('b')
c = Node('c')
d = Node('d')
e = Node('e')
f = Node('f')

a.left = b
a.right = c
b.left = d

assert find_deepest_node_helper(a) == d

c.left = e
e.left = f


assert find_deepest_node_helper(a) == f

digit_mapping = {
    '2': ['a', 'b', 'c'],
    '3': ['d', 'e', 'f']
}


def get_letter_strings(number_string):
    if not number_string:
        return

    if len(number_string) == 1:
        return digit_mapping[number_string[0]]

    possible_strings = list()
    current_letters = digit_mapping[number_string[0]]
    strings_of_rem_nums = get_letter_strings(number_string[1:])
    for letter in current_letters:
        for string in strings_of_rem_nums:
            possible_strings.append(letter + string)

    return possible_strings


assert get_letter_strings("2") == [
    'a', 'b', 'c']
assert get_letter_strings("23") == [
    'ad', 'ae', 'af', 'bd', 'be', 'bf', 'cd', 'ce', 'cf']
assert get_letter_strings("32") == [
    'da', 'db', 'dc', 'ea', 'eb', 'ec', 'fa', 'fb', 'fc']

class FileProxy:
    def __init__(self, contents):
        self.contents = contents
        self.offset = 0
        self.buffer = ""

    def read_7(self):
        start = self.offset
        end = min(self.offset + 7, len(self.contents))
        self.offset = end
        return self.contents[start:end].strip()

    def read_n(self, n):
        while len(self.buffer) < n:
            additional_chars = self.read_7()
            if not (additional_chars):
                break
            self.buffer += additional_chars

        n_chars = self.buffer[:n]
        self.buffer = self.buffer[n:]
        return n_chars.strip()


fp = FileProxy("Hello world")
assert fp.read_7() == "Hello w"
assert fp.read_7() == "orld"
assert fp.read_7() == ""

fp = FileProxy("Hello world")
assert fp.read_n(8) == "Hello wo"
assert fp.read_n(8) == "rld"

fp = FileProxy("Hello world")
assert fp.read_n(4) == "Hell"
assert fp.read_n(4) == "o wo"
assert fp.read_n(4) == "rld"

    a
   / \
  b   c
 / \  /
d   e f

  a
 / \
 c  b
 \  / \
  f e  d

class Node:

    def __init__(self, val):
        self.val = val
        self.left = None
        self.right = None

    def __repr__(self):
        string = "{}=({},{})".format(self.val, self.left, self.right)
        return string


def invert_tree(root):
    if not root:
        return

    inverted_left = invert_tree(root.right)
    inverted_right = invert_tree(root.left)
    root.left = inverted_left
    root.right = inverted_right

    return root


a = Node('a')
b = Node('b')
c = Node('c')
d = Node('d')
e = Node('e')
f = Node('f')

a.left = b
a.right = c
b.left = d
b.right = e
c.left = f

inverted_a = invert_tree(a)
assert inverted_a.left == c
assert inverted_a.right == b
assert inverted_a.left.right == f
assert inverted_a.right.right == d

1 0 0 0 0
0 0 1 1 0
0 1 1 0 0
0 0 0 0 0
1 1 0 0 1
1 1 0 0 1

def add_island(x, y, world_map, visited):
    coord = "{}-{}".format(x, y)

    if coord in visited:
        return 0

    visited.add(coord)

    if x > 0 and world_map[x-1][y]:
        add_island(x-1, y, world_map, visited)
    if x < len(world_map) - 1 and world_map[x+1][y]:
        add_island(x+1, y, world_map, visited)
    if y > 0 and world_map[x][y-1]:
        add_island(x, y-1, world_map, visited)
    if y < len(world_map[0]) - 1 and world_map[x][y+1]:
        add_island(x, y+1, world_map, visited)

    return 1


def count_islands(world_map):
    count = 0
    visited = set()
    for i in range(len(world_map)):
        for k in range(len(world_map[0])):
            if world_map[i][k]:
                count += add_island(i, k, world_map, visited)

    return count


world_map = [
    [1, 0, 0, 0, 0],
    [0, 0, 1, 1, 0],
    [0, 1, 1, 0, 0],
    [0, 0, 0, 0, 0],
    [1, 1, 0, 0, 1],
    [1, 1, 0, 0, 1],
]
assert count_islands(world_map) == 4

def get_num(x, y, b):
    return x * b + y * abs(b-1)


assert get_num(3, 4, 1) == 3
assert get_num(3, 4, 0) == 4

def get_chars_removed_helper(string, stack, removed):

    if not string and not stack:
        return removed
    elif not string:
        return len(stack) + removed

    if string[0] == ')' and stack and stack[-1] == '(':
        stack.pop()
        return get_chars_removed_helper(string[1:], stack, removed)

    removed_chars_add = get_chars_removed_helper(
        string[1:], stack + [string[0]], removed)
    removed_chars_ignore = get_chars_removed_helper(
        string[1:], stack, removed + 1)

    return min(removed_chars_add, removed_chars_ignore)


def get_chars_removed(string):
    chars_removed = get_chars_removed_helper(string, list(), 0)
    return chars_removed


assert get_chars_removed("()())()") == 1
assert get_chars_removed(")(") == 2
assert get_chars_removed("()(((") == 3
assert get_chars_removed(")()(((") == 4

A N B
B NE C
C N A

A NW B
A N B

opposites = {
    'N': 'S', 'S': 'N', 'E': 'W', 'W': 'E'
}


class Node:
    def __init__(self, val):
        self.val = val
        self.neighbours = {
            'N': set(),
            'S': set(),
            'E': set(),
            'W': set()
        }

    def __repr__(self):
        string = "{}={}".format(self.val, self.neighbours)
        return string

    def __hash__(self):
        return hash(self.val)


class Map:

    def add_rule(self, node_1, direction, node_2):

        for char in direction:
            if node_1 in node_2.neighbours[char] or \
                    node_2 in node_1.neighbours[opposites[char]]:
                raise Exception

            for node in node_1.neighbours[char]:
                self.add_rule(node, char, node_2)

        for char in direction:
            node_2.neighbours[char].add(node_1)
            node_1.neighbours[opposites[char]].add(node_2)


a = Node('a')
b = Node('b')
c = Node('c')

m = Map()
m.add_rule(a, 'N', b)
m.add_rule(b, 'NE', c)
try:
    m.add_rule(c, 'N', a)
except Exception:
    print("Invalid rule")

def divide(dividend, divisor):
    if not divisor:
        return

    current_sum = 0
    quotient = 0
    while current_sum <= dividend:
        quotient += 1
        current_sum += divisor

    return quotient - 1


assert not divide(1, 0)
assert divide(1, 1) == 1
assert divide(0, 1) == 0
assert divide(12, 3) == 4
assert divide(13, 3) == 4
assert divide(25, 5) == 5
assert divide(25, 7) == 3

import sys


class Node:
    def __init__(self, val):
        self.val = val
        self.left = None
        self.right = None


def is_valid_bst_node_helper(node, lb, ub):

    if node and node.val <= ub and node.val >= lb:
        return is_valid_bst_node_helper(node.left, lb, node.val) and \
            is_valid_bst_node_helper(node.right, node.val, ub)

    return not node  # if node is None, it's a valid BST


def is_valid_bst(root):
    return is_valid_bst_node_helper(root, -sys.maxsize, sys.maxsize)


# Tests


assert is_valid_bst(None)

a = Node(3)
b = Node(2)
c = Node(6)
d = Node(1)
e = Node(3)
f = Node(4)

a.left = b
a.right = c
b.left = d
b.right = e
c.left = f
assert is_valid_bst(a)


a = Node(1)
b = Node(2)
c = Node(6)
d = Node(1)
e = Node(3)
f = Node(4)

a.left = b
a.right = c
b.left = d
b.right = e
c.left = f
assert not is_valid_bst(a)

a = Node(3)
b = Node(2)
c = Node(6)
d = Node(1)
e = Node(4)
f = Node(4)

a.left = b
a.right = c
b.left = d
b.right = e
c.left = f
assert not is_valid_bst(a)

from random import randint


def generate_random_num(n, excluded_nums):
    rand = randint(0, n-1)
    if rand in excluded_nums:
        return generate_random_num(n, excluded_nums)

    return rand


def run_experiment(num_samples, n, l):
    error_tolerance = 0.01
    results = dict()
    excluded_nums = set(l)

    for num in range(n):
        results[num] = 0

    for _ in range(num_samples):
        rand = generate_random_num(n, excluded_nums)
        results[rand] += 1
    expected_prob = 1/(n - len(excluded_nums))

    for num in results:
        results[num] /= num_samples
        if num in excluded_nums:
            assert not results[num]
        else:
            assert results[num] > expected_prob - error_tolerance or \
                results[num] < expected_prob + error_tolerance


run_experiment(100000, 6, [])
run_experiment(100000, 6, [1, 5])
run_experiment(100000, 6, [1, 3, 5])

# The function prints nine because it uses the variable
# i to determine what to return and i finishes looping
# at 9

functions = []
for i in range(10):
    functions.append(lambda: i)

i = 0
for f in functions:
    print(f())
    i += 1

def get_course_order_helper(prereqs, indep, order):
    if not indep:
        return None, None, None
    elif not prereqs:
        return prereqs, indep, order

    new_indep = set()
    for dc in prereqs:
        required = prereqs[dc] - indep
        if not len(required):
            new_indep.add(dc)
            order.append(dc)

    for course in new_indep:
        del prereqs[course]

    return get_course_order_helper(prereqs, indep.union(new_indep), order)


def get_course_order(prereqs):

    indep = set()
    order = list()
    for course in prereqs:
        if not prereqs[course]:
            indep.add(course)
            order.append(course)
        else:
            prereqs[course] = set(prereqs[course])

    for course in indep:
        del prereqs[course]

    _, _, order = get_course_order_helper(prereqs, indep, order)

    return order


prereqs = {
    'CSC100': [],
    'CSC200': [],
    'CSC300': []
}
assert get_course_order(prereqs) == ['CSC100', 'CSC200', 'CSC300']

prereqs = {
    'CSC300': ['CSC100', 'CSC200'],
    'CSC200': ['CSC100'],
    'CSC100': []
}
assert get_course_order(prereqs) == ['CSC100', 'CSC200', 'CSC300']

prereqs = {
    'CSC400': ['CSC200'],
    'CSC300': ['CSC100', 'CSC200'],
    'CSC200': ['CSC100'],
    'CSC100': []
}
assert get_course_order(prereqs) == ['CSC100', 'CSC200', 'CSC400', 'CSC300']

prereqs = {
    'CSC400': ['CSC300'],
    'CSC300': ['CSC100', 'CSC200'],
    'CSC200': ['CSC100'],
    'CSC100': ['CSC400']
}
assert not get_course_order(prereqs)

import sys


class Node:
    def __init__(self, val):
        self.val = val
        self.left = None
        self.right = None

    def __repr__(self):
        string = "val={}:(left={}, right={})".format(
            self.val, self.left, self.right)
        return string


def get_largest_bst_helper(node):
    if not node:
        return (True, node, 0, sys.maxsize, -sys.maxsize)
    if not node.left and not node.right:
        return (True, node, 1, node.val, node.val)

    left_is_bst, left_bst, left_nodes, left_minval, left_maxval = \
        get_largest_bst_helper(node.left)
    right_is_bst, right_bst, right_nodes, right_minval, right_maxval = \
        get_largest_bst_helper(node.right)

    if left_is_bst and right_is_bst:
        if node.left and node.right:
            if node.val >= left_maxval and node.val <= right_minval:
                return (True, node, left_nodes + right_nodes + 1,
                        left_minval, right_maxval)
        elif node.left and node.val >= left_maxval:
            return (True, node, left_nodes + 1, left_minval, node.val)
        elif node.right and node.val >= right_minval:
            return (True, node, left_nodes + 1, node.val, right_maxval)

    if left_nodes > right_nodes:
        return (False, left_bst, left_nodes, left_minval, node.val)
    else:
        return (False, right_bst, right_nodes, node.val, right_maxval)


def get_largest_bst(root):
    _, largest_bst, nodes, _, _ = get_largest_bst_helper(root)
    return (largest_bst, nodes)


# tests

a = Node(3)
b = Node(2)
c = Node(6)
d = Node(1)
e = Node(3)
f = Node(4)
a.left = b
a.right = c
b.left = d
b.right = e
c.left = f
assert get_largest_bst(a) == (a, 6)

a = Node(1)
b = Node(2)
c = Node(6)
d = Node(1)
e = Node(3)
f = Node(4)
a.left = b
a.right = c
b.left = d
b.right = e
c.left = f
assert get_largest_bst(a) == (b, 3)

a = Node(3)
b = Node(2)
c = Node(6)
d = Node(1)
e = Node(4)
f = Node(4)
a.left = b
a.right = c
b.left = d
b.right = e
c.left = f
assert get_largest_bst(a) == (b, 3)

a = Node(3)
b = Node(2)
c = Node(6)
d = Node(1)
e = Node(1)
f = Node(4)
a.left = b
a.right = c
b.left = d
b.right = e
c.left = f
assert get_largest_bst(a) == (c, 2)

class Node:
    def __init__(self, val):
        self.val = val
        self.left = None
        self.right = None


def get_max_path_sum(root, current_max_sum, overall_max_sum):
    if not root:
        return overall_max_sum

    current_max_sum = max(root.val, current_max_sum + root.val)
    overall_max_sum = max(overall_max_sum, current_max_sum)

    left_path_sum = get_max_path_sum(
        root.left, current_max_sum, overall_max_sum)
    right_path_sum = get_max_path_sum(
        root.right, current_max_sum, overall_max_sum)

    return max(overall_max_sum, left_path_sum, right_path_sum)


assert get_max_path_sum(None, 0, 0) == 0

a = Node(1)
assert get_max_path_sum(a, 0, 0) == 1

b = Node(2)
a.left = b
assert get_max_path_sum(a, 0, 0) == 3

c = Node(3)
a.right = c
assert get_max_path_sum(a, 0, 0) == 4

a.val = -1
assert get_max_path_sum(a, 0, 0) == 3

d = Node(4)
b.left = d
assert get_max_path_sum(a, 0, 0) == 6

def get_greater_permutation(arr):

    if len(arr) < 2:
        return

    for index in range(len(arr) - 1, -1, -1):
        if index > 0 and arr[index - 1] < arr[index]:
            break

    if index == 0:
        arr.reverse()
    else:
        for k in range(len(arr) - 1, index - 1, -1):
            if arr[k] > arr[index - 1]:
                tmp = arr[k]
                arr[k] = arr[index - 1]
                arr[index - 1] = tmp
                break

        sub_array = arr[index:]
        sub_array.reverse()
        arr[index:] = sub_array

    return arr


assert get_greater_permutation([1, 2, 3]) == [1, 3, 2]
assert get_greater_permutation([1, 3, 2]) == [2, 1, 3]
assert get_greater_permutation([3, 2, 1]) == [1, 2, 3]

def get_permutations(arr):
    if len(arr) < 2:
        return [arr]

    permutations = list()
    for i, num in enumerate(arr):
        arr_cp = arr[:i] + arr[i+1:]
        child_perms = get_permutations(arr_cp)
        for perm in child_perms:
            permutations.append([num] + perm)

    return permutations


assert get_permutations([]) == [[]]
assert get_permutations([1]) == [[1]]
assert get_permutations([1, 2]) == [[1, 2], [2, 1]]
assert get_permutations([1, 2, 3]) == \
    [[1, 2, 3], [1, 3, 2], [2, 1, 3],
     [2, 3, 1], [3, 1, 2], [3, 2, 1]]

    set(key, value, time): # sets key to value for t = time.
    get(key, time): # gets the key at t = time.

d.set(1, 1, 0) # set key 1 to value 1 at time 0
d.set(1, 2, 2) # set key 1 to value 2 at time 2
d.get(1, 1) # get key 1 at time 1 should be 1
d.get(1, 3) # get key 1 at time 3 should be 2

d.set(1, 1, 5) # set key 1 to value 1 at time 5
d.get(1, 0) # get key 1 at time 0 should be null
d.get(1, 10) # get key 1 at time 10 should be 1

d.set(1, 1, 0) # set key 1 to value 1 at time 0
d.set(1, 2, 0) # set key 1 to value 2 at time 0
d.get(1, 0) # get key 1 at time 0 should be 2

import bisect


class TimedMap:
    def __init__(self):
        self.map = dict()

    def __repr__(self):
        return str(self.map)

    def setval(self, key, value, time):
        if key not in self.map:
            self.map[key] = ([time], [value])
            return

        times, values = self.map[key]
        insertion_point = bisect.bisect(times, time)
        times.insert(insertion_point, time)
        values.insert(insertion_point, value)

    def getval(self, key, time):
        if key not in self.map:
            return

        times, values = self.map[key]
        insertion_point = bisect.bisect(times, time)
        if not insertion_point:
            return

        return values[insertion_point - 1]


d = TimedMap()
d.setval(1, 1, 0)
d.setval(1, 2, 2)
assert d.getval(1, 1) == 1
assert d.getval(1, 3) == 2

d = TimedMap()
d.setval(1, 1, 5)
assert not d.getval(1, 0)
assert d.getval(1, 10) == 1

d = TimedMap()
d.setval(1, 1, 0)
d.setval(1, 2, 0)
assert d.getval(1, 0) == 2

[
  ['A','B','C','E'],
  ['S','F','C','S'],
  ['A','D','E','E']
]

def check_new_coordinate(word, row, col, used_coordinates):
    expected_char = word[0]
    copy_coordinates = used_coordinates.copy()
    char = board[row][col]
    result = False
    if expected_char == char and "{}-{}".format(row, col) not in copy_coordinates:
        copy_coordinates.add("{}-{}".format(row, col))
        result = existence_helper(
            word[1:], board, row, col, copy_coordinates)
    return result


def existence_helper(word, board, crow, ccol, used_coordinates):
    if not word:
        return True

    top, bottom, left, right = (False, False, False, False)
    if crow > 0:
        top = check_new_coordinate(word, crow - 1, ccol, used_coordinates)
    if crow < len(board) - 1:
        bottom = check_new_coordinate(word, crow + 1, ccol, used_coordinates)
    if ccol > 0:
        left = check_new_coordinate(word, crow, ccol - 1, used_coordinates)
    if ccol < len(board[0]) - 1:
        right = check_new_coordinate(word, crow, ccol + 1, used_coordinates)

    return top or bottom or left or right


def exists(board, word):
    if not word:
        return False

    first_char = word[0]
    result = False
    for row in range(len(board)):
        for col in range(len(board[0])):
            if board[row][col] == first_char:
                result = result or existence_helper(
                    word[1:], board, row, col, set(["{}-{}".format(row, col)]))

    return result


board = [
    ['A', 'B', 'C', 'E'],
    ['S', 'F', 'C', 'S'],
    ['A', 'D', 'E', 'E']
]
assert exists(board, "ABCCED")
assert exists(board, "SEE")
assert not exists(board, "ABCB")

class NumRange:
    def __init__(self, start, end):
        self.start = start
        self.end = end

    def __hash__(self):
        return hash(self.start, self.end)

    def __eq__(self, other):
        return self.start == other.start and self.end == other.end

    def __repr__(self):
        return "[{}, {}]".format(self.start, self.end)


def add_number(num, starts, ends):
    if num + 1 in starts and num - 1 in ends:
        num_range_1 = ends[num - 1]
        num_range_2 = starts[num + 1]
        num_range = NumRange(num_range_1.start, num_range_2.end)
        starts[num_range.start] = num_range
        ends[num_range.end] = num_range
        del starts[num_range_2.start]
        del ends[num_range_1.end]
        return
    elif num + 1 in starts:
        num_range = starts[num + 1]
        num_range.start = num
        starts[num] = num_range
        del starts[num + 1]
        return
    elif num - 1 in ends:
        num_range = ends[num - 1]
        num_range.end = num
        ends[num] = num_range
        del ends[num - 1]
        return

    num_range = NumRange(num, num)
    starts[num] = num_range
    ends[num] = num_range


def get_seq_length(arr):
    starts = dict()
    ends = dict()

    for num in arr:
        add_number(num, starts, ends)

    max_len = 0
    for start in starts:
        num_range = starts[start]
        length = num_range.end - num_range.start + 1
        max_len = length if length > max_len else max_len

    return max_len


assert get_seq_length([100, 4, 200, 1]) == 1
assert get_seq_length([100, 4, 200, 1, 3]) == 2
assert get_seq_length([100, 4, 200, 1, 3, 2]) == 4
assert get_seq_length([100, 4, 200, 1, 3, 2, 5]) == 5

 (x,y) to
    (x+1, y),
    (x - 1, y),
    (x, y+1),
    (x, y-1),
    (x-1, y-1),
    (x+1,y+1),
    (x-1,y+1),
    (x+1,y-1)

def get_distance(current_point, next_point, accumulated_distance):
    x_diff = next_point[0] - current_point[0]
    y_diff = next_point[1] - current_point[1]

    if not x_diff:
        return abs(y_diff) + accumulated_distance
    if not y_diff:
        return abs(x_diff) + accumulated_distance

    updated_current = (current_point[0] + int(x_diff/abs(x_diff)),
                       current_point[1] + int(y_diff/abs(y_diff)))

    return get_distance(updated_current, next_point, accumulated_distance + 1)


def get_min_steps_helper(current_point, remaining_points, steps):
    if not remaining_points:
        return steps

    next_point = remaining_points[0]
    min_distance = get_distance(current_point, next_point, 0)

    return get_min_steps_helper(next_point, remaining_points[1:], steps + min_distance)


def get_min_steps(points):
    if not points:
        return 0

    return get_min_steps_helper(points[0], points[1:], 0)


assert get_min_steps([]) == 0
assert get_min_steps([(0, 0)]) == 0
assert get_min_steps([(0, 0), (1, 1), (1, 2)]) == 2
assert get_min_steps([(0, 0), (1, 1), (1, 2), (3, 4)]) == 4
assert get_min_steps([(0, 0), (1, 1), (1, 2), (3, 6)]) == 6

def is_prime(num, primes):
    for prime in primes:
        if prime == num:
            return True
        if not num % prime:
            return False
    return True


def get_primes(num):
    limit = (num // 2) + 1

    candidates = list()
    primes = list()
    for i in range(2, limit):
        if is_prime(i, primes):
            primes.append(i)
            candidates.append((i, num - i))

    new_candidates = list()
    for first, second in candidates[::-1]:
        if is_prime(second, primes):
            primes.append(second)
            new_candidates.append((first, second))

    return new_candidates[-1]


assert get_primes(4) == (2, 2)
assert get_primes(10) == (3, 7)
assert get_primes(100) == (3, 97)

def get_cont_arr(arr, target):
    summed = 0

    start, end = 0, 0
    i = 0
    while i < len(arr):
        if summed == target:
            return arr[start:end]
        elif summed > target:
            summed -= arr[start]
            start += 1
        else:
            summed += arr[i]
            end = i + 1
            i += 1


assert get_cont_arr([1, 2, 3, 4, 5], 0) == []
assert get_cont_arr([1, 2, 3, 4, 5], 1) == [1]
assert get_cont_arr([1, 2, 3, 4, 5], 5) == [2, 3]
assert get_cont_arr([5, 4, 3, 4, 5], 12) == [5, 4, 3]
assert get_cont_arr([5, 4, 3, 4, 5], 11) == [4, 3, 4]
assert get_cont_arr([1, 2, 3, 4, 5], 9) == [2, 3, 4]
assert get_cont_arr([1, 2, 3, 4, 5], 3) == [1, 2]

from queue import Queue


def get_min_string(string, charset):
    curr_queue = list()
    ind_queue = list()
    curr_seen = set()

    candidate = None
    i = 0
    while i < len(string):
        if string[i] in charset:
            curr_queue.append(string[i])
            ind_queue.append(i)
            curr_seen.add(string[i])

        shift = 0
        for k in range(len(curr_queue)//2):
            if curr_queue[k] == curr_queue[-k-1]:
                shift += 1
        curr_queue = curr_queue[shift:]
        ind_queue = ind_queue[shift:]

        if len(curr_seen) == len(charset):
            if not candidate or len(candidate) > (ind_queue[-1] - ind_queue[0] + 1):
                candidate = string[ind_queue[0]:ind_queue[-1]+1]

        i += 1

    return candidate


assert not get_min_string("abcdedbc", {'g', 'f'})
assert get_min_string("abccbbbccbcb", {'a', 'b', 'c'}) == "abc"
assert get_min_string("figehaeci", {'a', 'e', 'i'}) == "aeci"
assert get_min_string("abcdedbc", {'d', 'b', 'b'}) == "db"
assert get_min_string("abcdedbc", {'b', 'c'}) == "bc"
assert get_min_string("abcdecdb", {'b', 'c'}) == "bc"
assert get_min_string("abcdecdb", {'b', 'c', 'e'}) == "bcde"

# Solution works for both single and doubly linked lists


class Node:
    def __init__(self, val):
        self.val = val
        self.next = None

    def __repr__(self):
        return "{} -> {}".format(self.val, self.next)


def reverse(head):
    if not head.next:
        new_head = Node(head.val)
        return new_head, new_head

    rev_head, rev_tail = reverse(head.next)
    rev_tail.next = Node(head.val)

    return rev_head, rev_tail.next


def is_palindrome(head):
    if not head:
        return None

    reversed_head = reverse(head)
    curr = head
    curr_rev = reversed_head[0]
    while curr:
        if curr.val != curr_rev.val:
            return False
        curr = curr.next
        curr_rev = curr_rev.next

    return True


# Tests

a0 = Node('a')
a1 = Node('a')
b0 = Node('b')
c0 = Node('c')

a0.next = b0
b0.next = c0

assert not is_palindrome(a0)
b0.next = a1
assert is_palindrome(a0)

a0 = Node('a')
assert is_palindrome(a0)
b0 = Node('b')
a0.next = b0
assert not is_palindrome(a0)

# source - https://gist.github.com/kylebebak/ee67befc156831b3bbaa88fb197487b0

import time


def debounce(s):
    """
    Decorator ensures function that can only be called once every `s` seconds.
    """
    interval = s * (10**(-3))

    def decorate(f):
        current_time = None

        def wrapped(*args, **kwargs):
            nonlocal current_time
            start_time = time.time()
            if current_time is None or start_time - current_time >= interval:
                result = f(*args, **kwargs)
                current_time = time.time()
                return result
        return wrapped
    return decorate


@debounce(3000)
def add_nums(x, y):
    return x + y


assert add_nums(1, 1) == 2
time.sleep(1)
assert not add_nums(1, 2)
time.sleep(1)
assert not add_nums(1, 3)
time.sleep(1)
assert add_nums(1, 4) == 5

# assuming only integers > 0 are allowed


def reaches_last_helper(arr, start_index, target_index):
    if start_index == target_index:
        return True

    hop = arr[start_index]
    if not hop or (start_index + hop > target_index):
        return False

    return reaches_last_helper(arr, start_index + hop, target_index)


def reaches_last(arr):
    return reaches_last_helper(arr, 0, len(arr) - 1)


assert reaches_last([2, 0, 1, 0])
assert not reaches_last([1, 1, 0, 1])
assert not reaches_last([2, 1])

  1
 / \
2   3
   / \
  4   5

class Node:
    def __init__(self, val):
        self.val = val
        self.left = None
        self.right = None

    def _print(self):
        print(self.val)
        if self.left:
            self.left._print()
        if self.right:
            self.right._print()


# Tests
a = Node(1)
b = Node(2)
c = Node(3)
d = Node(4)
e = Node(5)

a.left = b
a.right = c
c.left = d
c.right = e

a._print()

def can_shift(target, string):
    return \
        target and string and \
        len(target) == len(string) and \
        string in target * 2


assert can_shift("abcde", "cdeab")
assert not can_shift("abc", "acb")

# 85 is the odd-bit filter '01010101'


def swap_bits(num):
    return ((num & 85) << 1) | ((num & (85 << 1)) >> 1)


assert swap_bits(0) == 0
assert swap_bits(255) == 255
assert swap_bits(210) == 225
assert swap_bits(170) == 85
assert swap_bits(226) == 209

   1
  / \
 2   3
    / \
   4   5

class Node:
    def __init__(self, val):
        self.val = val
        self.left = None
        self.right = None

    def __repr__(self):
        return str(self.val)


def get_all_paths(node):
    if not node:
        return []

    node_paths = list()
    left_paths = get_all_paths(node.left)
    for path in left_paths:
        node_paths.append([node.val] + path)

    right_paths = get_all_paths(node.right)
    for path in right_paths:
        node_paths.append([node.val] + path)

    return node_paths if node_paths else [[node.val]]


# Tests

a = Node(1)
b = Node(2)
c = Node(3)
d = Node(4)
e = Node(5)

a.left = b
a.right = c
c.left = d
c.right = e

assert get_all_paths(a) == [[1, 2], [1, 3, 4], [1, 3, 5]]
assert get_all_paths(b) == [[2]]
assert get_all_paths(c) == [[3, 4], [3, 5]]

def add_needed_char(needed, char):
    if char not in needed:
        needed[char] = 0
    needed[char] += 1


def remove_gained_char(needed, char):
    needed[char] -= 1


def get_anagram_starts(string, word):
    if len(word) > len(string):
        return []

    anagram_indices = list()
    charset = set(word)

    needed = dict()
    for i, char_needed in enumerate(word):
        add_needed_char(needed, char_needed)

    for i in range(len(word)):
        char_gained = string[i]
        remove_gained_char(needed, char_gained)

    # This is a constant time operation because it has
    # a fixed upper bound of 26 read operations
    if all([x < 1 for x in needed.values()]):
        anagram_indices.append(0)

    for i in range(len(word), len(string)):
        window_start = i - len(word)
        char_removed = string[window_start]
        char_gained = string[i]

        if char_removed in charset:
            add_needed_char(needed, char_removed)

        if char_gained in needed:
            remove_gained_char(needed, char_gained)

        if all([x < 1 for x in needed.values()]):
            anagram_indices.append(window_start + 1)

    return anagram_indices


# Tests
assert get_anagram_starts("abxaba", "ab") == [0, 3, 4]
assert get_anagram_starts("cataract", "tac") == [0, 5]

# The problem description is needlessly complicated.
# The problem is the same as finding the intersection of linked list


class Node:
    def __init__(self):
        self.parent = None


def get_list_length(node):
    if not node:
        return 0

    return 1 + get_list_length(node.parent)


def get_lca(node_a, node_b):
    len_a = get_list_length(node_a)
    len_b = get_list_length(node_b)

    (longer, max_len, shorter, min_len) = \
        (node_a, len_a, node_b, len_b) if len_a > len_b \
        else (node_b, len_b, node_a, len_a)

    for _ in range(max_len - min_len):
        longer = longer.parent

    while longer and shorter:
        if longer == shorter:
            return longer

        longer = longer.parent
        shorter = shorter.parent


# Test
def test_1():
    a = Node()
    b = Node()
    c = Node()
    d = Node()
    e = Node()
    f = Node()
    g = Node()

    a.parent = c
    c.parent = e
    e.parent = f

    b.parent = d
    d.parent = f

    f.parent = g

    assert get_lca(a, b) == f


def test_2():
    a = Node()
    b = Node()
    c = Node()
    d = Node()
    e = Node()
    f = Node()
    g = Node()

    a.parent = c
    c.parent = e

    b.parent = d
    d.parent = e

    e.parent = f
    f.parent = g

    assert get_lca(a, b) == e
    assert get_lca(c, b) == e
    assert get_lca(e, b) == e


test_1()
test_2()

def reverse_words(string):
    return " ".join(reversed(string.split()))


assert reverse_words("hello world here") == "here world hello"

def reverse_words(string, delimiters):
    words = list()
    delims = list()
    delim_positions = list()  # stores positions of the delimiters seen

    start = 0
    i = 0
    while i < len(string):
        char = string[i]

        if char in delimiters:
            word = string[start:i]
            if i - start > 1:
                words.append(word)
            delims.append(char)
            delim_positions.append(len(words) + len(delims) - 1)
            start = i + 1

        i += 1

    # get last word if present
    if i - start > 1:
        words.append(string[start:i])

    words.reverse()  # reverse just the words

    reversed_order = list()
    word_index = 0
    delim_index = 0

    # merging the reversed words and the delimiters
    for i in range(len(words) + len(delims)):
        if delim_index < len(delim_positions) and delim_positions[delim_index] == i:
            # insert next delimiter if the position is saved for a delimiter
            reversed_order.append(delims[delim_index])
            delim_index += 1
        else:
            reversed_order.append(words[word_index])
            word_index += 1

    reversed_string = "".join(reversed_order)

    return reversed_string


assert reverse_words("hello/world:here/",
                     set([':', '/'])) == "here/world:hello/"
assert reverse_words(":hello//world:here/",
                     set([':', '/'])) == ":here//world:hello/"
assert reverse_words("hello//world:here",
                     set([':', '/'])) == "here//world:hello"
assert reverse_words("hello/world:here",
                     set([':', '/'])) == "here/world:hello"

class Node:
    def __init__(self, val):
        self.val = val
        self.left = None
        self.right = None

    def __repr__(self):
        return str(self.val)

    def is_exact_tree(self, other):
        if self.val != other.val:
            return False
        if bool(self.left) ^ bool(other.left):
            return False
        if bool(self.right) ^ bool(other.right):
            return False

        check = True
        if self.left:
            check = check and self.left.is_exact_tree(other.left)
        if self.right:
            check = check and self.right.is_exact_tree(other.right)

        return check

    def is_subtree(self, other):
        if self.is_exact_tree(other):
            return True

        if self.left and self.left.is_subtree(other):
            return True

        if self.right and self.right.is_subtree(other):
            return True

        return False


# Tests

s_0 = Node(0)
s_1 = Node(1)
s_2 = Node(2)
s_0.left = s_1
s_0.right = s_2
s_3 = Node(3)
s_4 = Node(4)
s_2.left = s_3
s_2.right = s_4

t_0 = Node(2)
t_1 = Node(3)
t_2 = Node(4)
t_0.left = t_1
t_0.right = t_2

r_0 = Node(2)
r_1 = Node(3)
r_2 = Node(5)
r_0.left = r_1
r_0.right = r_2

assert s_2.is_exact_tree(t_0)
assert s_0.is_subtree(t_0)
assert not s_0.is_subtree(r_0)

from random import random, randint


class Node:
    def __init__(self, val):
        self.val = val
        self._left = None
        self._right = None

    def __repr__(self):
        string = "{"
        string += "{}: ".format(self.val)
        string += "{"
        string += "l: {}, ".format(self._left if self._left else -1)
        string += "r: {}".format(self._right if self._right else -1)
        string += "}"
        string += "}"

        return string

    @staticmethod
    def generate():
        return Node(randint(1, 100000))

    @property
    def left(self):
        if not self._left:
            self._left = Node.generate()
        return self._left

    @property
    def right(self):
        if not self._right:
            self._right = Node.generate()
        return self._right


tree_size = 100

a = Node.generate()
ref = a
nodes = set()
i = 0
while i < tree_size:
    ref = ref.left if random() < 0.5 else ref.right
    nodes.add(ref)

    i += 1

assert len(nodes) == tree_size
print(a)

import sys


class Node:
    def __init__(self, val):
        self.val = val
        self.left = None
        self.right = None

    def __repr__(self):
        return "{}=(l={}, r={})".format(self.val, self.left, self.right)


def get_maxsum_level_helper(level, nodes, parent_sum):
    child_nodes = list()
    nodes_sum = 0
    for node in nodes:
        nodes_sum += node.val
        if node.left:
            child_nodes.append(node.left)
        if node.right:
            child_nodes.append(node.right)

    max_sum = max(nodes_sum, parent_sum)
    if child_nodes:
        max_sum = get_maxsum_level_helper(level + 1, child_nodes, max_sum)

    return max_sum


def get_maxsum_level(root):
    max_sum = get_maxsum_level_helper(0, [root], -sys.maxsize)
    return max_sum


a = Node(1)
b = Node(2)
c = Node(3)
a.left = b
a.right = c

d = Node(4)
e = Node(5)
b.left = d
b.right = e

f = Node(6)
g = Node(7)
c.left = f
c.right = g

h = Node(8)
d.right = h

assert get_maxsum_level(a) == 22
a.val = 100
assert get_maxsum_level(a) == 100
b.val = 150
assert get_maxsum_level(a) == 153
h.val = 200
assert get_maxsum_level(a) == 200

def merge_sorted_lists(arr1, arr2):
    i, k = 0, 0
    merged = list()
    while i < len(arr1) and k < len(arr2):
        if arr1[i] <= arr2[k]:
            merged.append(arr1[i])
            i += 1
        else:
            merged.append(arr2[k])
            k += 1

    merged += arr1[i:]
    merged += arr2[k:]

    return merged


def sort_squares(arr):
    first_pos_index = 0
    for num in arr:
        if num >= 0:
            break
        first_pos_index += 1

    neg_nums = [x ** 2 for x in reversed(arr[:first_pos_index])]
    pos_nums = [x ** 2 for x in arr[first_pos_index:]]

    return merge_sorted_lists(pos_nums, neg_nums)


assert sort_squares([]) == []
assert sort_squares([0]) == [0]
assert sort_squares([-1, 1]) == [1, 1]
assert sort_squares([0, 2, 3]) == [0, 4, 9]
assert sort_squares([-9, -2, 0]) == [0, 4, 81]
assert sort_squares([-9, -2, 0, 2, 3]) == [0, 4, 4, 9, 81]

import sys


class Interval:
    def __init__(self, start, end):
        self.start = start
        self.end = end

    def __hash__(self):
        return hash(str(self))

    def __repr__(self):
        return "[{}-{}]".format(self.start, self.end)


def get_smallest_stab_set_helper(remaining_intervals, used_points,
                                 remaining_points, num_to_intervals):

    if not remaining_intervals:
        return used_points

    min_len = sys.maxsize
    smallest_stab_set = None
    for current_point in remaining_points:
        if current_point not in num_to_intervals:
            continue

        current_point_intervals = num_to_intervals[current_point]
        new_rem_intervals = remaining_intervals - current_point_intervals

        new_used_points = used_points.copy()
        new_used_points.add(current_point)
        new_rem_points = remaining_points.copy()
        new_rem_points.remove(current_point)

        stab_set = get_smallest_stab_set_helper(
            new_rem_intervals, new_used_points, new_rem_points, num_to_intervals)
        if len(stab_set) < min_len:
            smallest_stab_set = stab_set
            min_len = len(stab_set)

    return smallest_stab_set


def get_smallest_stab_set(interval_tuples):
    intervals = set()
    num_to_intervals = dict()

    endpoints = set()
    for (start, end) in interval_tuples:
        endpoints.add(end)

        interval = Interval(start, end)
        intervals.add(interval)

        for num in range(start, end + 1):
            if num not in num_to_intervals:
                num_to_intervals[num] = set()
            num_to_intervals[num].add(interval)

    smallest_stab_set = get_smallest_stab_set_helper(
        intervals, set(), endpoints, num_to_intervals)

    return smallest_stab_set


assert get_smallest_stab_set([[0, 3]]) == {3}
assert get_smallest_stab_set([[0, 3], [2, 6]]) == {3}
assert get_smallest_stab_set([[0, 3], [2, 6], [3, 4]]) == {3}
assert get_smallest_stab_set([[0, 3], [2, 6], [3, 4], [6, 7]]) == {3, 6}
assert get_smallest_stab_set([[0, 3], [2, 6], [3, 4], [6, 9]]) == {3, 9}
assert get_smallest_stab_set([[0, 3], [2, 6], [3, 4], [6, 100]]) == {3, 100}

class SampleClass:
    instances = dict()
    even_instance = False

    def __init__(self, instance_num):
        self.instance_num = instance_num

    @staticmethod
    def initialize():
        SampleClass.instances[0] = SampleClass(0)
        SampleClass.instances[1] = SampleClass(1)

    @staticmethod
    def get_instance():
        if not SampleClass.instances:
            SampleClass.initialize()

        SampleClass.even_instance = not SampleClass.even_instance
        return SampleClass.instances[int(SampleClass.even_instance)]


# Tests


SampleClass.initialize()

i1 = SampleClass.get_instance()
assert i1.instance_num == 1
i2 = SampleClass.get_instance()
assert i2.instance_num == 0
i3 = SampleClass.get_instance()
assert i3.instance_num == 1
i4 = SampleClass.get_instance()
assert i4.instance_num == 0
i5 = SampleClass.get_instance()
assert i5.instance_num == 1

def is_palindrome(string):
    return bool(string) and string == string[::-1]


def make_palindrome(string, num_delete):
    if is_palindrome(string):
        return True
    if not num_delete:
        return False

    for i, _ in enumerate(string):
        new_string = string[:i] + string[i+1:]
        if make_palindrome(new_string, num_delete - 1):
            return True

    return False


# Tests
assert make_palindrome("a", 0)
assert make_palindrome("aaa", 2)
assert not make_palindrome("add", 0)
assert make_palindrome("waterrfetawx", 2)
assert not make_palindrome("waterrfetawx", 1)
assert make_palindrome("waterrfetawx", 3)
assert make_palindrome("malayalam", 0)
assert make_palindrome("malayalam", 1)
assert make_palindrome("asdf", 5)
assert not make_palindrome("asdf", 2)

0 3 1 1
2 0 0 4
1 5 3 1

def get_max_coins_helper(matrix, crow, ccol, rows, cols):
    cval = matrix[crow][ccol]

    if crow == rows - 1 and ccol == cols - 1:
        return cval

    down, right = cval, cval
    if crow < rows - 1:
        down += get_max_coins_helper(
            matrix, crow + 1, ccol, rows, cols)
    if ccol < cols - 1:
        right += get_max_coins_helper(
            matrix, crow, ccol + 1, rows, cols)

    return max(down, right)


def get_max_coins(matrix):
    if matrix:
        return get_max_coins_helper(
            matrix, 0, 0, len(matrix), len(matrix[0]))


coins = [[0, 3, 1, 1],
         [2, 0, 0, 4],
         [1, 5, 3, 1]]
assert get_max_coins(coins) == 12

coins = [[0, 3, 1, 1],
         [2, 8, 9, 4],
         [1, 5, 3, 1]]
assert get_max_coins(coins) == 25

def strip_neg(num):
    if num[0] != '-':
        return num
    elif len(num) > 1:
        return num[1:]


def is_valid_number_helper(string, dec):
    if not string:
        return True

    char = string[0]
    if (dec and char == '.') or (not char.isdigit() and char != '.'):
        return False
    elif char == '.':
        dec = True

    return is_valid_number_helper(string[1:], dec)


def is_valid_number(string):
    if not string:
        return False

    split_list = string.split('e')
    if len(split_list) > 2:
        return False

    if len(split_list) == 2:
        string_1 = strip_neg(split_list[0])
        string_2 = strip_neg(split_list[1])
        return string_1 and string_2 and \
            is_valid_number_helper(string_1, False) and \
            is_valid_number_helper(string_2, False)
    else:
        string = strip_neg(split_list[0])
        return string and is_valid_number_helper(string, False)


# Tests
assert is_valid_number("10")
assert is_valid_number("-10")
assert is_valid_number("10.1")
assert is_valid_number("-10.1")
assert is_valid_number("1e5")
assert is_valid_number("-5")
assert is_valid_number("1e-5")
assert is_valid_number("1e-5.2")
assert not is_valid_number("a")
assert not is_valid_number("x 1")
assert not is_valid_number("a -2")
assert not is_valid_number("-")

from math import log, ceil


def get_num_expected(coin_tosses):
    return ceil(log(coin_tosses, 2))


assert get_num_expected(1) == 0
assert get_num_expected(2) == 1
assert get_num_expected(100) == 7
assert get_num_expected(200) == 8

    10
   /   \
 5      15
       /  \
     11    15

class Node:
    def __init__(self, val):
        self.val = val
        self.left = None
        self.right = None

    def __repr__(self):
        return str(self.val)


def get_array(root):
    arr = [root]

    if not root.left and not root.right:
        return arr

    if root.left:
        arr = get_array(root.left) + arr
    if root.right:
        arr = arr + get_array(root.right)

    return arr


def search_pair(root, val):
    arr = get_array(root)
    i, k = 0, len(arr) - 1
    while i < k:
        summed = arr[i].val + arr[k].val
        if summed == val:
            return (arr[i], arr[k])
        elif summed < val:
            i += 1
        else:
            k -= 1


# Tests
a = Node(10)
b = Node(5)
c = Node(15)
d = Node(11)
e = Node(15)
a.left = b
a.right = c
c.left = d
c.right = e

assert search_pair(a, 15) == (b, a)
assert search_pair(a, 20) == (b, e)
assert search_pair(a, 30) == (c, e)
assert search_pair(a, 26) == (d, e)

# Solution 1
def rotate_list_once(arr):
    first = arr[0]
    for i in range(len(arr) - 1):
        arr[i] = arr[i + 1]
    arr[-1] = first
    return arr


def rotate_list(arr, k):
    for _ in range(k):
        arr = rotate_list_once(arr)

    return arr


# Solution 2
def rotate_list_alt(arr, k):
    return arr[k:] + arr[:k]


# Tests
assert rotate_list([1, 2, 3, 4, 5, 6], 0) == [1, 2, 3, 4, 5, 6]
assert rotate_list_alt([1, 2, 3, 4, 5, 6], 0) == [1, 2, 3, 4, 5, 6]

assert rotate_list([1, 2, 3, 4, 5, 6], 2) == [3, 4, 5, 6, 1, 2]
assert rotate_list_alt([1, 2, 3, 4, 5, 6], 2) == [3, 4, 5, 6, 1, 2]

assert rotate_list([1, 2, 3, 4, 5, 6], 4) == [5, 6, 1, 2, 3, 4]
assert rotate_list_alt([1, 2, 3, 4, 5, 6], 4) == [5, 6, 1, 2, 3, 4]

FACTOR = 10


class Node:
    def __init__(self, val):
        self.val = val
        self.next = None

    def __repr__(self):
        return "{} -> {}".format(self.val, self.next)

    @staticmethod
    def convert_num_to_list(num):
        numstr = str(num)
        dummy_head = Node(0)
        prev = dummy_head
        for num in numstr[::-1]:
            curr = Node(int(num))
            prev.next = curr
            prev = curr

        return dummy_head.next

    @staticmethod
    def convert_list_to_num(head):
        curr = head
        num = 0
        factor = 1
        while curr:
            num += factor * curr.val
            curr = curr.next
            factor *= FACTOR

        return num

    @staticmethod
    def add_nums(list_a, list_b):
        new_dummy_head = Node(0)
        prev_res = new_dummy_head

        curr_a, curr_b = list_a, list_b
        carry = 0

        while carry or curr_a or curr_b:
            res_digit = 0
            if carry:
                res_digit += carry
            if curr_a:
                res_digit += curr_a.val
                curr_a = curr_a.next
            if curr_b:
                res_digit += curr_b.val
                curr_b = curr_b.next

            carry = res_digit // FACTOR
            curr_res = Node(res_digit % FACTOR)

            prev_res.next = curr_res
            prev_res = curr_res

        return new_dummy_head.next


assert Node.convert_list_to_num(
    Node.add_nums(Node.convert_num_to_list(0),
                  Node.convert_num_to_list(1))) == 1
assert Node.convert_list_to_num(
    Node.add_nums(Node.convert_num_to_list(1000),
                  Node.convert_num_to_list(1))) == 1001
assert Node.convert_list_to_num(
    Node.add_nums(Node.convert_num_to_list(99),
                  Node.convert_num_to_list(25))) == 124

def toh_helper(disks, source, inter, target):
    if disks == 1:
        target.append(source.pop())
    else:
        toh_helper(disks - 1, source, target, inter)
        print(source, inter, target)
        target.append(source.pop())
        print(source, inter, target)
        toh_helper(disks - 1, inter, source, target)

    print(source, inter, target)


def towers_of_hanoi(n):
    if not n:
        return

    print("{} Towers of Hanoi".format(n))
    stack_1, stack_2, stack_3 = \
        list(range(1, n + 1))[::-1], list(), list()
    toh_helper(n, stack_1, stack_2, stack_3)


towers_of_hanoi(3)
towers_of_hanoi(4)
towers_of_hanoi(5)
towers_of_hanoi(6)

TOLERANCE = 10 ** -6


def almost_equal(first, second):
    # check equality with some acceptable error tolerance
    return \
        second > first - TOLERANCE and \
        second < first + TOLERANCE


def get_sqrt_helper(n, start, end):
    mid = start + ((end - start) / 2)

    if almost_equal(mid * mid, n):
        return mid
    elif mid * mid > n:
        return get_sqrt_helper(n, start, mid)
    else:
        return get_sqrt_helper(n, mid, end)


def get_sqrt(n):
    return get_sqrt_helper(n, 0, n)


assert almost_equal(get_sqrt(9), 3)
assert almost_equal(get_sqrt(2), 1.41421356237)
assert almost_equal(get_sqrt(10000), 100)

def profit_helper(prices, curr_index, curr_profit, buys_left, sells_left):

    if curr_index == len(prices) or not sells_left:
        # reached end of chronology or exhausted trades
        return curr_profit

    if buys_left == sells_left:
        # buy or wait
        return max(
            # buy
            profit_helper(prices, curr_index + 1, curr_profit - prices[curr_index],
                          buys_left - 1, sells_left),
            # wait
            profit_helper(prices, curr_index + 1, curr_profit,
                          buys_left, sells_left)
        )
    else:
        # sell or hold
        return max(
            # sell
            profit_helper(prices, curr_index + 1, curr_profit + prices[curr_index],
                          buys_left, sells_left - 1),
            # hold
            profit_helper(prices, curr_index + 1, curr_profit,
                          buys_left, sells_left)
        )


def get_max_profit(prices, k):
    return profit_helper(prices, 0, 0, k, k)


assert get_max_profit([5, 2, 4, 0, 1], 2) == 3
assert get_max_profit([5, 2, 4], 2) == 2
assert get_max_profit([5, 2, 4], 1) == 2

class Node:
    def __init__(self, val):
        self.val = val
        self.next = None
        self.rand = None

    def __repr__(self):
        return self.val


def deep_clone(source):
    node_to_index = dict()
    node_index_to_rand_index = dict()

    curr = source
    i = 0
    while curr:
        node_to_index[curr] = i
        curr = curr.next
        i += 1

    curr = source
    i = 0
    while curr:
        rand_index = node_to_index[curr.rand]
        node_index_to_rand_index[i] = rand_index
        curr = curr.next
        i += 1

    dummy_head = Node('0')
    tail = dummy_head
    curr = source
    index_to_node = dict()
    i = 0
    while curr:
        new_node = Node(curr.val)
        index_to_node[i] = new_node
        curr = curr.next
        i += 1
        tail.next = new_node
        tail = new_node

    curr = dummy_head.next
    i = 0
    while curr:
        rand_index = node_index_to_rand_index[i]
        curr.rand = index_to_node[rand_index]
        curr = curr.next
        i += 1

    return dummy_head.next


# Tests

a = Node('a')
b = Node('b')
a.next = b
c = Node('c')
b.next = c
d = Node('d')
c.next = d
e = Node('e')
d.next = e

a.rand = a
b.rand = a
c.rand = e
d.rand = c
e.rand = c

cloned = deep_clone(a)
assert cloned.val == 'a'
assert cloned.rand.val == 'a'
assert cloned.next.val == 'b'
assert cloned.next.rand.val == 'a'

from time import time
from random import random, randrange
import bisect

REQUESTS_PER_FILE = 100


class PersistedFile:
    # in a memory efficient implementation, this would be persisted to disk
    # once full and only the path and metadata would remain in memory
    def __init__(self):
        self.start_timestamp = None
        self.end_timestamp = None
        self.request_timestamps = list()

    def __repr__(self):
        return "start={}, end={}, size={}".format(
            self.start_timestamp, self.end_timestamp, len(self.request_timestamps))


class RequestQuery:
    def __init__(self):
        self.current_file = PersistedFile()
        self.prev_files = list()

    def record(self, timestamp):
        if not self.current_file.start_timestamp:
            self.current_file.start_timestamp = timestamp
        self.current_file.request_timestamps.append(timestamp)
        self.current_file.end_timestamp = timestamp

        if len(self.current_file.request_timestamps) == REQUESTS_PER_FILE:
            self.prev_files.append(self.current_file)
            self.current_file = PersistedFile()

    def total(self):
        return (len(self.prev_files) * REQUESTS_PER_FILE) + \
            len(self.current_file.request_timestamps)

    def range(self, lower, upper):
        all_files = self.prev_files + [self.current_file]
        start_times = [x.start_timestamp for x in all_files]
        end_times = [x.end_timestamp for x in all_files]

        start_file_index = bisect.bisect_left(start_times, lower) - 1
        end_file_index = bisect.bisect_left(end_times, upper)
        start_file = all_files[start_file_index]
        end_file = all_files[end_file_index]

        start_file_pos = bisect.bisect(start_file.request_timestamps, lower)
        end_file_pos = bisect.bisect(end_file.request_timestamps, upper)

        num_req = 0
        num_req += len(start_file.request_timestamps[start_file_pos:])
        num_req += len(end_file.request_timestamps[:end_file_pos])
        num_req += (end_file_index - start_file_index) * REQUESTS_PER_FILE

        return num_req


def run_experiments(requests):
    rq = RequestQuery()
    lower, upper = None, None

    for i in range(requests):
        rq.record(i)

        if random() < 0.001:
            if not lower:
                lower = i
            else:
                upper = randrange(lower, i)

            if lower and upper:
                num_req = rq.range(lower, upper)
                print("{} requests made between {} and {}".format(
                    num_req, lower, upper))
                print("Total: {}".format(rq.total()))
                lower, upper = None, None


run_experiments(112367)

   10
  /  \
 5    30
     /  \
   22    35

class Node:
    def __init__(self, val):
        self.val = val
        self.left = None
        self.right = None
        self.parent = None

    def __repr__(self):
        return str(self.val)


def inorder_helper(root):
    list_rep = [root]
    if root.left:
        list_rep = inorder_helper(root.left) + list_rep
    if root.right:
        list_rep = list_rep + inorder_helper(root.right)

    return list_rep


def find_next_inorder(target_node):
    root = target_node
    while root.parent:
        root = root.parent
    all_nodes = inorder_helper(root)
    for i, node in enumerate(all_nodes):
        if node == target_node:
            if i == len(all_nodes) - 1:
                return None
            return all_nodes[i + 1]


# Tests

root = Node(10)
root.left = Node(5)
root.right = Node(30)
root.left.parent = root
root.right.parent = root
root.right.left = Node(22)
root.right.right = Node(35)
root.right.left.parent = root.right
root.right.right.parent = root.right

assert not find_next_inorder(root.right.right)
assert find_next_inorder(root.right.left) == root.right
assert find_next_inorder(root) == root.right.left
assert find_next_inorder(root.left) == root

class SparseArray:

    def __init__(self):
        self.storage = dict()

    def __repr__(self):
        return str(self.storage)

    def init(self, arr, size):
        for i, num in enumerate(arr):
            if num:
                self.storage[i] = num

    def set_val(self, i, val):
        if not val:
            del self.storage[i]
        else:
            self.storage[i] = val

    def get_val(self, i):
        if i not in self.storage:
            return None

        return self.storage[i]


# Tests

arr = [1, 0, 0, 0, 3, 0, 2]

sa = SparseArray()
sa.init(arr, len(arr))
assert sa.storage == {0: 1, 4: 3, 6: 2}

sa.set_val(2, 4)
assert sa.get_val(2) == 4
sa.set_val(4, 1)
assert sa.get_val(4) == 1
sa.set_val(0, 0)
assert not sa.get_val(0)

  10
 /  \
5    5
 \     \
   2    1
       /
     -1

import sys


class Node:
    def __init__(self, val):
        self.val = val
        self.left = None
        self.right = None

    def __repr__(self):
        return str(self.val)


def min_path_helper(root, path, path_sum):

    candidate_sum = path_sum + root.val
    candidate_path = path + [root.val]

    if not root.left and not root.right:
        return (candidate_sum, candidate_path)

    left_min_val, right_min_val = sys.maxsize, sys.maxsize
    if root.left:
        left_min_val, left_path = min_path_helper(
            root.left, candidate_path, candidate_sum)
    if root.right:
        right_min_val, right_path = min_path_helper(
            root.right, candidate_path, candidate_sum)

    return (left_min_val, left_path) if left_min_val < right_min_val \
        else (right_min_val, right_path)


def find_min_path(root):
    _, min_path = min_path_helper(root, list(), 0)
    return min_path


# Tests

a = Node(10)
b = Node(5)
c = Node(5)
a.left = b
a.right = c
d = Node(2)
b.right = d
e = Node(1)
c.right = e
f = Node(-1)
e.left = f
assert find_min_path(a) == [10, 5, 1, -1]

f.val = 5
assert find_min_path(a) == [10, 5, 2]

[[1, 0, 0, 0],
 [1, 0, 1, 1],
 [1, 0, 1, 1],
 [0, 1, 0, 0]]

def extendable_row(matrix, erow, scol, ecol):
    return all(matrix[erow][scol:ecol])


def extendable_col(matrix, ecol, srow, erow):
    for row in range(srow, erow):
        if not matrix[row][ecol]:
            return False

    return True


def area_helper(matrix, num_rows, num_cols, srow, erow, scol, ecol):
    current_area = (erow - srow) * (ecol - scol)
    row_ex_area, col_ex_area = 0, 0

    ex_row = erow < num_rows and extendable_row(matrix, erow, scol, ecol)
    if ex_row:
        row_ex_area = area_helper(matrix, num_rows, num_cols,
                                  srow, erow + 1, scol, ecol)

    ex_col = ecol < num_cols and extendable_col(matrix, ecol, srow, erow)
    if ex_col:
        col_ex_area = area_helper(matrix, num_rows, num_cols,
                                  srow, erow, scol, ecol + 1)

    return max(current_area, row_ex_area, col_ex_area)


def get_largest_area(matrix):
    max_area = 0
    if not matrix:
        return max_area

    num_rows, num_cols = len(matrix), len(matrix[0])

    for i in range(num_rows):
        for j in range(num_cols):
            upper_bound_area = (num_rows - i) * (num_cols - j)
            if matrix[i][j] and upper_bound_area > max_area:
                area = area_helper(
                    matrix, num_rows, num_cols, i, i + 1, j, j + 1)
                max_area = area if area > max_area else max_area

    return max_area


# Tests

matrix = [[1, 0, 0, 0],
          [1, 0, 1, 1],
          [1, 0, 1, 1],
          [0, 1, 0, 0]]
assert get_largest_area(matrix) == 4


matrix = [[1, 0, 0, 0],
          [1, 0, 1, 1],
          [1, 0, 1, 1],
          [0, 1, 1, 1]]
assert get_largest_area(matrix) == 6

matrix = [[1, 1, 1, 1],
          [1, 1, 1, 1],
          [1, 1, 1, 1],
          [1, 1, 1, 1]]
assert get_largest_area(matrix) == 16

matrix = [[0, 0, 0, 0],
          [0, 0, 0, 0],
          [0, 0, 0, 0],
          [0, 0, 0, 0]]
assert get_largest_area(matrix) == 0

matrix = [[1, 1, 1, 1],
          [1, 1, 1, 1],
          [1, 1, 0, 0],
          [0, 0, 0, 0]]
assert get_largest_area(matrix) == 8

matrix = [[1, 1, 0, 0],
          [1, 0, 0, 0],
          [1, 0, 0, 0],
          [1, 0, 0, 0]]
assert get_largest_area(matrix) == 4

class BitArray:
    def __init__(self, size):
        self.set_indices = set()
        self.size = size

    def get_list_rep(self):
        arr = list()
        for i in range(self.size):
            if i in self.set_indices:
                arr.append(1)
            else:
                arr.append(0)
        return arr

    def set_val(self, i, val):
        if i >= self.size:
            raise LookupError("Invalid Index")

        if val and i not in self.set_indices:
            self.set_indices.add(i)
        elif not val and i in self.set_indices:
            self.set_indices.remove(i)

    def get_val(self, i):
        if i >= self.size:
            raise LookupError("Invalid Index")
        return int(i in self.set_indices)


# Tests
ba = BitArray(10)
assert ba.get_list_rep() == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
ba.set_val(3, 1)
assert ba.get_list_rep() == [0, 0, 0, 1, 0, 0, 0, 0, 0, 0]
ba.set_val(6, 1)
ba.set_val(8, 1)
ba.set_val(3, 0)
assert ba.get_list_rep() == [0, 0, 0, 0, 0, 0, 1, 0, 1, 0]


# Exceptions
try:
    ba.set_val(10, 1)
except LookupError as le:
    print(le)
try:
    ba.get_val(10)
except LookupError as le:
    print(le)

def get_min_coins(amount, denoms):
    if amount == 0:
        return 0

    denom_to_use, index_cutoff = None, None
    for i, denom in enumerate(denoms):
        if amount >= denom:
            denom_to_use = denom
            index_cutoff = i
            break

    coins_used = amount // denom_to_use

    return coins_used + get_min_coins(amount - (denom_to_use * coins_used),
                                      denoms[index_cutoff + 1:])


# Tests
denoms = [25, 10, 5, 1]
assert get_min_coins(16, denoms) == 3
assert get_min_coins(90, denoms) == 5
assert get_min_coins(100, denoms) == 4

class PeekableInterface(object):
    def __init__(self, iterator):
        pass

    def peek(self):
        pass

    def next(self):
        pass

    def hasNext(self):
        pass

class PeekableInterface(object):
    def __init__(self, iterator):
        self.iterator = iterator
        self.next_val = next(iterator)
        self.has_next_val = True

    def peek(self):
        return self.next_val

    def next(self):
        next_val = self.next_val
        try:
            self.next_val = next(iterator)
        except StopIteration:
            self.has_next_val = False
            self.next_val = None
        return next_val

    def has_next(self):
        return self.has_next_val


# Tests

sample_list = [1, 2, 3, 4, 5]
iterator = iter(sample_list)
peekable = PeekableInterface(iterator)

assert peekable.peek() == 1
assert peekable.has_next()

assert peekable.next() == 1
assert peekable.next() == 2
assert peekable.next() == 3

assert peekable.peek() == 4
assert peekable.has_next()

assert peekable.next() == 4
assert peekable.has_next()
assert peekable.peek() == 5
assert peekable.next() == 5

assert not peekable.has_next()
assert not peekable.peek()

def get_singles(arr):
    xored = arr[0]
    for num in arr[1:]:
        xored ^= num
    x, y = 0, 0

    rightmost_set_bit = (xored & ~(xored - 1))
    for num in arr:
        if num & rightmost_set_bit:
            x ^= num
        else:
            y ^= num

    return (x, y)


# Tests

get_singles([2, 4, 6, 8, 10, 2, 6, 10]) == (4, 8)
get_singles([2, 4, 8, 8, 10, 2, 6, 10]) == (4, 6)

class Stack:
    def __init__(self):
        self.list = []

    def pop(self, stack_number):
        pass

    def push(self, item, stack_number):
        pass

class Stack:
    def __init__(self):
        self.list = []

    def __repr__(self):
        return str(self.list)

    def pop(self, stack_number):
        if not stack_number < len(self.list):
            return

        stack = self.list[stack_number]
        if not stack:
            return

        val = stack.pop()
        return val

    def push(self, item, stack_number):
        if stack_number < len(self.list):
            stack = self.list[stack_number]
            stack.append(item)
        elif stack_number == len(self.list):
            new_stack = list()
            new_stack.append(item)
            self.list.append(new_stack)


# Tests
st = Stack()

st.push(1, 0)
assert st.list == [[1]]
st.push(2, 1)
st.push(3, 2)
assert st.list == [[1], [2], [3]]
val = st.pop(3)
assert not val
val = st.pop(2)
assert val == 3
assert st.list == [[1], [2], []]
st.push(6, 0)
st.push(7, 0)
assert st.list == [[1, 6, 7], [2], []]
val = st.pop(0)
assert st.list == [[1, 6], [2], []]

def valid_paren(string, stack=list()):

    if not string and not stack:
        return True
    elif not string:
        return False

    cchar = string[0]
    remaining = string[1:]
    if cchar == '*':
        return \
            valid_paren('(' + remaining, stack) or \
            valid_paren(')' + remaining, stack) or \
            valid_paren(remaining, stack)

    cstack = stack.copy()
    if cchar == ')' and not stack:
        return False
    elif cchar == ')':
        cstack.pop()
    else:
        cstack.append(cchar)

    return valid_paren(remaining, cstack)


# Tests
assert valid_paren("(()*")
assert valid_paren("(*)")
assert not valid_paren(")*(")

def swap_indices(arr, i, k):
    tmp = arr[i]
    arr[i] = arr[k]
    arr[k] = tmp


def separate_with_pivot(arr, i, k, x):
    if not arr:
        return

    while i < k:
        if arr[i] >= x and arr[k] < x:
            swap_indices(arr, i, k)
        else:
            if arr[i] < x:
                i += 1
            if arr[k] >= x:
                k -= 1

    return i + 1 if (arr[i] < x and i + 1 < len(arr)) else i


def pivot_list(arr, x):
    mid = separate_with_pivot(arr, 0, len(arr) - 1, x)
    separate_with_pivot(arr, mid, len(arr) - 1, x + 1)

    return arr



# Tests
assert pivot_list([9, 12, 3, 5, 14, 10, 10], 10) == [9, 5, 3, 10, 10, 14, 12]
assert pivot_list([9, 12, 3, 5, 14, 10, 10], 8) == [5, 3, 12, 9, 14, 10, 10]
assert pivot_list([9, 12, 14, 10, 10], 8) == [9, 12, 14, 10, 10]
assert pivot_list([3, 5], 8) == [3, 5]
assert pivot_list([8, 8, 8], 8) == [8, 8, 8]
assert pivot_list([], 8) == []

def get_mapping_indices(arr):
    nl_indices = dict()
    sorted_tuples = [(x, i) for i, x in enumerate(arr)]
    sorted_tuples.sort(key=lambda x: x[0])

    for k, (_, i) in enumerate(sorted_tuples[:-1]):
        min_dist = len(arr)
        for m in range(k + 1, len(sorted_tuples)):
            dist = abs(i - sorted_tuples[m][1])
            if dist < min_dist:
                min_dist = dist
                nl_indices[i] = sorted_tuples[m][1]

    return nl_indices


def nearest_larger(arr, index):
    nl_indices = get_mapping_indices(arr)

    if index not in nl_indices:
        return None

    return nl_indices[index]


# Tests
assert nearest_larger([4, 1, 3, 5, 6], 0) == 3
assert nearest_larger([4, 1, 3, 5, 6], 1) == 0 or \
    nearest_larger([4, 1, 3, 5, 6], 1) == 2
assert not nearest_larger([4, 1, 3, 5, 6], 4)
assert nearest_larger([4, 1, 3, 5, 6], 3) == 4

class Node:
    def __init__(self, x):
        self.val = x
        self.next = None

    def __str__(self):
        string = "["
        node = self
        while node:
            string += "{} ->".format(node.val)
            node = node.next
        string += "None]"
        return string


def get_nodes(values):
    next_node = None
    for value in values[::-1]:
        node = Node(value)
        node.next = next_node
        next_node = node

    return next_node


def get_list(head):
    node = head
    nodes = list()
    while node:
        nodes.append(node.val)
        node = node.next
    return nodes


def swap_two_helper(node):
    if not node or not node.next:
        return node

    first = node
    second = node.next
    tail = swap_two_helper(second.next)

    second.next = first
    first.next = tail

    return second


def swap_two(head):
    dummy_head = Node(0)
    dummy_head.next = head

    return swap_two_helper(head)



# Tests
assert get_list(swap_two(get_nodes([1]))) == [1]
assert get_list(swap_two(get_nodes([1, 2]))) == [2, 1]
assert get_list(swap_two(get_nodes([1, 2, 3, 4]))) == [2, 1, 4, 3]
assert get_list(swap_two(get_nodes([1, 2, 3, 4, 5]))) == [2, 1, 4, 3, 5]
assert get_list(swap_two(get_nodes([1, 2, 3, 4, 5, 6]))) == [2, 1, 4, 3, 6, 5]

   0
  / \
 1   0
    / \
   1   0
  / \
 0   0

   0
  / \
 1   0
    /
   1

class Node:
    def __init__(self, val):
        self.val = val
        self.left = None
        self.right = None

    def __repr__(self):
        string = "{}=[l={}, r={}]".format(self.val, self.left, self.right)
        return string

    def prune(self):
        if not self.left and not self.right and not self.val:
            return None

        if self.left:
            self.left = self.left.prune()
        if self.right:
            self.right = self.right.prune()

        return self


# Tests
root = Node(0)
root.left = Node(1)
root.right = Node(0)
root.right.left = Node(1)
root.right.right = Node(0)
root.right.left.left = Node(0)
root.right.left.right = Node(0)

assert root.right.right
assert root.right.left.left
assert root.right.left.right
root.prune()

assert not root.right.right
assert not root.right.left.left
assert not root.right.left.right

assert root.left
assert root.right

def merge_sorted(arr_1, arr_2):
    merged_array = list()
    ind_1, ind_2 = 0, 0
    while ind_1 < len(arr_1) and ind_2 < len(arr_2):
        if arr_1[ind_1] <= arr_2[ind_2]:
            merged_array.append(arr_1[ind_1])
            ind_1 += 1
        else:
            merged_array.append(arr_2[ind_2])
            ind_2 += 1

    while ind_1 < len(arr_1):
        merged_array.append(arr_1[ind_1])
        ind_1 += 1
    while ind_2 < len(arr_2):
        merged_array.append(arr_2[ind_2])
        ind_2 += 1

    return merged_array


def reverse(lst, i, j):
    return list(reversed(lst[i:j+1]))


def custom_sort(lst):
    # create segments of sorted sub-arrays
    start, end = None, None
    last_end = -1
    sorted_segments = list()
    for i in range(1, len(lst)):
        if lst[i] < lst[i-1]:
            if not start:
                segment = lst[last_end+1: i-1]
                if segment:
                    sorted_segments.append(segment)
                start = i - 1
        elif start:
            end = i - 1
            if end > start:
                sorted_segments.append(reverse(lst, start, end))
                last_end = end
                start, end = None, None
    if start:
        end = len(lst) - 1
        if end > start:
            sorted_segments.append(reverse(lst, start, end))
    else:
        segment = lst[last_end+1:]
        if segment:
            sorted_segments.append(segment)

    # merge the sorted sub-arrays
    final_sorted = list()
    for segment in sorted_segments:
        final_sorted = merge_sorted(final_sorted, segment)

    return final_sorted


# Tests
assert custom_sort([0, 6, 4, 2, 5, 3, 1]) == [
    0, 1, 2, 3, 4, 5, 6]
assert custom_sort([0, 6, 4, 2, 5, 3, 1, 10, 9]) == [
    0, 1, 2, 3, 4, 5, 6, 9, 10]
assert custom_sort([0, 6, 4, 2, 5, 3, 1, 2, 3]) == [
    0, 1, 2, 2, 3, 3, 4, 5, 6]
assert custom_sort([0, 6, 4, 2, 5, 3, 1, 11]) == [
    0, 1, 2, 3, 4, 5, 6, 11]

def get_gray_code(n):
    """
    n: bits 
    """
    if n == 0:
        return ['']

    lower_grey_codes = get_gray_code(n - 1)
    l0 = ['0' + x for x in lower_grey_codes]
    l1 = ['1' + x for x in reversed(lower_grey_codes)]

    return l0 + l1


# Tests
assert get_gray_code(1) == ['0', '1']
assert get_gray_code(2) == ['00', '01', '11', '10']
assert get_gray_code(3) == ['000', '001', '011',
                            '010', '110', '111', '101', '100']
assert get_gray_code(4) == ['0000', '0001', '0011', '0010', '0110', '0111',
                            '0101', '0100', '1100', '1101', '1111', '1110', '1010', '1011', '1001', '1000']

class SubarraySumOptimizer:
    def __init__(self, arr):
        self.arr = arr
        total = 0
        self.larr = [total]
        for num in self.arr:
            total += num
            self.larr.append(total)

    def sum(self, start, end):
        if start < 0 or end > len(self.arr) or start > end:
            return 0
        return self.larr[end] - self.larr[start]


# Tests
sso = SubarraySumOptimizer([1, 2, 3, 4, 5])
assert sso.sum(1, 3) == 5
assert sso.sum(0, 5) == 15
assert sso.sum(0, 4) == 10
assert sso.sum(3, 4) == 4
assert sso.sum(3, 3) == 0

import math


def calculate_distance(source, target):
    return math.sqrt(
        (source[0] - target[0]) ** 2 +
        (source[1] - target[1]) ** 2
    )


def get_closest_points(source, targets, k):
    if k >= len(targets):
        return targets

    closest_points = \
        sorted(targets, key=lambda x: calculate_distance(source, x))[:k]

    return closest_points



# Tests
assert calculate_distance((0, 0), (3, 4)) == 5
assert get_closest_points(
    (1, 2), [(0, 0), (5, 4), (3, 1)], 2) == [(0, 0), (3, 1)]

B B W
W W W
W W W
B B B

B B G
G G G
G G G
B B B

# pixel is a tuple of (x, y) co-ordinates in the matrix


def get_adj_pixels(pixel, matrix, rows, cols):
    adj_pixels = list()

    # add row above if it exists
    if pixel[0] > 0:
        adj_pixels.append((pixel[0]-1, pixel[1]))
        if pixel[1] > 0:
            adj_pixels.append((pixel[0]-1, pixel[1]-1))
        if pixel[1] < cols - 1:
            adj_pixels.append((pixel[0]-1, pixel[1]+1))

    # add row below if it exists
    if pixel[0] < rows - 1:
        adj_pixels.append((pixel[0]+1, pixel[1]))
        if pixel[1] > 0:
            adj_pixels.append((pixel[0]+1, pixel[1]-1))
        if pixel[1] < cols - 1:
            adj_pixels.append((pixel[0]+1, pixel[1]+1))

    # add left cell if it exists
    if pixel[1] > 0:
        adj_pixels.append((pixel[0], pixel[1]-1))

    # add right cell if it exists
    if pixel[1] < cols - 1:
        adj_pixels.append((pixel[0], pixel[1]+1))

    return adj_pixels


def change_color(pixel, matrix, new_color):
    if not matrix:
        return matrix

    # switch to 0-indexed co-ordinates
    x, y = pixel[0] - 1, pixel[1] - 1

    rows = len(matrix)
    cols = len(matrix[0])
    if x < 0 or y < 0 or x >= rows or y >= cols:
        return matrix

    c = matrix[x][y]
    adj_pixels = get_adj_pixels((x, y), matrix, rows, cols)

    for ap in adj_pixels:
        if matrix[ap[0]][ap[1]] == c:
            matrix[ap[0]][ap[1]] = new_color
    matrix[x][y] = new_color

    return matrix


# Tests
matrix = [['B', 'B', 'W'],
          ['W', 'W', 'W'],
          ['W', 'W', 'W'],
          ['B', 'B', 'B']]
assert change_color((2, 2), matrix, 'G') == \
    [['B', 'B', 'G'],
     ['G', 'G', 'G'],
     ['G', 'G', 'G'],
     ['B', 'B', 'B']]

from random import random
import bisect


class ProbablisticGenerator:

    def __init__(self, numbers, probabilities):
        assert sum(probabilities) == 1

        self.numbers = numbers
        self.cum_probs = list()
        current_cum_prob = 0
        for prob in probabilities:
            current_cum_prob += prob
            self.cum_probs.append(current_cum_prob)

    def generate_number(self):
        rand = random()
        index = bisect.bisect_left(self.cum_probs, rand)

        return self.numbers[index]


# Tests
numbers = [1, 2, 3, 4]
probs = [0.1, 0.5, 0.2, 0.2]
pg = ProbablisticGenerator(numbers, probs)

num_exp = 10000
outcomes = dict()
for num in numbers:
    outcomes[num] = 0

for _ in range(num_exp):
    gen_num = pg.generate_number()
    outcomes[gen_num] += 1

for num, prob in zip(numbers, probs):
    outcomes[num] = round(outcomes[num] / num_exp, 1)
    assert outcomes[num] == prob

def get_smallest_dist(text, w1, w2):
    dist = None
    ls_word, ls_index = None, None
    for index, word in enumerate(text.split()):
        if word == w1 or word == w2:
            if (word == w1 and ls_word == w2) or \
                    (word == w2 and ls_word == w1):
                dist = index - ls_index - 1
            ls_word = word
            ls_index = index

    return dist


# Tests
assert not get_smallest_dist(
    "hello", "hello", "world")
assert get_smallest_dist(
    "hello world", "hello", "world") == 0
assert get_smallest_dist(
    "dog cat hello cat dog dog hello cat world", "hello", "world") == 1
assert get_smallest_dist(
    "dog cat hello cat dog dog hello cat world", "dog", "world") == 2

import sys
from heapq import heappush, heappop


class Stack:

    def __init__(self):
        self.counter = sys.maxsize
        self.stack = list()

    def push(self, item):
        heappush(self.stack, (self.counter, item))
        self.counter -= 1

    def pop(self):
        if not self.stack:
            return None

        _, item = heappop(self.stack)
        return item


# Tests
stk = Stack()
stk.push(1)
stk.push(7)
stk.push(4)
assert stk.pop() == 4
stk.push(2)
assert stk.pop() == 2
assert stk.pop() == 7
assert stk.pop() == 1
assert not stk.pop()

import math


def get_majority_element(arr):
    threshold = math.floor(len(arr) / 2)
    occurrences = dict()
    for num in arr:
        if num not in occurrences:
            occurrences[num] = 0
        occurrences[num] += 1
    for num in occurrences:
        if occurrences[num] > threshold:
            return num



# Tests
assert get_majority_element([]) == None
assert get_majority_element([0]) == 0
assert get_majority_element([0, 2, 2]) == 2
assert get_majority_element([1, 2, 1, 1, 3, 4, 1]) == 1

import math


def get_candidate_squares(num):
    candidates = list()
    for candidate_root in range(1, int(num/2)):
        candidate = candidate_root * candidate_root
        if candidate > num:
            break
        candidates.append(candidate)
    candidates.reverse()
    return candidates


def get_min_squares_helper(num, candidates):
    candidate_square = candidates[0]
    max_used = int(num / candidate_square)
    remaining = num % candidate_square

    if remaining == 0:
        return max_used

    return max_used + get_min_squares_helper(remaining, candidates[1:])


def get_min_squares(num):
    candidates = get_candidate_squares(num)
    return get_min_squares_helper(num, candidates)


# Tests
assert get_min_squares(13) == 2
assert get_min_squares(25) == 1
assert get_min_squares(27) == 3

def check_palindrome_rearrangement(string):
    chars = set()
    for char in string:
        if char not in chars:
            chars.add(char)
        else:
            chars.remove(char)

    return len(chars) < 2


# Tests
assert check_palindrome_rearrangement("carrace")
assert not check_palindrome_rearrangement("daily")
assert not check_palindrome_rearrangement("abac")
assert check_palindrome_rearrangement("abacc")
assert check_palindrome_rearrangement("aabb")
assert not check_palindrome_rearrangement("aabbcccd")

[[0, 0, 1],
 [0, 0, 1],
 [1, 0, 0]]

class Coord:
    def __init__(self, x, y):
        self.x = x
        self.y = y

    def __repr__(self):
        return "Coord=(x={}, y={})".format(self.x, self.y)

    def __eq__(self, other):
        return self.x == other.x and self.y == other.y

    def __hash__(self):
        return hash((self.x, self.y))


def get_adjacent_cells(coord, rows, cols):
    adj_cells = set()

    if coord.x > 0:
        adj_cells.add(Coord(coord.x-1, coord.y))
    if coord.x < rows - 1:
        adj_cells.add(Coord(coord.x+1, coord.y))
    if coord.y > 0:
        adj_cells.add(Coord(coord.x, coord.y-1))
    if coord.y < cols - 1:
        adj_cells.add(Coord(coord.x, coord.y+1))

    return adj_cells


def valid_path_helper(matrix, coord, rows, cols, current_path):
    if coord.x == rows - 1 and coord.y == cols - 1:
        # base case when already at bottom-right cell
        return 1

    # get adjacent cells as candidates
    adj_cells = get_adjacent_cells(coord, rows, cols)

    # exclude already traversed cells as candidates
    next_candidates = adj_cells - current_path

    # exclude wall cells (=1) as candidates
    next_candidates = [nc for nc in next_candidates if matrix[nc.x][nc.y] == 0]

    new_path = current_path.copy()
    new_path.add(coord)
    path_count = 0
    for cand in next_candidates:
        sub_path_count = valid_path_helper(
            matrix, cand, rows, cols, new_path)
        path_count += sub_path_count

    return path_count


def find_paths(matrix):
    num_paths = valid_path_helper(
        matrix, Coord(0, 0), len(matrix), len(matrix[0]), set())
    return num_paths


# Tests
matrix = [[0, 0, 1],
          [0, 0, 1],
          [1, 0, 0]]
assert find_paths(matrix) == 2

matrix = [[0, 0, 1],
          [1, 0, 1],
          [1, 0, 0]]
assert find_paths(matrix) == 1

matrix = [[0, 0, 0],
          [1, 1, 0],
          [0, 0, 0],
          [0, 1, 1],
          [0, 0, 0]]
assert find_paths(matrix) == 1

matrix = [[0, 0, 0],
          [1, 0, 0],
          [0, 0, 0],
          [0, 1, 1],
          [0, 0, 0]]
assert find_paths(matrix) == 4

def get_first_recurring(string):
    seen = set()
    for char in string:
        if char in seen:
            return char
        seen.add(char)

    return None


# Tests
assert get_first_recurring("acbbac") == "b"
assert not get_first_recurring("abcdef")

   a
  /|\
 b c d
    / \
   e   f
  / \
 g   h

class Node:
    def __init__(self, iden):
        self.iden = iden
        self.max_path = 0
        self.child_dists = list()

    def __repr__(self):
        return "Node(id={},chi={},mp={})".format(
            self.iden, self.child_dists, self.max_path)


def get_path_maxlen(root):
    if not root.child_dists:
        return 0

    path_lens = list()
    child_max_path_lens = list()
    for child, dist in root.child_dists:
        path_lens.append(child.max_path + dist)
        child_max_path_lens.append(get_path_maxlen(child))

    child_max_path_len = max(child_max_path_lens)

    return max(sum(sorted(path_lens)[-2:]), child_max_path_len)


def update_max_paths(root):
    if not root.child_dists:
        root.max_path = 0
        return

    root_paths = list()
    for child, dist in root.child_dists:
        update_max_paths(child)
        root_paths.append(child.max_path + dist)

    root.max_path = max(root_paths)


def get_longest_path(root):
    update_max_paths(root)
    return get_path_maxlen(root)


# Tests
a = Node('a')
b = Node('b')
c = Node('c')
d = Node('d')
e = Node('e')
f = Node('f')
g = Node('g')
h = Node('h')

e.child_dists = [(g, 1), (h, 1)]
d.child_dists = [(e, 2), (f, 4)]
a.child_dists = [(b, 3), (c, 5), (d, 8)]

assert get_longest_path(a) == 17

def reverse_bits(num):
    inverted = list()
    for char in num:
        if char == '0':
            inverted.append('1')
        else:
            inverted.append('0')

    return "".join(inverted)


# Tests
assert reverse_bits('101') == '010'
assert reverse_bits('11110000111100001111000011110000') == \
    '00001111000011110000111100001111'

class Trie:
    def __init__(self):
        self.size = 0
        self.letter_map = dict()

    def __repr__(self):
        return str(self.letter_map)

    def add_word(self, word):
        if not word:
            return
        letter = word[0]

        sub_trie = None
        if letter in self.letter_map:
            sub_trie = self.letter_map[letter]
        else:
            sub_trie = Trie()
            self.letter_map[letter] = sub_trie

        self.size += 1
        sub_trie.add_word(word[1:])

    def get_sup(self, word, prev):
        # get shortest unique prefix
        if self.size < 2:
            return prev

        letter = word[0]
        sub_trie = self.letter_map[letter]
        return sub_trie.get_sup(word[1:], prev + letter)


def get_sups(words):
    trie = Trie()
    for word in words:
        trie.add_word(word)

    sups = list()
    for word in words:
        sups.append(trie.get_sup(word, ""))

    return sups


# Tests
assert get_sups(["dog", "cat", "apple", "apricot", "fish"]) == \
    ["d", "c", "app", "apr", "f"]

OPERATORS = {'+', '*', '/', '-'}


def evaluate_expression(exp_list):
    stack = list()

    for exp in exp_list:
        if exp in OPERATORS:
            op2 = stack.pop()
            op1 = stack.pop()
            ans = eval(str(op1) + exp + str(op2))
            stack.append(ans)
        else:
            stack.append(exp)

    return stack[0]


# Tests
assert evaluate_expression([5, 3, '+']) == 8
assert evaluate_expression(
    [15, 7, 1, 1, '+', '-', '/', 3, '*',
     2, 1, 1, '+', '+', '-']) == 5

def find_duplicate(arr, n):
    expected_sum = int((n * (n+1)) / 2)
    actual_sum = sum(arr)

    return actual_sum - expected_sum


# Tests

assert find_duplicate([1, 1, 2], 2) == 1
assert find_duplicate([1, 2, 3, 3], 3) == 3
assert find_duplicate([1, 2, 3, 4, 3], 4) == 3

def get_smaller_right(arr):
    smaller_right_arr = list()
    for i in range(len(arr)):
        smaller_count = 0
        for j in range(i + 1, len(arr)):
            if arr[j] < arr[i]:
                smaller_count += 1
        smaller_right_arr.append(smaller_count)

    return smaller_right_arr


# Tests

assert get_smaller_right([3, 4, 9, 6, 1]) == [1, 1, 2, 1, 0]

class TwoDimIterator:

    def __init__(self, arrays):
        self.arrays = arrays
        self.gen = self.get_generator()
        self.next_val = next(self.gen)

    def get_generator(self):
        for array in self.arrays:
            for num in array:
                yield num

    def has_next(self):
        return self.next_val != None

    def next(self):
        val = self.next_val
        try:
            self.next_val = next(self.gen)
        except StopIteration:
            self.next_val = None

        return val


# Tests

tdi = TwoDimIterator([[0, 1, 2], [3], [], [4, 5, 6]])

assert tdi.has_next()
assert tdi.next() == 0
assert tdi.next() == 1
assert tdi.next() == 2
assert tdi.has_next()
assert tdi.next() == 3
assert tdi.next() == 4
assert tdi.next() == 5
assert tdi.has_next()
assert tdi.next() == 6
assert not tdi.has_next()
assert not tdi.next()

def is_palindrome(word):
    return word == word[::-1]


def get_unique_index_tuples(words):
    index_tuples = list()
    for i, word_i in enumerate(words):
        for j, word_j in enumerate(words):
            if i != j:
                composite = word_i + word_j
                if is_palindrome(composite):
                    index_tuples.append((i, j))

    return index_tuples


# Tests
assert get_unique_index_tuples(["code", "edoc", "da", "d"]) == [
    (0, 1), (1, 0), (2, 3)]

[[1, 2, 3],
 [4, 5, 6],
 [7, 8, 9]]

[[7, 4, 1],
 [8, 5, 2],
 [9, 6, 3]]

def rotate_matrix(m):
    num_layers = len(m) // 2
    max_ind = len(m) - 1

    for layer in range(num_layers):
        # rotate all numbers
        for ind in range(layer, max_ind - layer):
            # rotate 4 numbers
            temp = m[layer][ind]
            m[layer][ind] = m[max_ind - ind][layer]
            m[max_ind - ind][layer] = m[max_ind - layer][max_ind - ind]
            m[max_ind - layer][max_ind - ind] = m[ind][max_ind - layer]
            m[ind][max_ind - layer] = temp


# Tests
matrix_1 = [[1, 2, 3],
            [4, 5, 6],
            [7, 8, 9]]
rotate_matrix(matrix_1)
assert matrix_1 == [[7, 4, 1],
                    [8, 5, 2],
                    [9, 6, 3]]

matrix_2 = [[1, 2, 3, 4],
            [5, 6, 7, 8],
            [9, 10, 11, 12],
            [13, 14, 15, 16]]
rotate_matrix(matrix_2)
assert matrix_2 == [[13, 9, 5, 1],
                    [14, 10, 6, 2],
                    [15, 11, 7, 3],
                    [16, 12, 8, 4]]

import sys


class Node:
    def __init__(self, x):
        self.val = x
        self.next = None

    def __str__(self):
        string = "["
        node = self
        while node:
            string += "{} ->".format(node.val)
            node = node.next
        string += "None]"
        return string


def get_nodes(values):
    next_node = None
    for value in values[::-1]:
        node = Node(value)
        node.next = next_node
        next_node = node

    return next_node


def get_list(head):
    node = head
    nodes = list()
    while node:
        nodes.append(node.val)
        node = node.next
    return nodes


def merge_sorted_lists(list_a, list_b):
    head = Node(-sys.maxsize)
    node = head
    node_a = list_a
    node_b = list_b

    while node_a and node_b:
        if node_a.val < node_b.val:
            tmp = node_a
            node_a = node_a.next
        else:
            tmp = node_b
            node_b = node_b.next
        tmp.next = None
        node.next = tmp
        node = node.next

    if node_a:
        node.next = node_a
    if node_b:
        node.next = node_b

    return head.next


def sort_ll_helper(llist, node_count):
    if node_count == 1:
        return llist

    mid = node_count // 2
    right_head = llist
    left_tail = None
    for _ in range(mid):
        left_tail = right_head
        right_head = right_head.next

    left_tail.next = None

    sorted_left = sort_ll_helper(llist, mid)
    sorted_right = sort_ll_helper(right_head, node_count - mid)

    return merge_sorted_lists(sorted_left, sorted_right)


def sort_ll(llist):
    count = 0
    node = llist
    while node:
        count += 1
        node = node.next

    return sort_ll_helper(llist, count)


# Tests
llist = get_nodes([4, 1, -3, 99])
assert get_list(sort_ll(llist)) == [-3, 1, 4, 99]

import sys

chars = set("abcdefghijklmnopqrstuvwxyz")


def transition_helper(start, end, dictionary, changes, seen):
    if start == end:
        return changes

    candidates = list()
    for index, _ in enumerate(start):
        for char in chars:
            candidate = start[:index] + char + start[index + 1:]
            if candidate in dictionary and candidate not in seen:
                candidates.append(candidate)

    min_results = list()
    min_len = sys.maxsize
    for candidate in candidates:
        new_seen = seen.copy()
        new_seen.add(candidate)
        result_changes = transition_helper(
            candidate, end, dictionary, changes + [candidate], new_seen)
        if result_changes and len(result_changes) < min_len:
            min_len = len(result_changes)
            min_results = result_changes

    return min_results


def get_transition(start, end, dictionary):
    result = transition_helper(start, end, dictionary, [start], {start})
    return result


# Tests
assert get_transition("dog", "cat", {"dot", "dop", "dat", "cat"}) == \
    ["dog", "dot", "dat", "cat"]
assert not get_transition("dog", "cat", {"dot", "tod", "dat", "dar"})

import sys

ENTER = "enter"
EXIT = "exit"


def get_busiest_slot(events):
    ts_entries, ts_exits = dict(), dict()
    max_time, min_time = -sys.maxsize, sys.maxsize

    for event in events:
        ts_dict = None
        timestamp = event["timestamp"]
        if event["type"] == ENTER:
            ts_dict = ts_entries
        else:
            ts_dict = ts_exits

        ts_dict[timestamp] = event["count"]
        if timestamp < min_time:
            min_time = timestamp
        elif timestamp > max_time:
            max_time = timestamp

    people_inside = 0
    max_people_inside = 0
    start_time, end_time = None, None
    for timestamp in range(min_time, max_time + 1):
        if timestamp in ts_entries:
            people_inside += ts_entries[timestamp]
            if people_inside > max_people_inside:
                max_people_inside = people_inside
                start_time = timestamp
        if timestamp in ts_exits:
            if people_inside == max_people_inside:
                end_time = timestamp
            people_inside -= ts_exits[timestamp]

    return (start_time, end_time)


# Tests
events = [
    {"timestamp": 1526579928, "count": 3, "type": "enter"},
    {"timestamp": 1526579982, "count": 4, "type": "enter"},
    {"timestamp": 1526580054, "count": 5, "type": "exit"},
    {"timestamp": 1526580128, "count": 1, "type": "enter"},
    {"timestamp": 1526580382, "count": 3, "type": "exit"}
]
assert get_busiest_slot(events) == (1526579982, 1526580054)

from itertools import permutations


def get_indices(s, words):
    perms = list(permutations(words))
    perms = [x + y for (x, y) in perms]

    indices = [s.find(x) for x in perms]
    indices = [x for x in indices if x >= 0]

    return sorted(indices)


# Tests
assert get_indices("dogcatcatcodecatdog", ["cat", "dog"]) == [0, 13]
assert not get_indices("barfoobazbitbyte", ["cat", "dog"])

{
    "key": 3,
    "foo": {
        "a": 5,
        "bar": {
            "baz": 8
        }
    }
}

{
    "key": 3,
    "foo.a": 5,
    "foo.bar.baz": 8
}

def is_dict(var):
    return str(type(var)) == "<class 'dict'>"


def flatten_helper(d, flat_d, path):
    if not is_dict(d):
        flat_d[path] = d
        return

    for key in d:
        new_keypath = "{}.{}".format(path, key) if path else key
        flatten_helper(d[key], flat_d, new_keypath)


def flatten(d):
    flat_d = dict()
    flatten_helper(d, flat_d, "")
    return flat_d


# Tests

d = {
    "key": 3,
    "foo": {
        "a": 5,
        "bar": {
            "baz": 8
        }
    }
}

assert flatten(d) == {
    "key": 3,
    "foo.a": 5,
    "foo.bar.baz": 8
}

* Ad-hoc polymorphism
    * Allow multiple functions that perform an operation on different 
    * `add(int, int)` and `add(str, str)` would be separately implemented
* Parametric polymorphism
    * This allows a function to deal with generics, and therefore on any concrete definition of the generic.
    * e.g. A `List` type in Java, regardless of which objects are in the list
* Subtype polymorphism
    * This allows subclass instances to be treated by a function they same way as it would superclass instances
    * e.g. Instances of `Cat` will be operated on a function the same way as instances of it's superclass `Animal`.

[
  ('a', 'a', 0.9),
  ('a', 'b', 0.075),
  ('a', 'c', 0.025),
  ('b', 'a', 0.15),
  ('b', 'b', 0.8),
  ('b', 'c', 0.05),
  ('c', 'a', 0.25),
  ('c', 'b', 0.25),
  ('c', 'c', 0.5)
]

from random import random
import bisect


def get_transition_map(transition_probs):
    transition_map = dict()
    for source, target, prob in transition_probs:
        if source not in transition_map:
            transition_map[source] = ([], [])

        if not transition_map[source][0]:
            transition_map[source][0].append(prob)
        else:
            prev_prob = transition_map[source][0][-1]
            transition_map[source][0].append(prev_prob + prob)
        transition_map[source][1].append(target)

    return transition_map


def get_new_state(state_trans_probs):
    rand = random()
    probs, states = state_trans_probs
    index = bisect.bisect(probs, rand)

    return states[index]


def calculate_visits(start_state, transition_probs, steps):
    transition_map = get_transition_map(transition_probs)

    visit_counter = dict()
    for state in transition_map:
        visit_counter[state] = 0

    for _ in range(steps):
        visit_counter[start_state] += 1

        state_trans_probs = transition_map[start_state]
        start_state = get_new_state(state_trans_probs)

    return visit_counter


# Tests
transition_probs = [
    ('a', 'a', 0.9),
    ('a', 'b', 0.075),
    ('a', 'c', 0.025),
    ('b', 'a', 0.15),
    ('b', 'b', 0.8),
    ('b', 'c', 0.05),
    ('c', 'a', 0.25),
    ('c', 'b', 0.25),
    ('c', 'c', 0.5)
]
visit_counter = calculate_visits('a', transition_probs, 50000)
assert visit_counter['a'] > visit_counter['b']
assert visit_counter['a'] > visit_counter['c']
assert visit_counter['b'] > visit_counter['c']

def is_char_mapped(str_a, str_b):
    if len(str_a) != len(str_b):
        return False

    char_map = dict()
    for char_a, char_b in zip(str_a, str_b):
        if char_a not in char_map:
            char_map[char_a] = char_b
        elif char_map[char_a] != char_b:
            return False

    return True


# Tests
assert is_char_mapped("abc", "bcd")
assert not is_char_mapped("foo", "bar")

class Node:
    def __init__(self, x):
        self.val = x
        self.next = None

    def __str__(self):
        string = "["
        node = self
        while node:
            string += "{} ->".format(node.val)
            node = node.next
        string += "None]"
        return string


def get_nodes(values):
    next_node = None
    for value in values[::-1]:
        node = Node(value)
        node.next = next_node
        next_node = node

    return next_node


def get_list(head):
    node = head
    nodes = list()
    while node:
        nodes.append(node.val)
        node = node.next
    return nodes


def rotate_ll(llist, k):
    cnode = llist
    head = cnode
    size = 0
    while cnode:
        tail = cnode
        cnode = cnode.next
        size += 1

    new_head = llist
    new_tail = None
    for _ in range(size - k):
        new_tail = new_head
        new_head = new_head.next

    tail.next = head
    new_tail.next = None

    return new_head


# Tests

assert get_list(rotate_ll(get_nodes([7, 7, 3, 5]), 2)) == [3, 5, 7, 7]
assert get_list(rotate_ll(get_nodes([1, 2, 3, 4, 5]), 3)) == [3, 4, 5, 1, 2]

# I would think that there is no difference between either game
# because the `nth` and the `(n-1)th` dice rolls should be
# independent events

from random import randint


def roll_dice(sought_values, index, prev_tosses):
    rand = randint(1, 6)

    if sought_values[index] == rand:
        index += 1

        if index == len(sought_values):
            return prev_tosses + 1

    return roll_dice(sought_values, index, prev_tosses + 1)


def simulate_game(sought_values):
    penalty = roll_dice(sought_values, 0, 0)
    return penalty


# Tests

num_exp = 100000
sought_value_pairs = [[5, 6], [5, 5]]

for sought_values in sought_value_pairs:
    total_penalty = 0
    for _ in range(num_exp):
        total_penalty += simulate_game(sought_values)
    avg_penalty = total_penalty / num_exp

    #  the expected value is approx. 12 on average for a single game
    assert round(avg_penalty) == 12

    5
   / \
  3   7
 / \   \
2   4   8

class Node:
    def __init__(self, data):
        self.data = data
        self.left = None
        self.right = None

    def __repr__(self):
        return "{} => (l: {}, r: {})".format(
            self.data, self.left, self.right)


def get_tree(seq):
    head = Node(seq[-1])
    if len(seq) == 1:
        return head

    for i in range(len(seq) - 1):
        if seq[i] > head.data:
            sep_ind = i
            break

    leq, gt = seq[:sep_ind], seq[sep_ind:-1]

    head.left = get_tree(leq) if leq else None
    head.right = get_tree(gt) if gt else None

    return head


# Tests
tree = get_tree([2, 4, 3, 8, 7, 5])
assert tree.data == 5
assert tree.left.data == 3
assert tree.right.data == 7
assert tree.left.left.data == 2
assert tree.left.right.data == 4
assert tree.right.right.data == 8

from queue import Queue


def interleave_stack(stack, queue, index=1):
    for _ in range(len(stack) - index):
        que.put(stack.pop())

    while que.qsize():
        stk.append(que.get())

    if len(stack) - index > 1:
        interleave_stack(stack, queue, index + 1)


# Tests
stk = [1, 2, 3, 4, 5]
que = Queue()
interleave_stack(stk, que)
assert stk == [1, 5, 2, 4, 3]

stk = [1, 2, 3, 4]
que = Queue()
interleave_stack(stk, que)
assert stk == [1, 4, 2, 3]

def is_palindrome(string):
    return bool(string) and string == string[::-1]


def split_into_pals(string, curr="", prev_pals=[]):

    if not string and not curr:
        return prev_pals
    elif not string:
        return prev_pals + list(curr)

    candidate = curr + string[0]

    alt_1 = []
    if is_palindrome(candidate):
        alt_1 = split_into_pals(string[1:], "", prev_pals + [candidate])
    alt_2 = split_into_pals(string[1:], candidate, prev_pals)

    return alt_1 if bool(alt_1) and len(alt_1) < len(alt_2) else alt_2


# Tests
assert split_into_pals("racecarannakayak") == ["racecar", "anna", "kayak"]
assert split_into_pals("abc") == ["a", "b", "c"]
assert split_into_pals("madam") == ["madam"]
assert split_into_pals("madama") == ["madam", "a"]

from copy import deepcopy


class Node:
    def __init__(self, id_str):
        self.id = id_str

    def __repr__(self):
        return str(self.id)

    def __hash__(self):
        return hash(self.id)

    def __eq__(self, other):
        return self.id == other.id


class Graph:
    def __init__(self):
        self.nodes = set()
        self.adj_lists = dict()

    def add_edge(self, node_a, node_b):
        for node in [node_a, node_b]:
            if node not in self.nodes:
                self.nodes.add(node)
                self.adj_lists[node] = set()

        self.adj_lists[node_a].add(node_b)
        self.adj_lists[node_b].add(node_a)


def are_connected(g, source, target, seen=set()):
    if source == target:
        return True

    seen_cp = seen.copy()
    seen_cp.add(source)

    return any(are_connected(g, x, target, seen_cp)
               for x in g.adj_lists[source] if x not in seen)


def is_min_graph(g):
    if all(len(x) == 1 for x in g.adj_lists.values()):
        return True

    for node in g.nodes:
        cp_g = deepcopy(g)

        assert node in cp_g.nodes
        adj_nodes = list(cp_g.adj_lists[node])
        cp_g.adj_lists.pop(node)

        for an in adj_nodes:
            cp_g.adj_lists[an].remove(node)

        for i in range(len(adj_nodes)):
            for j in range(i + 1, len(adj_nodes)):
                if are_connected(cp_g, adj_nodes[i], adj_nodes[j]):
                    return False

    return True


# Tests
a = Node('a')
b = Node('b')
c = Node('c')
d = Node('d')

g = Graph()
g.add_edge(a, b)
assert is_min_graph(g)

g.add_edge(b, c)
assert is_min_graph(g)

g.add_edge(a, c)
assert not is_min_graph(g)

g.add_edge(a, d)
assert not is_min_graph(g)

# Process of a URL being fetched

1. Check browsers host resolution cache.
2. If IP not found, request DNS for the IP of the host/load balancing host.
3. Send a GET request to the host
4. Host responds with a payload (usually in HTML)
5. Browser renders HTML

SMALLEST_PRIME = 2


def is_prime(cand, primes):
    for prime in primes:
        res = cand / prime
        if not res % 1:
            return False

    return True


def get_possible_primes(num):
    primes = [SMALLEST_PRIME]

    for cand in range(SMALLEST_PRIME + 1, num//2 + 1):
        if is_prime(cand, primes):
            primes.append(cand)

    return primes


def get_factors(num, primes):
    factors = dict()

    pi = 0
    while num > 1:
        if pi >= len(primes):
            break
        if not num % primes[pi]:
            if primes[pi] not in factors:
                factors[primes[pi]] = 0
            factors[primes[pi]] += 1
            num /= primes[pi]
        else:
            pi += 1
    return factors


def get_gcd(nums):
    min_num = min(nums)
    primes = get_possible_primes(min_num)
    base_factors = get_factors(min_num, primes)

    factorized_nums = dict()
    for num in nums:
        factorized_nums[num] = get_factors(num, primes)

    common_factors = dict()
    for base_factor in base_factors:
        common_factors[base_factor] = 0
        num_factors = list()
        for num in nums:
            factors = factorized_nums[num]
            num_factors.append(factors[base_factor])
        common_factors[base_factor] = min(num_factors)

    gcd = 1
    for factor in common_factors:
        gcd *= factor ** common_factors[factor]

    return gcd


# Tests
assert get_gcd([42, 56, 14]) == 14
assert get_gcd([3, 5]) == 1
assert get_gcd([9, 15]) == 3

{
    "top_left": (1, 4),
    "dimensions": (3, 3) # width, height
}

{
    "top_left": (0, 5),
    "dimensions" (4, 3) # width, height
}

class Point:
    def __init__(self, x, y):
        self.x = x
        self.y = y

    def __repr__(self):
        return "(x={},y={})".format(self.x, self.y)


class Rectangle:
    def __init__(self, json):
        self.tl = Point(json["top_left"][0], json["top_left"][1])
        width, height = json["dimensions"]
        self.br = Point(self.tl.x + width, self.tl.y - height)

    def __repr__(self):
        return "(tl={},br={})".format((self.tl), (self.br))

    def get_area(self):
        return (self.br.x - self.tl.x) * (self.tl.y - self.br.y)

    def envelopes(self, other):
        return self.tl.x < other.tl.x and self.tl.y > other.tl.y and \
            self.br.x > other.br.x and self.br.y < other.br.y

    def is_disjoint_with(self, other):
        return self.br.y > other.tl.y or other.br.y > self.tl.y or \
            self.tl.x > other.br.x or other.tl.x > self.br.x


def calculate_intersect_area(r1, r2):
    if r1.envelopes(r2):
        area = r2.get_area()
    elif r2.envelopes(r1):
        area = r1.get_area()
    elif r1.is_disjoint_with(r2) or r2.is_disjoint_with(r1):
        area = 0
    else:
        heights = list(sorted([r1.tl.y, r1.br.y, r2.tl.y, r2.br.y]))[1:-1]
        height = heights[1] - heights[0]
        widths = list(sorted([r1.tl.x, r1.br.x, r2.tl.x, r2.br.x]))[1:-1]
        width = widths[1] - widths[0]
        area = height * width

    return area


# Tests
r1 = Rectangle({"top_left": (1, 4), "dimensions": (3, 3)})
r2 = Rectangle({"top_left": (0, 5), "dimensions": (4, 3)})
assert calculate_intersect_area(r1, r2) == 6

r1 = Rectangle({"top_left": (1, 1), "dimensions": (1, 1)})
r2 = Rectangle({"top_left": (5, 5), "dimensions": (1, 1)})
assert calculate_intersect_area(r1, r2) == 0

r1 = Rectangle({"top_left": (0, 5), "dimensions": (5, 5)})
r2 = Rectangle({"top_left": (1, 4), "dimensions": (2, 2)})
assert calculate_intersect_area(r1, r2) == 4

r1 = Rectangle({"top_left": (0, 5), "dimensions": (5, 5)})
r2 = Rectangle({"top_left": (4, 4), "dimensions": (3, 3)})
assert calculate_intersect_area(r1, r2) == 3

def get_diff(s1, s1_sum, s2, s2_sum, score):
    min_diff, min_cand = score, None
    for i, num in enumerate(s1):
        new_s1_sum, new_s2_sum = s1_sum - num, s2_sum + num
        new_score = abs(new_s1_sum - new_s2_sum)
        if new_score < min_diff:
            min_diff = new_score
            min_cand = (s1[:i] + s1[i + 1:], new_s1_sum,
                        s2 + [num], new_s2_sum)

    if not min_cand:
        return (set(s1), set(s2))

    return get_diff(min_cand[0], min_cand[1], min_cand[2], min_cand[3], min_diff)


def divide_numbers(nums):
    sum_nums = sum(nums)
    best_sets = get_diff(nums.copy(), sum_nums, [], 0, sum_nums)

    return best_sets


# Tests
assert divide_numbers([5, 10, 15, 20, 25]) == ({5, 15, 20}, {10, 25})
assert divide_numbers([5, 10, 15, 20]) == ({10, 15}, {20, 5})

{
    "top_left": (1, 4),
    "dimensions": (3, 3) # width, height
},
{
    "top_left": (-1, 3),
    "dimensions": (2, 1)
},
{
    "top_left": (0, 5),
    "dimensions": (4, 3)
}

class Point:
    def __init__(self, x, y):
        self.x = x
        self.y = y

    def __repr__(self):
        return "(x={},y={})".format(self.x, self.y)


class Rectangle:
    def __init__(self, json):
        self.tl = Point(json["top_left"][0], json["top_left"][1])
        width, height = json["dimensions"]
        self.br = Point(self.tl.x + width, self.tl.y - height)

    def __repr__(self):
        return "(tl={},br={})".format((self.tl), (self.br))

    def envelopes(self, other):
        return self.tl.x <= other.tl.x and self.tl.y >= other.tl.y and \
            self.br.x >= other.br.x and self.br.y <= other.br.y


def contains_overlapping_pair(rectangles):

    for i in range(len(rectangles) - 1):
        for j in range(i + 1, len(rectangles)):
            if rectangles[i].envelopes(rectangles[j]) or \
                    rectangles[j].envelopes(rectangles[i]):
                return True

    return False


# Tests

# example provided in the question is incorrect
r1 = Rectangle({"top_left": (1, 4), "dimensions": (3, 3)})
r2 = Rectangle({"top_left": (-1, 3), "dimensions": (2, 1)})
r3 = Rectangle({"top_left": (0, 5), "dimensions": (4, 4)})
assert contains_overlapping_pair([r1, r2, r3])

r1 = Rectangle({"top_left": (1, 4), "dimensions": (3, 3)})
r2 = Rectangle({"top_left": (-1, 3), "dimensions": (2, 1)})
r3 = Rectangle({"top_left": (0, 5), "dimensions": (4, 3)})
assert not contains_overlapping_pair([r1, r2, r3])

def make_functions():
    flist = []

    for i in [1, 2, 3]:
        def print_i():
            print(i)
        flist.append(print_i)

    return flist

functions = make_functions()
for f in functions:
    f()

# Unchanged code prints 3, 3, 3
# To make it print 1, 2, 3, use the following version


def make_functions():
    flist = []

    for i in [1, 2, 3]:
        def print_i(i):
            print(i)
        flist.append((print_i, i))

    return flist


functions = make_functions()
for f, i in functions:
    f(i)

def get_longest_uqsub(arr, seen=set()):
    if not arr:
        return len(seen)

    curr = arr[0]
    if curr in seen:
        return len(seen)

    seen_cp = seen.copy()
    seen_cp.add(curr)

    return max(get_longest_uqsub(arr[1:], seen_cp), 
               get_longest_uqsub(arr[1:]))



# Tests
assert get_longest_uqsub([]) == 0
assert get_longest_uqsub([5, 5, 5]) == 1
assert get_longest_uqsub([5, 1, 3, 5, 2, 3, 4, 1]) == 5
assert get_longest_uqsub([5, 1, 3, 5, 2, 3, 4]) == 4
assert get_longest_uqsub([5, 1, 3, 5, 2, 3]) == 4

def get_max_circ_sarray(arr):
    warr = arr * 2

    items = []
    csum = msum = 0

    for num in warr:
        while len(items) >= len(arr) or (items and items[0] < 1):
            csum -= items[0]
            items = items[1:]

        items.append(num)
        csum += num

        msum = max(msum, csum)

    return msum


# Tests
assert get_max_circ_sarray([8, -1, 3, 4]) == 15
assert get_max_circ_sarray([-4, 5, 1, 0]) == 6

def get_min_removals(intervals, reserved_intervals=list(), removed=0):
    print(reserved_intervals)

    if not intervals:
        return removed

    curr_interval = intervals[0]
    if_removed = get_min_removals(
        intervals[1:], reserved_intervals, removed + 1)

    for ri in reserved_intervals:
        if curr_interval[0] in ri or curr_interval[1] in ri:
            return if_removed

    new_reserved_intervals = reserved_intervals + \
        [range(curr_interval[0], curr_interval[1])]

    return min(if_removed, get_min_removals(intervals[1:], new_reserved_intervals, removed))


# Tests
assert get_min_removals([(0, 1), (1, 2)]) == 0
assert get_min_removals([(7, 9), (2, 4), (5, 8)]) == 1
assert get_min_removals([(7, 9), (2, 4), (5, 8), (1, 3)]) == 2

def end_reachable(arr):
    if len(arr) < 2:
        return True

    for i in range(2, len(arr) + 1):
        if arr[len(arr) - i] >= i - 1:
            return end_reachable(arr[:len(arr) - i + 1])


# Tests
assert end_reachable([1, 3, 1, 2, 0, 1])
assert not end_reachable([1, 2, 1, 0, 0])

def get_max_profit(prices, fee, reserve=0, buyable=True):
    if not prices:
        return reserve

    price_offset = -prices[0] - fee if buyable else prices[0]
    return max(
        get_max_profit(prices[1:], fee, reserve, buyable),
        get_max_profit(prices[1:], fee, reserve + price_offset, not buyable)
    )



# Tests
assert get_max_profit([1, 3, 2, 8, 4, 10], 2) == 9
assert get_max_profit([1, 3, 2, 1, 4, 10], 2) == 7

def get_intersections(parr, qarr):
    segments = list(zip(parr, qarr))

    count = 0
    for i in range(len(segments)):
        for k in range(i):
            p1, p2 = segments[i], segments[k]
            if (p1[0] < p2[0] and p1[1] > p2[1]) or \
                    (p1[0] > p2[0] and p1[1] < p2[1]):
                count += 1

    return count


# Tests
assert get_intersections([1, 4, 5], [4, 2, 3]) == 2
assert get_intersections([1, 4, 5], [2, 3, 4]) == 0

def get_num_betn(matrix, i1, j1, i2, j2):
    num_1, num_2 = matrix[i1][j1], matrix[i2][j2]
    sm, lg = (num_1, num_2) if num_1 < num_2 else (num_2, num_1)
    count = 0
    for row in matrix:
        count += len([x for x in row if (x > sm and x < lg)])

    return count


# Tests
matrix = [
    [1, 2, 3, 4],
    [5, 8, 9, 13],
    [6, 10, 12, 14],
    [7, 11, 15, 16]
]
assert get_num_betn(matrix, 1, 3, 3, 1) == 1

matrix = [
    [1, 2, 3, 4],
    [5, 6, 7, 8],
    [10, 11, 12, 13],
    [20, 21, 22, 23]
]
assert get_num_betn(matrix, 1, 0, 3, 3) == 10

  5
 / \
2  -5

class Node:
    def __init__(self, val):
        self.val = val
        self.left = None
        self.right = None


def get_freq_tree_sum(root, counts):
    if not root:
        return 0

    tree_sum = root.val + \
        get_freq_tree_sum(root.left, counts) + \
        get_freq_tree_sum(root.right, counts)

    if not tree_sum in counts:
        counts[tree_sum] = 0
    counts[tree_sum] += 1

    return tree_sum


def get_freq_tree_sum_helper(root):
    counts = dict()
    get_freq_tree_sum(root, counts)

    return max(counts.items(), key=lambda x: x[1])[0]


# Tests
root = Node(5)
root.left = Node(2)
root.right = Node(-5)
assert get_freq_tree_sum_helper(root) == 2

def rotate_index(arr, k, src_ind, src_num, count=0):
    if count == len(arr):
        return

    des_ind = (src_ind + k) % len(arr)
    des_num = arr[des_ind]

    arr[des_ind] = src_num

    rotate_index(arr, k, des_ind, des_num, count + 1)


def rotate_k(arr, k):
    if k < 1:
        return arr

    start = 0
    rotate_index(arr, k, start, arr[start])


# Tests
arr = [1, 2, 3, 4, 5]
rotate_k(arr, 2)
assert arr == [4, 5, 1, 2, 3]
rotate_k(arr, 2)
assert arr == [2, 3, 4, 5, 1]
rotate_k(arr, 4)
assert arr == [3, 4, 5, 1, 2]

def get_largest_subset(arr, prev_num=1, curr_ind=0, prev_subset=[]):
    if curr_ind == len(arr):
        return prev_subset

    curr_num = arr[curr_ind]

    alt_0 = get_largest_subset(arr, prev_num, curr_ind + 1, prev_subset)
    if curr_num % prev_num == 0:
        alt_1 = get_largest_subset(
            arr, curr_num, curr_ind + 1, prev_subset + [curr_num])
        return alt_1 if len(alt_1) > len(alt_0) else alt_0

    return alt_0


def get_largest_subset_helper(arr):
    arr.sort()
    return get_largest_subset(arr)


# Tests
assert get_largest_subset([]) == []
assert get_largest_subset([2]) == [2]
assert get_largest_subset([2, 3]) == [3]
assert get_largest_subset([3, 5, 10, 20, 21]) == [5, 10, 20]
assert get_largest_subset([1, 3, 6, 24]) == [1, 3, 6, 24]
assert get_largest_subset([3, 9, 15, 30]) == [3, 15, 30]

def correct_braces(braces):
    # get rid of all initial closing braces
    i = 0
    while i < len(braces) and braces[i] == ')':
        i += 1
    braces = braces[i:]

    # base case for recursion
    if not braces:
        return ''

    # check for the first balanced group of braces
    open_braces = 0
    for i, brace in enumerate(braces):
        if brace == '(':
            open_braces += 1
        elif brace == ')':
            open_braces -= 1

        if not open_braces:
            break

    # if there is one, process the rest separately, else truncate the excess opening braces
    return braces[open_braces:] if open_braces else braces[:i+1] + correct_braces(braces[i+1:])


# Tests
assert correct_braces("()(()") == "()()"
assert correct_braces("()(()))") == "()(())"
assert correct_braces(")(())") == "(())"
assert correct_braces("())(") == "()"

def get_stab_points(intervals):
    starts, ends = zip(*intervals)
    return (min(ends), max(starts))


# Tests
assert get_stab_points([(1, 4), (4, 5), (7, 9), (9, 12)]) == (4, 9)
assert get_stab_points([(1, 4), (-2, 6), (4, 5), (7, 9), (9, 12)]) == (4, 9)
assert get_stab_points([(1, 4), (-2, 0), (4, 5), (7, 9)]) == (0, 7)

  1
 2 3
1 5 1

def get_max_path(triangle, index, level, path, path_val):
    if level == len(triangle):
        return path, path_val

    ind_a, ind_b = index, index + 1
    val_a, val_b = triangle[level][ind_a], triangle[level][ind_b]

    path_a, path_val_a = \
        get_max_path(triangle, ind_a, level + 1,
                     path + [val_a], path_val + val_a)
    path_b, path_val_b = \
        get_max_path(triangle, ind_b, level + 1,
                     path + [val_b], path_val + val_b)

    return (path_a, path_val_a) if path_val_a > path_val_b else (path_b, path_val_b)


def get_max_path_helper(triangle):
    return get_max_path(triangle, index=0, level=1,
                        path=[triangle[0][0]], path_val=triangle[0][0])[0]


# Tests
assert get_max_path_helper([[1], [2, 3], [1, 5, 1]]) == [1, 3, 5]
assert get_max_path_helper([[1], [2, 3], [7, 5, 1]]) == [1, 2, 7]

DEC_FACT = 10


def is_palindrome(num, size):
    if size == 0 or size == 1:
        return True

    fdig_factor = DEC_FACT ** (size - 1)
    fdig = num // fdig_factor
    ldig = num % DEC_FACT

    if fdig != ldig:
        return False

    new_num = (num - (fdig * fdig_factor)) // DEC_FACT
    return is_palindrome(new_num, size - 2)


def is_palindrome_helper(num):
    size = 0
    num_cp = num
    while num_cp:
        num_cp = num_cp // DEC_FACT
        size += 1

    return is_palindrome(num, size)



# Tests
assert is_palindrome_helper(121)
assert is_palindrome_helper(888)
assert not is_palindrome_helper(678)
assert not is_palindrome_helper(1678)
assert is_palindrome_helper(1661)

def get_smallest(arr, start, end):
    mid = start + ((end - start) // 2)

    if arr[start] <= arr[mid]:
        if arr[end] < arr[mid]:
            return get_smallest(arr, mid + 1, end)
        else:
            return arr[start]
    elif arr[start] >= arr[mid]:
        if arr[end] > arr[mid]:
            return get_smallest(arr, start, end)
        else:
            return arr[end]


def get_smallest_helper(arr):
    smallest = get_smallest(arr, 0, len(arr) - 1)
    return smallest


# Tests
assert get_smallest_helper([5, 7, 10, 3, 4]) == 3
assert get_smallest_helper([4, 5, 7, 10, 3]) == 3
assert get_smallest_helper([3, 4, 5, 7, 10]) == 3

class Node:
    def __init__(self):
        self.left = None
        self.right = None


def count_nodes(root, lspine=0, rspine=0):
    if not root:
        return 0

    if not lspine:
        node = root
        while node:
            node = node.left
            lspine += 1
    if not rspine:
        node = root
        while node:
            node = node.right
            rspine += 1

    if lspine == rspine:
        return 2**lspine - 1

    return 1 + \
        count_nodes(root.left, lspine=lspine-1) + \
        count_nodes(root.right, rspine=rspine-1)


# Tests
a = Node()
b = Node()
c = Node()
a.left = b
a.right = c
assert count_nodes(a) == 3
d = Node()
b.left = d
assert count_nodes(a) == 4
e = Node()
b.right = e
assert count_nodes(a) == 5
f = Node()
c.left = f
assert count_nodes(a) == 6

from bisect import bisect


def get_next_perm(num):
    num_str = str(num)

    # if the number is already maxed out, return it
    max_val_str = "".join(sorted(num_str, reverse=True))
    if max_val_str == num_str:
        return num

    # find the point n the number at which there is
    # a chance to increase the number by changing order
    right_nums = list()
    num_to_replace = None
    for i in range(len(num_str) - 2, -1, -1):
        right_nums.append(num_str[i + 1])
        if num_str[i] < num_str[i + 1]:
            num_to_replace = num_str[i]
            break

    # identify the replacement of the digit to be moved
    rep_index = bisect(right_nums, num_to_replace)
    replacement = right_nums[rep_index]

    # replace digit
    right_nums[rep_index] = num_to_replace
    leftover_nums = num_str[:i]

    # contruct new number
    final_str = "{}{}{}".format(leftover_nums, replacement,
                                "".join(sorted(right_nums)))

    return int(final_str)


# Tests
assert get_next_perm(98754) == 98754
assert get_next_perm(48975) == 49578
assert get_next_perm(48759) == 48795
assert get_next_perm(49875) == 54789
assert get_next_perm(408975) == 409578

def permute(arr, perms):
    evicted = dict()
    for i, (num, new_pos) in enumerate(zip(arr, perms)):
        if i in evicted:
            num = evicted[i]
            del evicted[i]

        if new_pos > i:
            evicted[new_pos] = arr[new_pos]

        arr[new_pos] = num

    return arr


# Tests
assert permute(['a', 'b', 'c'], [2, 1, 0]) == ['c', 'b', 'a']
assert permute(['a', 'b', 'c', 'd'], [2, 1, 0, 3]) == ['c', 'b', 'a', 'd']
assert permute(['a', 'b', 'c', 'd'], [3, 0, 1, 2]) == ['b', 'c', 'd', 'a']

class Node:
    def __init__(self, val):
        self.val = val

    def __repr__(self):
        return str(self.val)


class Graph:
    def __init__(self):
        self.nodes, self.edges = set(), dict()
        self.set_1, self.set_2 = set(), set()

    def is_bipartite(self):
        sorted_nodes = sorted(self.edges.items(),
                              key=lambda x: len(x[1]), reverse=True)
        for node, _ in sorted_nodes:
            if node in self.set_2:
                continue
            self.set_1.add(node)

            if self.edges[node]:
                for other_node in self.edges[node]:
                    self.set_2.add(other_node)

        for node in self.set_2:
            if self.edges[node]:
                for other_node in self.edges[node]:
                    if other_node in self.set_2:
                        return False

        return True


# Tests
g = Graph()
a = Node('a')
b = Node('b')
c = Node('c')
d = Node('d')
e = Node('e')
f = Node('f')
g.nodes = set([a, b, c, d, e, f])

g.edges[a] = set([d])
g.edges[b] = set([d, e, f])
g.edges[c] = set([f])
g.edges[d] = set([a, b])
g.edges[e] = set([b])
g.edges[f] = set([b, c])
assert g.is_bipartite()

g.edges = dict()
g.nodes = set([a, b, c, d, e, f])
g.edges[a] = set([d])
g.edges[b] = set([d, e, f])
g.edges[c] = set([f])
g.edges[d] = set([a, b])
g.edges[e] = set([b, f])
g.edges[f] = set([b, c, e])
assert not g.is_bipartite()

class Node:
    def __init__(self, x):
        self.val = x
        self.next = None

    def __str__(self):
        string = "["
        node = self
        while node:
            string += "{} ->".format(node.val)
            node = node.next
        string += "None]"
        return string


def get_nodes(values):
    next_node = None
    for value in values[::-1]:
        node = Node(value)
        node.next = next_node
        next_node = node

    return next_node


def get_list(head):
    node = head
    nodes = list()
    while node:
        nodes.append(node.val)
        node = node.next
    return nodes


def partition(llist, k):
    head = llist
    prev, curr = head, head.next

    while curr:
        if curr.val < k:
            prev.next = curr.next
            curr.next = head
            head = curr
            curr = prev.next
        else:
            prev = curr
            curr = curr.next

    return head


# Tests
assert get_list(partition(get_nodes([5, 1, 8, 0, 3]), 3)) == [0, 1, 5, 8, 3]

# This solution generalizes to n strings

ALPHABET = "abcdefghijklmnopqrstuvwxyz"


def get_lcs(strings, context, indices):
    lcs_len = len(context)
    for letter in ALPHABET:
        new_indices = list()
        for j, string in enumerate(strings):
            index = string.find(letter, indices[j] + 1)
            if index == -1:
                break
            new_indices.append(index)
        if len(new_indices) == 3:
            length_cs = get_lcs(strings, context + letter, new_indices)
            if length_cs > lcs_len:
                lcs_len = length_cs

    return lcs_len


def get_lcs_helper(strings):
    return get_lcs(strings, "", [-1]*len(strings))


# Tests
assert get_lcs_helper(["epidemiologist", "refrigeration",
                       "supercalifragilisticexpialodocious"]) == 5

import sys
from random import randint

cache = dict()


def get_collatz_seq(num, prev=list()):
    prev.append(num)

    if num in cache:
        return prev + cache[num]

    if num == 1:
        return prev

    if num % 2 == 0:
        num //= 2
    else:
        num = 3*num + 1

    return get_collatz_seq(num, prev)


# Tests
experiments = 10
for _ in range(experiments):
    num = randint(1, sys.maxsize)
    cs = get_collatz_seq(num)
    assert cs[-1] == 1


def get_longest_collatz(limit):
    longest_cs, length = None, -1
    for num in range(1, limit + 1):
        if num in cache:
            cs = cache[num]
        else:
            cs = get_collatz_seq(num)
            cache[num] = cs
        if len(cs) > length:
            length = len(cs)
            longest_cs = cs

    return longest_cs


print(len(get_longest_collatz(100)))

def get_occurrences(string, pattern):
    sl, pl = len(string), len(pattern)
    occurrences = list()

    for i in range(sl - pl + 1):
        if string[i:i+pl] == pattern:
            occurrences.append(i)

    return occurrences


# Tests
assert get_occurrences("abracadabra", "abr") == [0, 7]
assert not get_occurrences("abracadabra", "xyz")
assert not get_occurrences("abr", "abracadabra")
assert get_occurrences("aaaa", "aa") == [0, 1, 2]

alphabet = "ABCDEFGHIJKLMNOPQRSTUVWXYZ"


def get_alpha_encoding(num):
    num_chars = 1
    min_range, max_range = 1, 26
    while num > max_range:
        num_chars += 1
        min_range = max_range
        max_range += len(alphabet) ** num_chars

    chars = list()
    for _ in range(num_chars):
        interval = ((max_range - min_range + 1) // len(alphabet))
        char_pos = 0
        prev, curr = min_range, min_range + interval
        while num >= curr:
            char_pos += 1
            prev = curr
            curr = prev + interval
        chars.append(alphabet[char_pos])
        num -= prev
        min_range, max_range = prev, curr

    return "".join(chars)


# Tests
assert get_alpha_encoding(1) == "A"
assert get_alpha_encoding(20) == "T"
assert get_alpha_encoding(27) == "AA"

def generate_valid_ips(string, curr, all_ips):
    if len(curr) > 4 or (len(curr) < 4 and not string):
        return
    elif len(curr) == 4 and not string:
        all_ips.add(".".join(curr))
        return

    def recurse(index):
        generate_valid_ips(string[index:], curr + [string[0:index]], all_ips)

    recurse(1)
    first = int(string[0])
    if first and len(string) > 1:
        recurse(2)
        if len(string) > 2 and first < 3:
            recurse(3)


def generate_valid_ip_helper(string):
    all_ips = set()
    generate_valid_ips(string, list(), all_ips)
    return all_ips


# Tests
assert generate_valid_ip_helper("2542540123") == \
    {'254.25.40.123', '254.254.0.123'}
assert generate_valid_ip_helper("0000") == \
    {'0.0.0.0'}
assert generate_valid_ip_helper("255255255255") == \
    {'255.255.255.255'}
assert generate_valid_ip_helper("100100110") == \
    {'100.10.0.110', '10.0.100.110', '100.100.11.0', '100.100.1.10'}

def get_lcos(num):
    current = longest = 0

    def reset_current():
        nonlocal current, longest
        if current > longest:
            longest = current
        current = 0

    while num:
        if num % 2:
            current += 1
        else:
            reset_current()
        num = num >> 1

    reset_current()

    return longest


# Tests
assert get_lcos(0) == 0
assert get_lcos(4) == 1
assert get_lcos(6) == 2
assert get_lcos(15) == 4
assert get_lcos(21) == 1
assert get_lcos(156) == 3

             5
          /     \
        3         7
      /  \      /   \
    1     4    6     9
   /                /
  0                8

class Node:
    def __init__(self, data):
        self.data = data
        self.left = None
        self.right = None
        self.depth = None

    def __repr__(self):
        return "Node[val={}]".format(self.data)


def compute_bottom_view(root, depths, depth, width):
    root.depth = depth

    if width not in depths or depths[width].depth < depth:
        depths[width] = root

    if root.right:
        compute_bottom_view(root.right, depths, depth + 1, width + 1)
    if root.left:
        compute_bottom_view(root.left, depths, depth + 1, width - 1)


def get_bottom_view(root):
    depths = dict()
    compute_bottom_view(root, depths, 0, 0)

    sorted_items = sorted(depths.items(), key=lambda x: x[0])
    return [x[1].data for x in sorted_items]


# Tests
root = Node(5)
root.left = Node(3)
root.left.left = Node(1)
root.left.left.left = Node(0)
root.left.right = Node(4)
root.right = Node(7)
root.right.left = Node(6)
root.right.right = Node(9)
root.right.right.left = Node(8)
assert get_bottom_view(root) == [0, 1, 3, 6, 8, 9]

{
    'M': 1000,
    'D': 500,
    'C': 100,
    'L': 50,
    'X': 10,
    'V': 5,
    'I': 1
}

values = {
    'M': 1000,
    'D': 500,
    'C': 100,
    'L': 50,
    'X': 10,
    'V': 5,
    'I': 1
}


def convert_roman_to_decimal(roman):
    if not roman:
        return 0

    pchar = roman[-1]
    decimal = values[pchar]
    for char in reversed(roman[:-1]):
        decimal += values[char] * (-1 if values[char] < values[pchar] else 1)
        pchar = char

    return decimal


# Tests
assert convert_roman_to_decimal("I") == 1
assert convert_roman_to_decimal("IV") == 4
assert convert_roman_to_decimal("XL") == 40
assert convert_roman_to_decimal("XIV") == 14

def get_next_sparse(num):
    str_bin = str(bin(num))[2:]

    new_str_bin = ""
    prev_digit = None
    flag = False
    for i, digit in enumerate(str_bin):
        if digit == '1' and prev_digit == '1':
            flag = True

        if flag:
            new_str_bin += '0' * (len(str_bin) - i)
            break
        else:
            new_str_bin += digit
        prev_digit = digit

    if flag:
        if new_str_bin[0] == '1':
            new_str_bin = '10' + new_str_bin[1:]
        else:
            new_str_bin = '1' + new_str_bin

    new_num = int(new_str_bin, base=2)

    return new_num


# Tests
assert get_next_sparse(21) == 21
assert get_next_sparse(25) == 32
assert get_next_sparse(255) == 256

class Node:
    def __init__(self, iden):
        self.iden = iden

    def __hash__(self):
        return hash(self.iden)

    def __eq__(self, other):
        return self.iden == other.iden

    def __repr__(self):
        return str(self.iden)


class Edge:
    def __init__(self, src, tgt):
        self.src = src
        self.tgt = tgt

    def __hash__(self):
        return hash((self.src, self.tgt))

    def __eq__(self, other):
        return self.src == other.src and self.tgt == other.tgt

    def __repr__(self):
        return "{}->{}".format(self.src, self.tgt)

    def reverse(self):
        tmp_node = self.src
        self.src = self.tgt
        self.tgt = tmp_node


class Graph:
    def __init__(self):
        self.nodes = set()
        self.edges = set()

    def add_node(self, node):
        if node in self.nodes:
            return
        self.nodes.add(node)

    def add_edge(self, src_node, tgt_node):
        self.edges.add(Edge(src_node, tgt_node))

    def reverse_edges(self):
        self.edges = [Edge(x.tgt, x.src) for x in self.edges]

    def get_edges(self):
        return self.edges


# Tests
g = Graph()
a = Node('a')
b = Node('b')
c = Node('c')

g.add_node(a)
g.add_node(b)
g.add_node(c)
g.add_edge(a, b)
g.add_edge(b, c)
edges = g.get_edges()
assert Edge(a, b) in edges and Edge(b, c) in edges and len(edges) == 2

g.reverse_edges()
edges = g.get_edges()
assert Edge(b, a) in edges and Edge(c, b) in edges and len(edges) == 2

from enum import Enum

ROWS = 6
COLS = 7


class Color(Enum):
    RED = 1
    BLACK = 2


class Board:
    def __init__(self):
        self.grid = list()
        for _ in range(COLS):
            col = list()
            for _ in range(ROWS):
                col.append(None)
            self.grid.append(col)
        self.occupancy = [0] * COLS


class IllegalMove(Exception):
    pass


def play_piece(board, played_column, played_color):
    if board.occupancy[played_column] == 6:
        raise IllegalMove("Illegal move in this column")

    played_row = board.occupancy[played_column]
    board.grid[played_column][played_row] = played_color
    board.occupancy[played_column] += 1

    # check vertical
    consecutive = 0
    if len(board.grid[played_column]) > 4:
        for color in board.grid[played_column]:
            if color == played_color:
                consecutive += 1
            else:
                consecutive = 0

            if consecutive == 4:
                return True

    # check horizontal
    consecutive = 0
    for i in range(COLS):
        color = board.grid[i][played_row]
        if color == played_color:
            consecutive += 1
        else:
            consecutive = 0

        if consecutive == 4:
            return True

    # check positive-slope diagonal
    consecutive = 0
    offset = min(played_column, played_row)
    col = played_column - offset
    row = played_row - offset
    while col < COLS and row < ROWS:
        color = board.grid[col][row]
        if color == played_color:
            consecutive += 1
        else:
            consecutive = 0

        if consecutive == 4:
            return True

    # check negative-slope diagonal
    consecutive = 0
    col = played_column + offset
    row = played_row - offset
    while col > 0 and row < ROWS:
        color = board.grid[col][row]
        if color == played_color:
            consecutive += 1
        else:
            consecutive = 0

        if consecutive == 4:
            return True

    return False


def play_game():

    board = Board()
    print("New board initialized")

    turn = 0
    players = [Color.RED, Color.BLACK]
    while True:
        player = players[turn % (len(players))]
        print("{}'s turn.".format(player))
        col_num = int(input("Enter a column number: "))

        try:
            won = play_piece(board, col_num, player)
        except IllegalMove as e:
            print(e)
            continue

        if won:
            print("{} wins".format(player))
            break

        turn += 1


play_game()

def get_max_possible(coins, amount=0, turn=True):
    if not coins:
        return amount

    if turn:
        alt_1 = get_max_possible(coins[1:], amount + coins[0], False)
        alt_2 = get_max_possible(coins[:-1], amount + coins[-1], False)
        return max(alt_1, alt_2)

    first, last = coins[0], coins[-1]
    if first > last:
        coins = coins[1:]
    else:
        coins = coins[:-1]

    return get_max_possible(coins, amount, True)


# Test
assert get_max_possible([1, 2, 3, 4, 5]) == 9

def get_nth_sevenish(n):
    if n < 1:
        raise Exception("Invalid value for 'n'")

    power = 0
    sevenish_nums = list()
    while len(sevenish_nums) < n:
        num = 7 ** power
        new_sevenish_nums = [num]
        for old in sevenish_nums:
            if len(sevenish_nums) + len(new_sevenish_nums) == n:
                return new_sevenish_nums[-1]
            new_sevenish_nums.append(num + old)

        sevenish_nums += new_sevenish_nums
        power += 1

    return sevenish_nums[-1]


# Tests
assert get_nth_sevenish(1) == 1
assert get_nth_sevenish(2) == 7
assert get_nth_sevenish(3) == 8
assert get_nth_sevenish(10) == 350

PATH_SEPARATOR = "/"


def shorten_path(path):
    stack = list()
    dirs = path.split(PATH_SEPARATOR)

    for dir_name in dirs:
        if dir_name == ".":
            continue
        elif dir_name == "..":
            stack.pop()
        else:
            stack.append(dir_name)

    spath = PATH_SEPARATOR.join(stack)
    return spath


# Tests
assert shorten_path("/usr/bin/../bin/./scripts/../") == "/usr/bin/"

class Node:
    def __init__(self, val):
        self.val = val
        self.left = None
        self.right = None
        self.parent = None

    def __repr__(self):
        return "{}=[l={}, r={}]".format(self.val, self.left, self.right)


def add_reverse_links(root, parent=None):
    root.parent = parent

    if root.left:
        add_reverse_links(root.left, root)
    if root.right:
        add_reverse_links(root.right, root)


def print_inorder(root):
    if root.left:
        print_inorder(root.left)

    print(root.val)

    if root.right:
        print_inorder(root.right)


# Tests
a = Node('a')
b = Node('b')
c = Node('c')
d = Node('d')
e = Node('e')
f = Node('f')
g = Node('g')
h = Node('h')

a.left = b
a.right = c
b.left = d
b.right = e
c.left = f
c.right = g
d.right = h
# print(a)

add_reverse_links(a)
assert h.parent == d
assert g.parent == c

print_inorder(a)

def findSmallest(arr):
    res = 1
    for num in arr:
        if num > res:
            break
        res += num
    return res


# Tests
assert findSmallest([1, 2, 3, 10]) == 7
assert findSmallest([1, 2, 10]) == 4
assert findSmallest([0, 10]) == 1

def last_exec(n, k):
    last_exec = None
    next_exec_index = 0

    prisoners = list(range(1, n + 1))

    while prisoners:
        next_exec_index = (next_exec_index + k - 1) % len(prisoners)
        last_exec = prisoners[next_exec_index]
        prisoners = prisoners[:next_exec_index] + \
            prisoners[next_exec_index + 1:]

    return last_exec


# Tests
assert last_exec(5, 2) == 3
assert last_exec(3, 2) == 3
assert last_exec(5, 3) == 4

def update_letter_order(sorted_words, letters):
    order = list()
    new_words = dict()
    prev_char = None
    for word in sorted_words:
        if word:
            char = word[0]
            if char != prev_char:
                order.append(char)
            if char not in new_words:
                new_words[char] = list()
            new_words[char].append(word[1:])
            prev_char = char

    for index, char in enumerate(order):
        letters[char] |= set(order[index + 1:])

    for char in new_words:
        update_letter_order(new_words[char], letters)


def find_path(letters, start, path, length):
    if len(path) == length:
        return path

    if not letters[start]:
        return None

    for next_start in letters[start]:
        new_path = find_path(letters, next_start, path + [next_start], length)
        if new_path:
            return new_path


def update_letter_order_helper(sorted_words):
    letters = dict()
    for word in sorted_words:
        for letter in word:
            if letter not in letters:
                letters[letter] = set()

    update_letter_order(sorted_words, letters)

    max_children = max([len(x) for x in letters.values()])
    potential_heads = [x for x in letters if len(letters[x]) == max_children]

    path = None
    for head in potential_heads:
        path = find_path(letters, head, path=[head], length=len(letters))
        if path:
            break

    return path


# Tests
assert update_letter_order_helper(
    ['xww', 'wxyz', 'wxyw', 'ywx', 'ywz']) == ['x', 'z', 'w', 'y']

NUM_ROWS, NUM_COLS = 4, 4
WORD_END_CHAR = '0'


class Trie:
    def __init__(self):
        self.size = 0
        self.letter_map = dict()

    def __repr__(self):
        return str(self.letter_map)

    def add_word(self, word):
        if not word:
            self.letter_map[WORD_END_CHAR] = None
            return
        letter = word[0]

        sub_trie = None
        if letter in self.letter_map:
            sub_trie = self.letter_map[letter]
        else:
            sub_trie = Trie()
            self.letter_map[letter] = sub_trie

        self.size += 1
        sub_trie.add_word(word[1:])


class Coordinate():
    def __init__(self, x, y):
        self.x = x
        self.y = y

    def __hash__(self):
        return hash((self.x, self.y))

    def __eq__(self, other):
        return (self.x, self.y) == (other.x, other.y)

    def __ne__(self, other):
        return not(self == other)

    def __repr__(self):
        return "C(x={};y={})".format(self.x, self.y)


def get_adjacent_coords(x, y):
    adj_coords = set()

    red_x, red_y = max(0, x - 1), max(0, y - 1)
    inc_x, inc_y = min(NUM_ROWS - 1, x + 1), min(NUM_COLS - 1, y + 1)

    adj_coords.add(Coordinate(x, red_y))
    adj_coords.add(Coordinate(x, inc_y))
    adj_coords.add(Coordinate(red_x, y))
    adj_coords.add(Coordinate(red_x, red_y))
    adj_coords.add(Coordinate(red_x, inc_y))
    adj_coords.add(Coordinate(inc_x, y))
    adj_coords.add(Coordinate(inc_x, red_y))
    adj_coords.add(Coordinate(inc_x, inc_y))

    return adj_coords


def search_for_words(coord, dtrie, seen, board, sol_words, current):
    letter = board[coord.x][coord.y]
    if letter not in dtrie.letter_map:
        # no possibility of creating a word
        return

    current += letter
    next_trie = dtrie.letter_map[letter]
    if WORD_END_CHAR in next_trie.letter_map:
        # a word can end here
        sol_words.add(current)
        # shouldn't return because a valid word
        # might be extended

    adj_coords = get_adjacent_coords(coord.x, coord.y)
    for adj_coord in adj_coords:
        if adj_coord in seen:
            continue

        seen_cp = seen.copy()
        seen_cp.add(adj_coord)
        search_for_words(adj_coord, next_trie, seen_cp,
                         board, sol_words, current)


def solve_boggle(board, dictionary):
    assert len(board) == NUM_ROWS
    assert len(board[0]) == NUM_COLS

    dtrie = Trie()
    for word in dictionary:
        dtrie.add_word(word)

    sol_words = set()
    for i in range(NUM_ROWS):
        for k in range(NUM_COLS):
            coord = Coordinate(i, k)
            search_for_words(coord, dtrie, {coord}, board, sol_words, "")

    return sol_words


# Tests
board = [
    ["A", "L", "B", "P"],
    ["C", "O", "E", "Y"],
    ["F", "C", "H", "P"],
    ["B", "A", "D", "A"]
]
words_in_board = {
    "AFOCAL", "CHAPEL", "CLOCHE", "DHOLE", "LOCHE", "CHOLA", "CHELA",
    "HOLEY", "FOCAL", "FOLEY", "COLEY", "COLBY", "COHAB", "COBLE", "DACHA",
    "BACHA", "BACCO", "BACCA", "BLECH", "PHOCA", "ALOHA", "ALEPH", "CHAPE",
    "BOCCA", "BOCCE", "BOCHE", "LECH", "PECH", "OCHE", "FOAL", "YECH", "OBEY",
    "YEBO", "LOCA", "LOBE", "LOCH", "HYPE", "HELO", "PELA", "HOLE", "COCA"}
words_not_in_board = {
    "DUMMY", "WORDS", "FOR", "TESTING"
}
dictionary = words_in_board | words_not_in_board

found_words = solve_boggle(board, dictionary)

assert found_words == words_in_board

def get_largest(nums, prefix=""):
    num_dict = dict()
    for num in nums:
        str_num = str(num)
        fdig = str_num[0]
        if fdig not in num_dict:
            num_dict[fdig] = list()
        num_dict[fdig].append(str_num)

    sorted_arrs = sorted(num_dict.values(), key=lambda x: x[0], reverse=True)
    combined = list()
    for arr in sorted_arrs:
        if len(arr) == 1:
            combined.extend(arr)
            continue

        split_dict = dict()
        for num in arr:
            len_num = len(num)
            if len_num not in split_dict:
                split_dict[len_num] = list()
            split_dict[len_num].append(num)

        sorted_val_arrs = sorted(
            split_dict.values(), key=lambda x: len(x[0]))
        for val_arr in sorted_val_arrs:
            combined.extend(sorted(val_arr, reverse=True))

    return int(prefix.join(combined))


# Tests
assert get_largest([10, 7, 76, 415]) == 77641510

snakes = {16: 6, 48: 26, 49: 11, 56: 53, 62: 19, 64: 60, 87: 24, 93: 73, 95: 75, 98: 78}
ladders = {1: 38, 4: 14, 9: 31, 21: 42, 28: 84, 36: 44, 51: 67, 71: 91, 80: 100}

import sys

SNAKES = {16: 6, 48: 26, 49: 11, 56: 53, 62: 19,
          64: 60, 87: 24, 93: 73, 95: 75, 98: 78}
LADDERS = {1: 38, 4: 14, 9: 31, 21: 42,
           28: 84, 36: 44, 51: 67, 71: 91, 80: 100}
SHORCUTS = {**SNAKES, **LADDERS}
CACHE = dict()


def get_num_turns(pos, played_turns):
    if played_turns > 100 or pos > 100:
        return sys.maxsize

    if pos == 100:
        return played_turns

    if pos in CACHE:
        return CACHE[pos]

    if pos in SHORCUTS:
        num_turns = get_num_turns(SHORCUTS[pos], played_turns)
        CACHE[pos] = num_turns
        return CACHE[pos]

    possible_num_turns = list()
    for i in range(1, 7):
        num_turns = get_num_turns(pos + i, played_turns + 1)
        CACHE[pos + i] = num_turns
        possible_num_turns.append(num_turns)

    return min(possible_num_turns)


# Tests
assert get_num_turns(0, 0) == 24

def get_min_drops(N, k):
    if N == 0 or N == 1 or k == 1:
        return N

    possibilities = list()
    for i in range(1, N + 1):
        possibilities.append(
            max(get_min_drops(i-1, k-1),
                get_min_drops(N-i, k))
        )

    return min(possibilities) + 1


# Tests
assert get_min_drops(20, 2) == 6
assert get_min_drops(15, 3) == 5

from collections import Counter
from queue import Queue


def rearrange(string):
    c = Counter(string)
    sitems = sorted(c.items(), key=lambda x: x[1], reverse=True)

    strlen = len(string)
    if strlen % 2:
        if sitems[0][1] > (strlen // 2) + 1:
            return None
    else:
        if sitems[0][1] > (strlen // 2):
            return None

    q = Queue()
    for item in sitems:
        q.put(item)

    new_str = ""
    while not q.empty():
        item = q.get()
        new_str += item[0]
        item = (item[0], item[1] - 1)
        if item[1]:
            q.put(item)

    return new_str


# Tests
assert rearrange("aaabbc") == "abcaba"
assert rearrange("aaab") == None

mapsum.insert("columnar", 3)
assert mapsum.sum("col") == 3

mapsum.insert("column", 2)
assert mapsum.sum("col") == 5

class Trie:
    def __init__(self):
        self.size = 0
        self.value = 0
        self.letter_map = dict()

    def __repr__(self):
        return "{}: {}".format(self.letter_map, self.value)

    def add_word(self, word, value):
        if not word:
            self.value += value
            return
        letter = word[0]

        sub_trie = None
        if letter in self.letter_map:
            sub_trie = self.letter_map[letter]
        else:
            sub_trie = Trie()
            self.letter_map[letter] = sub_trie

        self.size += 1
        sub_trie.add_word(word[1:], value)
        self.value = sum([x.value for x in self.letter_map.values()])

    def find_prefix(self, word):
        if not word:
            return self.value

        letter = word[0]
        if letter in self.letter_map:
            sub_trie = self.letter_map[letter]
            return sub_trie.find_prefix(word[1:])

        return 0


class PrefixMapSum:

    def __init__(self, trie):
        self.trie = trie

    def insert(self, key, value):
        self.trie.add_word(key, value)

    def sum(self, prefix):
        return self.trie.find_prefix(prefix)


# Tests
pms = PrefixMapSum(Trie())
pms.insert("columnar", 3)
assert pms.sum("col") == 3
pms.insert("column", 2)
assert pms.sum("col") == 5

def get_fib(n):
    assert n > 0

    fib_a = 0
    fib_b = 1

    if n == 1:
        return fib_a
    elif n == 2:
        return fib_b

    fib_c = None
    for _ in range(n - 2):
        fib_c = fib_a + fib_b
        fib_a = fib_b
        fib_b = fib_c

    return fib_c


## Tests
assert get_fib(5) == 3
assert get_fib(2) == 1
assert get_fib(7) == 8

class Node:
    def __init__(self, val):
        self.val = val

    def __hash__(self):
        return hash(self.val)

    def __repr__(self):
        return str(self.val)


class Edge:
    def __init__(self, target, weight):
        self.target = target
        self.weight = weight

    def __hash__(self):
        return hash(self.target)

    def __repr__(self):
        return "-{}-> {}".format(self.weight, self.target)


class Graph:
    def __init__(self):
        self.nodes = set()
        self.edges = dict()

    def add_node(self, node):
        self.nodes.add(node)
        self.edges[node] = set()

    def add_edge(self, source, target, weight):
        if source not in self.nodes:
            self.add_node(source)
        if target not in self.nodes:
            self.add_node(target)

        self.edges[source].add(Edge(target, weight))
        self.edges[target].add(Edge(source, weight))


def get_max_span_helper(g, start, remaining, score):
    if not remaining:
        return score

    scores = list()
    for edge in g.edges[start]:
        if edge.target in remaining:
            rem_cp = remaining.copy()
            rem_cp.remove(edge.target)
            new_score = get_max_span_helper(
                g, edge.target, rem_cp, score + edge.weight)
            scores.append(new_score)

    return max(scores)


def get_max_span(g):
    remaining = g.nodes.copy()
    start_node = list(remaining)[0]
    remaining.remove(start_node)

    score = get_max_span_helper(g, start_node, remaining, 0)
    return score


# Tests
g = Graph()
a = Node('a')
b = Node('b')
c = Node('c')
g.add_edge(a, b, 1)
g.add_edge(a, c, 2)
g.add_edge(b, c, 3)


assert get_max_span(g) == 5

def find_min_max(nums):
    mini = maxi = nums[0]
    for num in nums[1:]:
        if num < mini:
            mini = num
            continue
        elif num > maxi:
            maxi = num

    return mini, maxi


# Tests
assert find_min_max([4, 3, 1, 2, 5]) == (1, 5)

## Transcribing a high-level solution I found

1. Draw a horizontal line to the right of each point and extend it to infinity
2. Count the number of times the line intersects with polygon edges.
3. A point is inside the polygon if either count of intersections is odd or point lies on an edge of polygon.  If none of the conditions is true, then point lies outside.

[Source](https://www.geeksforgeeks.org/how-to-check-if-a-given-point-lies-inside-a-polygon/)

        4
      / | \
    3   5   3
  /           \
9              9

class Node:
    def __init__(self, val):
        self.val = val
        self.children = list()

    def __repr__(self):
        return "{} -> {}".format(self.val, self.children)


def update_levels_dict(root, levels, lnum):
    if lnum not in levels:
        levels[lnum] = list()

    levels[lnum].append(root.val)
    for child in root.children:
        update_levels_dict(child, levels, lnum + 1)


def is_symmetric(tree):
    levels = dict()
    update_levels_dict(tree, levels, 0)

    for level in levels:
        arr = levels[level]
        if arr != arr[::-1]:
            return False

    return True


# Tests
e = Node(9)
f = Node(9)
d = Node(3)
d.children = [e]
c = Node(3)
c.children = [f]
b = Node(5)
a = Node(4)
a.children = [c, b, d]
assert is_symmetric(a)

c.val = 4
assert not is_symmetric(a)

from random import random

card_distribution = dict()


def generate_card_distribution():
    for i in range(1, 11):
        if i not in card_distribution:
            card_distribution[i] = 0

        if i == 10:
            card_distribution[i] += 4
        else:
            card_distribution[i] += 1
    summed = sum(card_distribution.values())

    prev = 0
    for key in card_distribution:
        card_distribution[key] = prev + (card_distribution[key]/summed)
        prev = card_distribution[key]


def get_next_card_value():
    rand = random()
    lower, upper = 0, None
    for key, value in card_distribution.items():
        upper = value
        if rand >= lower and rand <= upper:
            return key
        lower = upper


def play_turn(scores, dealer):
    if dealer and scores[1] < 16:
        next_card = get_next_card_value()
        scores[1] += next_card
        return True if scores[1] > 21 else False

    if scores[0] < 21:
        next_card = get_next_card_value()
        if scores[0] + next_card < 22:
            scores[0] += next_card

    return False


def play_game():
    scores = [0, 0]
    won = False
    dealer = False

    while not won:
        won = play_turn(scores, dealer)
        dealer = not dealer
        if scores[1] < scores[0]:
            print("Player wins")
            break


# Tests
generate_card_distribution()
play_game()

class Dialpad:
    def __init__(self):
        self.nodes = set(range(1, 10))
        self.edges = dict()
        self.edges[1] = {2, 4}
        self.edges[2] = {1, 3, 5}
        self.edges[3] = {2, 6}
        self.edges[4] = {1, 5, 7}
        self.edges[5] = {2, 4, 6, 8}
        self.edges[6] = {3, 5, 9}
        self.edges[7] = {4, 8}
        self.edges[8] = {5, 7, 9}
        self.edges[9] = {6, 8}


def count_code_helper(dp, code_len, curr, seen):
    if code_len == 0:
        return 1

    seen_cp = seen.copy()
    seen_cp.add(curr)

    nodes = dp.edges[curr]
    sub_count = 0
    for node in nodes:
        sub_count += count_code_helper(dp, code_len - 1, node, seen_cp)

    return sub_count


def count_codes(dp, code_len):
    if code_len == 1:
        return len(dp.nodes)

    count = 0
    for node in dp.nodes:
        count += count_code_helper(dp, code_len, node, set())

    return count


# Tests
dp = Dialpad()
assert count_codes(dp, 1) == 9
assert count_codes(dp, 2) == 68
assert count_codes(dp, 3) == 192

I think, at the most, `n-1` moves should be sufficient. 

def get_h_index(citations):
    citations.sort(reverse=True)

    for i, cit_count in enumerate(citations):
        if i >= cit_count:
            return i


# Tests
assert get_h_index([4, 3, 0, 1, 5]) == 3
assert get_h_index([4, 1, 0, 1, 1]) == 1
assert get_h_index([4, 4, 4, 5, 4]) == 4

class HourlySubscribers:
    def __init__(self):
        self.subscribers = [0] * 24

    def update(self, hour, value):
        self.subscribers[hour] += value

    def query(self, start, end):
        return sum(self.subscribers[start:end])


# Tests
hs = HourlySubscribers()
hs.update(2, 50)
hs.update(5, 110)
assert hs.query(1, 7) == 160

import sys


def split(arr, k):
    if k == 1:
        return ([arr], sum(arr))

    min_val = sys.maxsize
    min_cand = None
    for i in range(len(arr)):
        arr_1, sum_1 = ([arr[:i]], sum(arr[:i]))
        arr_2, sum_2 = split(arr[i:], k - 1)
        candidate = arr_1 + arr_2, max(sum_1, sum_2)
        if candidate[1] < min_val:
            min_val = candidate[1]
            min_cand = candidate

    return min_cand


def split_helper(arr, k):
    return split(arr, k)[1]


# Tests
assert split_helper([5, 1, 2, 7, 3, 4], 3) == 8

import time


def get_next_prime(primes_seen):
    num = primes_seen[-1] + 1
    while True:
        if all([num % x for x in primes_seen]):
            time.sleep(0.1)
            yield num
        num += 1


def print_primes():
    first_prime = 2
    primes_seen = [first_prime]
    print(first_prime)
    for next_prime in get_next_prime(primes_seen):
        primes_seen.append(next_prime)
        print(next_prime)


print_primes()

def get_min_jumps(arr):
    if len(arr) < 2:
        return 0

    start = arr[0]
    candidates = list()
    for i in range(1, min(start + 1, len(arr))):
        if arr[i] == 0:
            continue
        candidate = 1 + get_min_jumps(arr[i:])
        candidates.append(candidate)

    return min(candidates)


# Tests
assert get_min_jumps([6, 2, 4, 0, 5, 1, 1, 4, 2, 9]) == 2

def can_form_circle(curr_char, remaining_words, seen_circle, word_dict):
    if not remaining_words and curr_char == seen_circle[0][0]:
        print(seen_circle + [seen_circle[0]])
        return True

    if curr_char not in word_dict or not word_dict[curr_char]:
        return False

    next_words = word_dict[curr_char].copy()
    for next_word in next_words:
        word_dict_cp = word_dict.copy()
        word_dict_cp[curr_char].remove(next_word)
        if can_form_circle(next_word[-1], remaining_words - {next_word},
                           seen_circle + [next_word], word_dict_cp):
            return True

    return False


def create_word_dict(words):
    word_dict = dict()
    for word in words:
        start_char = word[0]
        if not start_char in word_dict:
            word_dict[start_char] = set()
        word_dict[start_char].add(word)
    return word_dict


def circle_helper(words):
    words = set(words)
    word_dict = create_word_dict(words)
    for word in words:
        curr_char = word[-1]
        if can_form_circle(curr_char, words - {word}, [word], word_dict):
            return True

    return False


# Tests
assert circle_helper(['chair', 'height', 'racket', 'touch', 'tunic'])
assert not circle_helper(['height', 'racket', 'touch', 'tunic'])
assert circle_helper(['abc', 'cba'])

class Node:
    def __init__(self):
        self.left = None
        self.right = None


def get_height(root):
    if not root:
        return 0

    left_height = get_height(root.left)
    right_height = get_height(root.right)

    return max(left_height, right_height) + 1


def is_balanced(root):
    left_height = get_height(root.left)
    right_height = get_height(root.right)

    return True if abs(left_height - right_height) < 2 else False


# Tests
a = Node()
b = Node()
c = Node()
a.left = b
assert is_balanced(a)
a.right = c
assert is_balanced(a)
d = Node()
e = Node()
b.left = d
d.left = e
assert not is_balanced(a)

def get_max(a, b):
    c = a-b
    k = (c >> 31) & 1
    return (a - k*c)


# Tests
assert get_max(5, 3) == 5
assert get_max(5, 10) == 10

import sys


def max_xor(arr):
    maxx = -sys.maxsize
    for i in range(len(arr) - 1):
        for k in range(i + 1, len(arr)):
            maxx = max(maxx, arr[i] ^ arr[k])

    return maxx


# Tests
assert max_xor([1, 2, 3, 4]) == 7

  SEND
+ MORE
--------
 MONEY

def get_num_from_string(char_map, string):
    power = 0
    total = 0
    for char in string[::-1]:
        total += char_map[char] * (10 ** power)
        power += 1

    return total


def is_valid_map(exp1, exp2, res, char_map):
    num1 = get_num_from_string(char_map, exp1)
    num2 = get_num_from_string(char_map, exp2)
    num3 = get_num_from_string(char_map, res)
    return num1 + num2 == num3


def evaluate_char_maps(exp1, exp2, res, char_maps):
    for char_map in char_maps:
        if is_valid_map(exp1, exp2, res, char_map):
            return char_map


def assign_letters(chars_left, nums_left, restrictions, char_map=dict()):
    if not chars_left:
        return [char_map]

    curr_char = list(chars_left)[0]
    char_maps = list()
    for num in nums_left:
        if num in restrictions[curr_char]:
            continue

        char_map_cp = char_map.copy()
        char_map_cp[curr_char] = num

        child_char_maps = assign_letters(
            chars_left - set([curr_char]),
            nums_left - set([num]),
            restrictions,
            char_map_cp)
        char_maps.extend(child_char_maps)

    return char_maps


def decode(exp1, exp2, res):
    characters = set(exp1) | set(exp2) | set(res)
    assert len(characters) < 11
    nums = set(range(0, 10))

    restrictions = dict()
    for char in characters:
        restrictions[char] = set()
    for word in [exp1, exp2, res]:
        restrictions[word[0]].add(0)

    char_maps = assign_letters(characters, nums, restrictions)
    return evaluate_char_maps(exp1, exp2, res, char_maps)


# Tests
assert decode("SEND", "MORE", "MONEY") == {
    'S': 9, 'E': 5, 'N': 6, 'D': 7, 'M': 1, 'O': 0, 'R': 8, 'Y': 2}

# Solution

* Stream the million numbers into a heap
* `O(log(n))` to insert each one

import math
from fractions import Fraction


def get_egypt_frac(fraction, prev_fracs=list()):
    if fraction.numerator == 1:
        prev_fracs.append(fraction)

        return prev_fracs

    egpyt_frac = Fraction(1, math.ceil(
        fraction.denominator / fraction.numerator))
    prev_fracs.append(egpyt_frac)

    new_frac = fraction - egpyt_frac
    return get_egypt_frac(new_frac, prev_fracs)


# Tests
assert get_egypt_frac(Fraction(4, 13)) == \
    [Fraction(1, 4), Fraction(1, 18), Fraction(1, 468)]

t     a     g
 h   s z   a
  i i   i z
   s     g

def print_zigzag(string, k):

    string_dict = dict()
    for row in range(k):
        string_dict[row] = ""

    crow = 0
    direction = -1
    for i in range(len(string)):
        for row in range(k):
            if row == crow:
                string_dict[row] += string[i]
            else:
                string_dict[row] += " "

        if crow == k-1 or crow == 0:
            direction *= -1

        crow += direction

    final_string = "\n".join([x for x in string_dict.values()])

    print(final_string)


# Tests
print_zigzag("thisisazigzag", 4)
print_zigzag("thisisazigzag", 5)

         a
      /     \
    b         c
  /            \
d                 e
  \             /   \
    f          g     h

class Node:
    def __init__(self, val):
        self.val = val
        self.left = None
        self.right = None

    def __repr__(self):
        return "{}=[{},{}]".format(self.val, self.left, self.right)

    def __hash__(self):
        return hash(self.val)


def recover_full(root):
    if not root.left and not root.right:
        return root
    elif root.left and root.right:
        root.left = recover_full(root.left)
        root.right = recover_full(root.right)
        return root
    elif root.left:
        return recover_full(root.left)
    elif root.right:
        return recover_full(root.right)


# Tests
a = Node("a")
b = Node("b")
c = Node("c")
d = Node("d")
e = Node("e")
f = Node("f")
g = Node("g")
h = Node("h")

a.left = b
a.right = c
b.left = d
d.right = f
c.right = e
e.left = g
e.right = h

print(a)
print(recover_full(a))

graph = [
    [0, 1, 3],
    [1, 2],
    [2],
    [3]
]

[1, 1, 1, 1]
[0, 1, 1, 0]
[0, 0, 1, 0]
[0, 0, 0, 1]

def update_transitive_closure(orig, node, adjacency_list, transitive_closure):
    if len(adjacency_list[node]) == 1:
        return

    for adj_node in adjacency_list[node]:
        if orig == adj_node or node == adj_node:
            continue
        transitive_closure[orig][adj_node] = 1
        update_transitive_closure(
            orig, adj_node, adjacency_list, transitive_closure)


def get_transitive_closure(adjacency_list):
    transitive_closure = \
        [[0 for _ in range(len(adjacency_list))]
         for _ in range(len(adjacency_list))]
    for i in range(len(adjacency_list)):
        transitive_closure[i][i] = 1

    for i in adjacency_list:
        update_transitive_closure(i, i, adjacency_list, transitive_closure)

    return transitive_closure


# Tests
adjacency_list = {
    0: [0, 1, 3],
    1: [1, 2],
    2: [2],
    3: [3]
}
assert get_transitive_closure(adjacency_list) == \
    [[1, 1, 1, 1],
     [0, 1, 1, 0],
     [0, 0, 1, 0],
     [0, 0, 0, 1]]

class Node:
    def __init__(self, x):
        self.val = x
        self.next = None

    def __str__(self):
        string = "["
        node = self
        while node:
            string += "{} ->".format(node.val)
            node = node.next
        string += "None]"
        return string


def get_nodes(values):
    next_node = None
    for value in values[::-1]:
        node = Node(value)
        node.next = next_node
        next_node = node

    return next_node


def get_list(head):
    node = head
    nodes = list()
    while node:
        nodes.append(node.val)
        node = node.next
    return nodes


def rearrange(llist):
    if not llist.next:
        return llist

    arr = get_list(llist)
    arr.sort()

    for i in range(2, len(arr), 2):
        tmp = arr[i]
        arr[i] = arr[i-1]
        arr[i-1] = tmp

    return get_nodes(arr)


# Tests
assert get_list(rearrange(get_nodes([1, 2, 3, 4, 5]))) == [1, 3, 2, 5, 4]

from heapq import heappush as hp


def get_sort_range(arr):
    if arr == sorted(arr):
        return ()

    options = list()
    for sort_start in range(len(arr) - 1):
        for sort_end in range(1, len(arr) + 1):
            a1 = arr[:sort_start]
            a2 = arr[sort_start:sort_end]
            a3 = arr[sort_end:]

            new_arr = a1 + sorted(a2) + a3
            if new_arr == sorted(new_arr):
                # options.append((sort_start, sort_end - 1))
                hp(options, (sort_end - sort_start, (sort_start, sort_end - 1)))

    return options[0][1]


# Test
assert get_sort_range([3, 5, 6, 7, 9]) == ()
assert get_sort_range([3, 7, 5, 6, 9]) == (1, 3)
assert get_sort_range([5, 4, 3, 2, 1]) == (0, 4)

       1
    /     \
  2         3
 / \       / \
4   5     6   7

class Node:
    def __init__(self, val):
        self.val = val
        self.ln = None
        self.rn = None

    def __repr__(self):
        return "Node=({}, ln={}, rn={})".format(
            self.val, self.ln, self.rn)


def get_bfs_alt(root, level, level_dict):
    if not root:
        return

    if level not in level_dict:
        level_dict[level] = list()
    level_dict[level].append(root.val)

    get_bfs_alt(root.ln, level + 1, level_dict)
    get_bfs_alt(root.rn, level + 1, level_dict)


def get_boustrophedon(root):
    level_dict = dict()
    get_bfs_alt(root, 0, level_dict)

    final_order = list()
    for i in range(len(level_dict)):
        final_order.extend(reversed(level_dict[i]) if i % 2 else level_dict[i])

    return final_order


# Tests
n1 = Node(1)
n2 = Node(2)
n3 = Node(3)
n4 = Node(4)
n5 = Node(5)
n6 = Node(6)
n7 = Node(7)

n2.ln = n4
n2.rn = n5
n3.ln = n6
n3.rn = n7
n1.ln = n2
n1.rn = n3

assert get_boustrophedon(n1) == [1, 3, 2, 4, 5, 6, 7]

Player 1: g
Player 2: h
Player 1: o
Player 2: s
Player 1: t [loses]

def get_optimal_chars(words):
    candidates = dict()
    for word in words:
        fc = word[0]
        if fc not in candidates:
            candidates[fc] = set()
        candidates[fc].add(len(word))

    opt_chars = set()
    for char in candidates:
        if all((not (x % 2)) for x in candidates[char]):
            opt_chars.add(char)

    return opt_chars


# Tests
assert get_optimal_chars(["cat", "calf", "dog", "bear"]) == set(['b'])
assert get_optimal_chars(["cat", "calf", "dog", "bear", "ao"]) == set(['b', 'a'])

def deduce_nums(arr):
    ln = len(arr)
    count_gt = sum([1 for x in arr if x == '+'])
    first = ln - count_gt - 1
    nums = [first]
    small, large = first - 1, first + 1
    for sym in arr[1:]:
        if sym == '+':
            nums.append(large)
            large += 1
        else:
            nums.append(small)
            small -= 1
    
    return nums


# Tests
assert deduce_nums([None, '+', '+', '-', '+']) == [1, 2, 3, 0, 4]

        *
      /   \
    *       *
   / \     / \
  *   a   t   *
 /             \
c               s

from queue import Queue


class Node:
    def __init__(self, char, count):
        self.ch = char
        self.ct = count
        self.lt = None
        self.rt = None

    def __repr__(self):
        return "{}=>[ct={},lt={},rt={}]".format(self.ch, self.ct, self.lt, self.rt)


def parse_queue_and_get_tree(nq):
    if nq.qsize() == 1:
        node = nq.get()
        return node

    n1 = nq.get()
    n2 = nq.get()

    par = Node(None, n1.ct + n2.ct)
    par.lt = n1
    par.rt = n2

    nq.put(par)

    return parse_queue_and_get_tree(nq)


def build_tree(words):
    ch_dict = dict()
    for word in words:
        for char in word:
            if not char in ch_dict:
                ch_dict[char] = 0
            ch_dict[char] += 1
    print(ch_dict)

    nodes = list()
    for char in ch_dict:
        nodes.append(Node(char, ch_dict[char]))
    nodes.sort(key=lambda x: x.ct)
    if not nodes:
        return Node(None, 0)

    nq = Queue()
    for node in nodes:
        nq.put(node)

    tree = parse_queue_and_get_tree(nq)
    return tree


def update_char_map(htree, char_map, hcode=""):
    if htree.ch:
        char_map[htree.ch] = hcode
        return

    update_char_map(htree.lt, char_map, hcode + "0")
    update_char_map(htree.rt, char_map, hcode + "1")


# Tests
htree = build_tree(["cats", "cars", "dogs"])
char_map = dict()
update_char_map(htree, char_map)
print(char_map)

htree = build_tree(["cat", "car", "dog"])
char_map = dict()
update_char_map(htree, char_map)
print(char_map)

* For each edge
    * Disconnect it
    * Choose a random node and try to visit all other nodes
    * If not possible label the edge as a 'bridge'

SEPARATORS = {',', ';', ':'}
TERM_MARKS = {'.', '?', '!'}


def is_valid(context, char, next_chars):
    curr_valid = True

    if not context and not char.istitle():
        return False

    if len(context) == 1:
        if char == ' ' or not char.istitle():
            pass
        else:
            return False

    if char in TERM_MARKS:
        return context[-1] not in (SEPARATORS | TERM_MARKS)

    if not next_chars:
        return char in TERM_MARKS and curr_valid

    return is_valid(context + char, next_chars[0], next_chars[1:]) if curr_valid else False


def is_valid_sentence(sentence):
    return is_valid("", sentence[0], sentence[1:])


# Test
assert is_valid_sentence("Valid sentence.")
assert not is_valid_sentence("Invalid sentence")
assert not is_valid_sentence("INvalid sentence.")
assert is_valid_sentence("A valid sentence.")

# NOTE: The answer in the problem description is incorrect since
# it doesn't include '100' or '110'


def generate_combos(chars, k, context=""):
    if not k:
        return set([context])

    combos = set()
    for ch in chars:
        combos |= generate_combos(chars, k-1, context + ch)

    return combos


def get_debruijn_seq(chars, combos, context=""):
    if not combos:
        return set([context])

    dseqs = set()
    if not context:
        for cb in combos:
            child_dseqs = get_debruijn_seq(
                chars, combos - set([cb]), cb)
            dseqs |= child_dseqs

        return dseqs

    for ch in chars:
        new_cb = context[-2:] + ch
        if new_cb in combos:
            child_dseqs = get_debruijn_seq(
                chars, combos - set([new_cb]), context + ch)
            dseqs |= child_dseqs

    return dseqs


# Tests
c, k = {'0', '1'}, 3
combos = generate_combos(c, k)
dseqs = get_debruijn_seq(c, combos)
assert all([all([cb in ds for cb in combos]) for ds in dseqs])

def get_segments(arr):
    asc = arr[1] > arr[0]
    prev = arr[0]
    start = 0
    segments = []
    for i, num in enumerate(arr[1:]):
        if (asc and num < prev) or (not asc and num > prev):
            segments.append((asc, i - start + 1))
            start = i + 1
            asc = not asc

        prev = num

    segments.append((asc, len(arr) - start))

    return segments


def get_bonuses(arr):
    if not arr:
        return []
    if len(arr) == 1:
        return [1]

    segments = get_segments(arr)
    bonuses = list()
    for segment in segments:
        asc, length = segment
        seg_bonuses = list(range(length))
        if not asc:
            seg_bonuses.reverse()
        bonuses.extend(seg_bonuses)

    bonuses = [x + 1 for x in bonuses]

    return bonuses


# Tests
assert get_bonuses([1000]) == [1]
assert get_bonuses([10, 40, 200, 1000, 60, 30]) == [1, 2, 3, 4, 2, 1]
assert get_bonuses([10, 40, 200, 1000, 900, 800, 30]) == [1, 2, 3, 4, 3, 2, 1]

ALPHA_SIZE = 26
APLHA_ASCII_OFFSET = 65


class WordCode:
    def __init__(self, word):
        self.word = word
        self.vec = [0 for _ in range(ALPHA_SIZE)]
        for ch in word:
            ind = ord(ch) - APLHA_ASCII_OFFSET
            self.vec[ind] += 1

    def __repr__(self):
        return "{}=>{}".format(self.word, self.vec)

    def __sub__(self, other):
        result = list()
        for i in range(ALPHA_SIZE):
            result.append(max(0, self.vec[i] - other.vec[i]))

        return result


def get_step_words(word, dictionary):
    step_words = set()
    wc = WordCode(word)
    for dword in dictionary:
        dwc = WordCode(dword)
        diff = dwc - wc
        if sum(diff) == 1:
            step_words.add(dword)

    return step_words


# Tests
assert get_step_words("APPLE", {"APPEAL"}) == {"APPEAL"}
assert get_step_words("APPLE", {"APPEAL", "APPLICT"}) == {"APPEAL"}
assert get_step_words("APPLE", {"APPEAL", "APPLICT", "APPLES"}) == {"APPEAL", "APPLES"}

...K....
........
.B......
......P.
.......R
..N.....
........
.....Q..

from enum import Enum


class Type(Enum):
    K = 0
    P = 1
    N = 2
    Q = 3
    R = 4
    B = 5


class Piece:
    def __init__(self, typ, loc):
        self.typ = typ
        self.loc = loc

    def __repr__(self):
        return "Piece=[type={}, loc={}]".format(self.typ, self.loc)


class Location:
    def __init__(self, x, y):
        self.x = x
        self.y = y

    def __repr__(self):
        return "Loc=[x={}, y={}]".format(self.x, self.y)


class Board:
    def __init__(self, matrix, pieces):
        self.matrix = matrix
        self.pieces = pieces


def read_board(board_str):
    rows = board_str.split("\n")
    pieces = list()
    king = None
    for i, row in enumerate(rows):
        for k, char in enumerate(row):
            if char == ".":
                continue

            pt = Type[char]
            loc = Location(i, k)
            piece = Piece(pt, loc)
            if pt == Type.K:
                king = piece
            else:
                pieces.append(piece)

    return king, pieces


def is_check_by_piece(kl, p):
    straight_attack = (p.loc.x == kl.x or p.loc.y == kl.y)

    dx = abs(p.loc.x - kl.x)
    dy = abs(p.loc.y - kl.y)
    diagonal_attack = (dx == dy)

    knight_attack = (dx * dy == 2)

    pawn_attack = (p.loc.y == kl.x - 1 or p.loc.y == kl.x + 1) and \
        p.loc.x == kl.x + 1

    if p.typ == Type.P:
        if pawn_attack:
            return True
    elif p.typ == Type.N:
        if knight_attack:
            return True
    elif p.typ == Type.R:
        if straight_attack:
            return True
    elif p.typ == Type.B:
        if diagonal_attack:
            return True
    elif p.typ == Type.Q:
        if straight_attack or diagonal_attack:
            return True


def in_check(board_str):
    king, pieces = read_board(board_str)

    for piece in pieces:
        if is_check_by_piece(king.loc, piece):
            print("In check by {}".format(piece))
            return True

    return False


# Tests
board_str = \
    "...K...." + "\n" + \
    "........" + "\n" + \
    ".B......" + "\n" + \
    "......P." + "\n" + \
    ".......R" + "\n" + \
    "..N....." + "\n" + \
    "........" + "\n" + \
    ".....Q.."
assert in_check(board_str)

def is_power_of_four(x):
    # https://stackoverflow.com/a/19611541/8650340

    return ((x & -x) & 0x55555554) == x


# Tests
assert is_power_of_four(4)
assert is_power_of_four(16)
assert is_power_of_four(64)
assert is_power_of_four(256)
assert not is_power_of_four(1)
assert not is_power_of_four(8)
assert not is_power_of_four(100)

def get_new_orientation_helper(dominos):
    changes = 0
    new_dominos = dominos.copy()

    for i in range(len(dominos)):
        if dominos[i] == 'L' and i > 0 and dominos[i-1] == '.' and dominos[i-2] != 'R':
            new_dominos[i-1] = 'L'
            changes += 1
        elif dominos[i] == 'R' and i < len(dominos) - 1 and dominos[i+1] == '.' and dominos[i+2] != 'L':
            new_dominos[i+1] = 'R'
            changes += 1

    return get_new_orientation_helper(new_dominos) if changes else dominos


def get_new_orientation(dominos):
    arr = list(dominos)
    arr = get_new_orientation_helper(arr)
    return "".join(arr)


# Tests
assert get_new_orientation(".L.R....L") == "LL.RRRLLL"
assert get_new_orientation("..R...L.L") == "..RR.LLLL"

edges = [
    (0, 1, 5),
    (0, 2, 3),
    (0, 5, 4),
    (1, 3, 8),
    (2, 3, 1),
    (3, 5, 10),
    (3, 4, 5)
]

def find_distance(target, edge_dict):
    if target == 0:
        return 0

    cand_target_distances = edge_dict[target]
    distances = list()
    for cand_tgt, cand_dist in cand_target_distances:
        dist = cand_dist + find_distance(cand_tgt, edge_dict)
        distances.append(dist)

    return min(distances)


def get_shortest_trip(edges, node_count):
    edge_dict = dict()
    for edge in edges:
        start, end, dist = edge
        if end not in edge_dict:
            edge_dict[end] = list()
        edge_dict[end].append((start, dist))

    distances = list()
    for target in set(range(1, node_count + 1)):
        dist = find_distance(target, edge_dict)
        distances.append(dist)

    return max(distances)


# Tests
edges = [
    (0, 1, 5),
    (0, 2, 3),
    (0, 5, 4),
    (1, 3, 8),
    (2, 3, 1),
    (3, 5, 10),
    (3, 4, 5)
]
assert get_shortest_trip(edges, 5) == 9

import bisect


def does_element_exist(arr, x):
    pos = bisect.bisect(arr, x)
    return pos and arr[pos - 1] == x


# Tests
assert does_element_exist([1, 3, 5, 7, 9], 3)
assert not does_element_exist([1, 3, 5, 7, 9], 6)
assert does_element_exist([1, 3, 5, 7, 9], 1)
assert not does_element_exist([1, 3, 5, 7, 9], 0)
assert not does_element_exist([1, 3, 5, 7, 9], 10)

def perm_counter(num_dice, face_range, total):
    if num_dice < 1 or total < 1:
        return 0
    elif num_dice == 1 and total in face_range:
        return 1

    return sum([perm_counter(num_dice - 1, face_range, total - x) for x in face_range])


def throw_dice(num_dice, faces, total):
    return perm_counter(num_dice, range(1, faces + 1), total)


# Tests
assert throw_dice(3, 6, 7) == 15

def get_fixed_point(arr):
    for i, num in enumerate(arr):
        if i == num:
            return i

    return False


# Tests
assert get_fixed_point([-6, 0, 2, 40]) == 2
assert get_fixed_point([1, 5, 7, 8]) == False

def eval_string(expr_string):
    return eval(expr_string)


# Tests
assert eval_string("-1 + (2 + 3)") == 4

1
11
21
1211
111221

def look_and_say(seq_count, num_str="1"):
    if seq_count == 1:
        return num_str

    tuples = [(0, num_str[0])]
    for char in num_str:
        prev_count, prev_char = tuples.pop()
        if char == prev_char:
            tuples.append((prev_count + 1, char))
        else:
            tuples.append((prev_count, prev_char))
            tuples.append((1, char))

    flat_list = [str(x) for tup in tuples for x in tup]
    new_num_str = "".join(flat_list)

    return look_and_say(seq_count - 1, new_num_str)


# Test
assert look_and_say(1) == "1"
assert look_and_say(5) == "111221"
assert look_and_say(6) == "312211"

def contains_pattern(string, pattern):
    if not string or not pattern:
        return False

    slen, plen = len(string), len(pattern)
    if plen > len(string):
        return False

    hashed_strings = set()
    for i in range(slen - plen + 1):
        hashed_strings.add(string[i:i+plen])

    return pattern in hashed_strings


# Tests
assert contains_pattern("abcabcabcd", "abcd")
assert not contains_pattern("abcabcabc", "abcd")

 Bytes   |           Byte format
-----------------------------------------------
   1     | 0xxxxxxx
   2     | 110xxxxx 10xxxxxx
   3     | 1110xxxx 10xxxxxx 10xxxxxx
   4     | 11110xxx 10xxxxxx 10xxxxxx 10xxxxxx

BLEN = 8
SHIFT_RES = {
    2: 6,
    3: 14,
    4: 30
}
TAIL_SHIFT = 6
TAIL_SHIFT_RES = 2


def is_valid_utf8(int_arr):
    ln = len(int_arr)
    if ln == 1:
        return int_arr[0] < 128

    first = int_arr[0]
    tail = int_arr[1:]

    sfirst = first >> (BLEN - ln - 1)
    if SHIFT_RES[ln] != sfirst:
        return False

    for num in tail:
        snum = num >> TAIL_SHIFT
        if snum != TAIL_SHIFT_RES:
            return False

    return True


# Tests
assert is_valid_utf8([226, 130, 172])
assert not is_valid_utf8([226, 194, 172])
assert not is_valid_utf8([226])
assert is_valid_utf8([100])
assert is_valid_utf8([194, 130])

from copy import deepcopy


class Node:
    def __init__(self, val):
        self.val = val
        self.l, self.r = None, None

    def __repr__(self):
        return "[{}=>(l={}, r={})]".format(self.val, self.l, self.r)


def get_trees(nodes):
    if not nodes:
        return []
    elif len(nodes) == 1:
        return deepcopy(nodes)

    trees = list()
    for ind, root in enumerate(nodes):
        lefts = get_trees(nodes[:ind]) if ind > 0 else list()
        rights = get_trees(nodes[ind + 1:]) if ind < len(nodes) - 1 else list()

        for left in lefts:
            for right in rights:
                root.l = deepcopy(left)
                root.r = deepcopy(right)
                trees.append(deepcopy(root))

    return trees


def create_trees(n):
    nodes = [Node(x) for x in range(n)]
    return get_trees(nodes)


# Tests
trees = create_trees(5)
print(trees)

{
    0: [1, 2],
    1: [0, 5],
    2: [0],
    3: [6],
    4: [],
    5: [1],
    6: [3]
}

import random


def populate_group(node, adj_list, group):
    group.add(node)

    adj_nodes = adj_list[node]
    if not adj_nodes:
        return

    for anode in adj_nodes:
        if anode not in group:
            populate_group(anode, adj_list, group)


def get_groups(nodes, adj_list, groups):
    num_nodes = len(nodes)
    while num_nodes:
        new_group = set()
        node = list(nodes)[0]
        populate_group(node, adj_list, new_group)
        groups.append(new_group)
        nodes -= new_group
        num_nodes = len(nodes)

    return groups


def get_num_groups(nodes, adj_list):
    groups = list()
    isolated = set()
    for node in nodes:
        if not adj_list[node]:
            isolated.add(node)

    for node in isolated:
        groups.append({node})
        nodes.remove(node)
        del adj_list[node]

    groups = get_groups(nodes, adj_list, groups)
    print(groups)
    return len(groups)


# Tests
adj_list = {
    0: [1, 2],
    1: [0, 5],
    2: [0],
    3: [6],
    4: [],
    5: [1],
    6: [3]
}
assert get_num_groups(set(range(7)), adj_list) == 3

class Node:
    def __init__(self, val):
        self.val = val
        self.adj_nodes = set()

    def __hash__(self):
        return hash(self.val)

    def __repr__(self):
        return self.val


class Graph:
    def __init__(self, nodes):
        self.nodes = nodes
        self.unseen_nodes = None

    def has_cycle_helper(self, node, path=list()):
        if node in self.unseen_nodes:
            self.unseen_nodes.remove(node)

        for adj_node in node.adj_nodes:
            if adj_node in path and adj_node != path[-1]:
                return True

            if self.unseen_nodes:
                return self.has_cycle_helper(adj_node, path + [node])

        return False

    def has_cycle(self):
        start_node = next(iter(self.nodes))
        self.unseen_nodes = self.nodes.copy()
        return self.has_cycle_helper(start_node)


# Tests
a = Node("a")
b = Node("b")
c = Node("c")

a.adj_nodes = {b}
b.adj_nodes = {c}
c.adj_nodes = {a}

g1 = Graph({a, b, c})
assert g1.has_cycle()

a.adj_nodes = {b, c}
b.adj_nodes = set()
c.adj_nodes = set()
g2 = Graph({a, b, c})
assert not g2.has_cycle()

[[3, 5, 1, 1],
 [2, 3, 3, 2],
 [5, 5],
 [4, 4, 2],
 [1, 3, 3, 3],
 [1, 1, 6, 1, 1]]

from collections import Counter


def get_min_cuts(brick_wall):

    for i in range(len(brick_wall)):
        # Make wall of cumulative brick lengths
        prev_bricks_len = 0
        for k in range(len(brick_wall[i])):
            brick_wall[i][k] += prev_bricks_len
            prev_bricks_len = brick_wall[i][k]
        brick_wall[i] = brick_wall[i][:-1]

    # Find the most common edge to cut down through
    brick_counter = Counter()
    for row in brick_wall:
        brick_counter.update(row)

    most_common_bricks = brick_counter.most_common()
    bricks_avoided = most_common_bricks[0][1] if most_common_bricks else 0

    return len(brick_wall) - bricks_avoided


# Tests
brick_wall = [[3, 5, 1, 1],
              [2, 3, 3, 2],
              [5, 5],
              [4, 4, 2],
              [1, 3, 3, 3],
              [1, 1, 6, 1, 1]]
assert get_min_cuts(brick_wall) == 2

brick_wall = [[1]]
assert get_min_cuts(brick_wall) == 1

brick_wall = [[1],
              [1, 2]]
assert get_min_cuts(brick_wall) == 1

brick_wall = [[1, 2],
              [1, 2]]
assert get_min_cuts(brick_wall) == 0

def contains_pytrip(arr):
    squared = [x * x for x in arr]
    set_of_squares = set(squared)
    for i in range(len(squared) - 1):
        for k in range(i + 1, len(squared) - 1):
            summed = squared[i] + squared[k]
            if summed in set_of_squares:
                return True

    return False


# Tests
assert contains_pytrip([3, 4, 5, 6, 7])
assert not contains_pytrip([3, 5, 6, 7])

from heapq import heappop, heappush

start_factor_counts = {2: 2, 3: 1, 5: 1}


def get_val_from_count(factor_counts):
    total = 1
    for key in factor_counts:
        total *= key * factor_counts[key]
    return total


def populate_heap(n, heap, regular_nums):
    if len(regular_nums) >= n:
        return

    lowest_val, lowest_factors = heappop(heap)
    regular_nums.add(lowest_val)
    for key in lowest_factors:
        lf_copy = lowest_factors.copy()
        lf_copy[key] += 1
        heappush(heap, (lowest_val * key, lf_copy))

    populate_heap(n, heap, regular_nums)


def get_n_regular(n, factor_counts=dict()):
    factor_counts = start_factor_counts

    heap, regular_nums = list(), set()
    heappush(heap, (get_val_from_count(factor_counts), factor_counts))
    populate_heap(n, heap, regular_nums)

    return sorted(regular_nums)


# Tests
assert get_n_regular(10) == [60, 120, 180, 240, 300, 360, 480, 540, 600, 720]

    1
   / \
  2   3
 / \   \
4   5   6

class Node:
    def __init__(self, val):
        self.val = val
        self.lev = None
        self.l = None
        self.r = None
        self.p = None

    def __repr__(self):
        return "{} = (l={}, r={})".format(self.val, self.l, self.r)

    def __hash__(self):
        return hash(self.val)


def populate_level_map(node, level_map, parent=None, level=0):
    if not node:
        return

    node.p = parent
    node.lev = level

    if level not in level_map:
        level_map[level] = set()
    level_map[level].add(node)

    populate_level_map(node.l, level_map, node, level + 1)
    populate_level_map(node.r, level_map, node, level + 1)


def get_cousins(root, node):
    level_map = dict()
    populate_level_map(root, level_map)

    cousins = set([x for x in level_map[node.lev] if x.p != node.p])
    return cousins


# Tests
a = Node(1)
b = Node(2)
c = Node(3)
d = Node(4)
e = Node(5)
f = Node(6)
a.l, a.r = b, c
b.l, b.r = d, e
c.r = f

assert get_cousins(a, d) == {f}
assert get_cousins(a, f) == {d, e}
assert get_cousins(a, a) == set()
assert get_cousins(a, c) == set()

def get_sunset_bldgs(buildings):
    sbs = list()

    for height in buildings:
        if sbs and sbs[-1] < height:
            sbs.pop()
        sbs.append(height)

    return sbs


# Tests
assert get_sunset_bldgs([3, 7, 8, 3, 6, 1]) == [8, 6, 1]

     ______  
    |      |        ___
 ___|      |___    |   | 
|   |   B  |   |   | C |
| A |      | A |   |   |
|   |      |   |   |   |
------------------------

import sys


def get_max_width(buildings):
    leftmost, rightmost = sys.maxsize, -sys.maxsize
    for start, end, _ in buildings:
        if start < leftmost:
            leftmost = start
        if end > rightmost:
            rightmost = end

    return rightmost - leftmost + 1


def get_skyline(buildings):
    skyline_width = get_max_width(buildings)
    fill_arr = [0 for _ in range(skyline_width)]

    for start, end, height in buildings:
        for col in range(start, end):
            fill_arr[col] = max(fill_arr[col], height)

    skyline = list()
    prev_height = None
    for col, col_height in enumerate(fill_arr):
        if not skyline or prev_height != col_height:
            skyline.append((col, col_height))
        prev_height = col_height

    return skyline


# Tests
assert get_skyline([(0, 15, 3), (4, 11, 5), (19, 23, 4)]) == \
    [(0, 3), (4, 5), (11, 3), (15, 0), (19, 4), (23, 0)]

[('a', 1), ('a', 3), ('a', 5),
 ('b', 2), ('b', 6),
 ('c', 1), ('c', 2), ('c', 3), ('c', 4), ('c', 5),
 ('d', 4), ('d', 5), ('d', 6), ('d', 7),
 ('e', 1), ('e', 3), ('e', 5), ('e', 6)]

from heapq import heappush


def get_similarity_score(users_a, users_b):
    union = users_a | users_b
    intersect = users_a & users_b

    return len(intersect) / len(union)


def get_similar_websites(visits, k=1):
    website_users = dict()
    for website, user in visits:
        if website not in website_users:
            website_users[website] = set()
        website_users[website].add(user)

    websites = list(website_users.keys())

    most_similar = list()
    for i in range(len(websites) - 1):
        for j in range(i + 1, len(websites)):
            web_a, web_b = websites[i], websites[j]
            sim_score = get_similarity_score(website_users[web_a], website_users[web_b])
            heappush(most_similar, (-sim_score, (web_a, web_b)))

    most_similar = [y for x, y in most_similar]

    return most_similar[:k]


# Tests
visits = [
    ("a", 1),
    ("a", 3),
    ("a", 5),
    ("b", 2),
    ("b", 6),
    ("c", 1),
    ("c", 2),
    ("c", 3),
    ("c", 4),
    ("c", 5),
    ("d", 4),
    ("d", 5),
    ("d", 6),
    ("d", 7),
    ("e", 1),
    ("e", 3),
    ("e", 5),
    ("e", 6),
]
assert get_similar_websites(visits, 1) == [("a", "e")]
assert get_similar_websites(visits, 3) == [("a", "e"), ("a", "c"), ("b", "d")]

4321 - 1234 = 3087
8730 - 0378 = 8352
8532 - 2358 = 6174

KAP_CONST = 6174


def apply_kproc(num, steps=0):
    if num == KAP_CONST:
        return steps

    digits = str(num)
    assert len(set(digits)) > 2

    asc_num = "".join(sorted(digits))
    dsc_num = "".join(sorted(digits, reverse=True))

    diff = int(dsc_num) - int(asc_num)
    return apply_kproc(diff, steps + 1)


# Tests
assert apply_kproc(KAP_CONST) == 0
assert apply_kproc(1234) == 3

# Source: https://en.wikipedia.org/wiki/Nim#Mathematical_theory


def has_forced_win(heaps):
    x = heaps[0]
    for heap in heaps[1:]:
        x ^= heap

    for heap in heaps:
        xa = heap ^ x
        if xa < heap:
            return True

    return False


# Tests
assert has_forced_win((3, 4, 5))

        Arrangement       |   Change
----------------------------------------
['R', 'G', 'B', 'G', 'B'] | (R, G) -> B
['B', 'B', 'G', 'B']      | (B, G) -> R
['B', 'R', 'B']           | (R, B) -> G
['B', 'G']                | (B, G) -> R
['R']                     |

COLORS = {"R", "G", "B"}


def get_odd_man(col_a, col_b):
    return list(COLORS - set([col_a, col_b]))[0]


def minimize(quixes):
    stack = list()
    for quix in quixes:
        if not stack or stack[-1] == quix:
            stack.append(quix)
            continue

        new = get_odd_man(quix, stack[-1])
        stack.pop()
        stack.append(new)
        while len(stack) > 1 and stack[-1] != stack[-2]:
            a, b = stack.pop(), stack.pop()
            stack.append(get_odd_man(a, b))

    return stack


# Tests
assert minimize(["R", "G", "B", "G", "B"]) == ["R"]

BOAT_LIMIT = 200


def get_min_boats_helper(people, boats_used):
    if len(people) < 2:
        return boats_used + len(people)

    first = people[0]
    remaining = people[1:]
    if first == BOAT_LIMIT:
        return get_min_boats_helper(remaining, boats_used + 1)

    allowed = BOAT_LIMIT - first
    second_index = len(remaining) - 1
    while allowed >= people[second_index]:
        second_index -= 1

    if second_index == len(remaining):
        return get_min_boats_helper(remaining, boats_used + 1)

    return get_min_boats_helper(remaining[:second_index] + remaining[second_index + 1:], boats_used + 1)


def get_min_boats(people):
    return get_min_boats_helper(sorted(people, reverse=True), 0)


# Tests
assert get_min_boats([100, 200, 150, 80]) == 3

students = {
    0: [3],
    1: [2],
    2: [1, 4],
    3: [0, 4, 5],
    4: [2, 3],
    5: [3]
}

students = {
    0: [3],
    1: [2],
    2: [1, 3, 4],
    3: [0, 2, 4, 5],
    4: [2, 3],
    5: [3]
}

class Group:
    def __init__(self):
        self.members = set()
        self.enemies = set()

    def __repr__(self):
        return str(self.members)

    def add_student(self, student, enemies):
        self.members.add(student)
        self.enemies |= set(enemies)


def get_groups(enemy_map):
    students = enemy_map.keys()
    first, second = Group(), Group()
    for student in students:
        if not first.members:
            first.add_student(student, enemy_map[student])
        elif student not in first.enemies:
            first.add_student(student, enemy_map[student])
        elif not second.members:
            second.add_student(student, enemy_map[student])
        elif student not in second.enemies:
            second.add_student(student, enemy_map[student])

    if len(first.members) + len(second.members) == len(students):
        return first.members, second.members

    return False


# Tests
enemy_map = {
    0: [3],
    1: [2],
    2: [1, 4],
    3: [0, 4, 5],
    4: [2, 3],
    5: [3]
}
assert get_groups(enemy_map) == ({0, 1, 4, 5}, {2, 3})

enemy_map = {
    0: [3],
    1: [2],
    2: [1, 3, 4],
    3: [0, 2, 4, 5],
    4: [2, 3],
    5: [3]
}
assert get_groups(enemy_map) == False

from typing import List


def construct_pyramid(length: int):
    assert length % 2

    peak = (length//2) + 1
    start = [x for x in range(1, peak)]
    pyramid = start + [peak] + list(reversed(start))

    return pyramid


def get_pyramid(stones: List[int]):
    len_stones = len(stones)
    len_pyr = len_stones if len_stones % 2 else len_stones - 1

    while len_pyr > 0:
        max_pyr = construct_pyramid(len_pyr)

        for offset in (0, len_stones - len_pyr):
            valid = True
            for pyr_index, pyr_num in enumerate(max_pyr):
                stone_index = pyr_index + offset
                if pyr_num > stones[stone_index]:
                    valid = False
                    break

            if valid:
                return ([0] * offset) + max_pyr + ([0] * (len_stones - offset - len_pyr))

        len_pyr -= 2

    return []


# Tests
assert get_pyramid([1, 1, 3, 3, 2, 1]) == [0, 1, 2, 3, 2, 1]
assert get_pyramid([1, 1, 1, 1, 1]) == [1, 0, 0, 0, 0]
assert get_pyramid([1, 1, 1, 5, 1]) == [0, 0, 1, 2, 1]

elevations = {0: 5, 1: 25, 2: 15, 3: 20, 4: 10}
paths = {
    (0, 1): 10,
    (0, 2): 8,
    (0, 3): 15,
    (1, 3): 12,
    (2, 4): 10,
    (3, 4): 5,
    (3, 0): 17,
    (4, 0): 10
}

import sys


def get_shortest_path(
        target, elevations, path_map, path_so_far,
        elevations_so_far, distance, switches):

    if 0 == target and path_so_far:
        return path_so_far, distance if switches < 2 else sys.maxsize

    min_dist, min_path = sys.maxsize, None
    for src, dist in path_map[target]:
        if src == target:
            continue

        new_switches = switches + 1 \
            if elevations_so_far and elevations[src] > elevations_so_far[0] \
            else switches

        new_path_so_far, new_dist = get_shortest_path(
            src, elevations, path_map, [src] + path_so_far,
            [elevations[target]] + elevations_so_far, distance + dist, new_switches)

        if new_dist < min_dist:
            min_dist = new_dist
            min_path = new_path_so_far

    return min_path, min_dist


def get_shortest_path_helper(elevations, paths):
    path_map = dict()
    for (src, tgt), dist in paths.items():
        if tgt not in path_map:
            path_map[tgt] = list()
        path_map[tgt].append((src, dist))

    shortest_path, _ = get_shortest_path(
        0, elevations, path_map, list(), list(), 0, 0)

    return shortest_path


# Tests
elevations = {0: 5, 1: 25, 2: 15, 3: 20, 4: 10}
paths = {
    (0, 1): 10,
    (0, 2): 8,
    (0, 3): 15,
    (1, 3): 12,
    (2, 4): 10,
    (3, 4): 5,
    (3, 0): 17,
    (4, 0): 10,
}
assert get_shortest_path_helper(elevations, paths) == [0, 2, 4]

    1
   1 1
  1 2 1
 1 3 3 1
1 4 6 4 1

def get_pastri_row(k, row=None):
    assert k and k > 0

    if not row:
        row = [0 for _ in range(k)]
        row[0] = 1

    if k == 1:
        return row

    row = get_pastri_row(k - 1, row)
    for i in range(len(row) - 1, 0, -1):
        row[i] += row[i - 1]

    return row


# Tests
assert get_pastri_row(1) == [1]
assert get_pastri_row(3) == [1, 2, 1]
assert get_pastri_row(5) == [1, 4, 6, 4, 1]

class Node:
    def __init__(self, val):
        self.val = val
        self.l = None
        self.r = None

    def __repr__(self):
        return "{}=[l={}, r={}]".format(self.val, self.l, self.r)


def get_hbal_tree(arr):
    if not arr:
        return None

    mid = len(arr) // 2
    node = Node(arr[mid])
    node.l = get_hbal_tree(arr[:mid])
    node.r = get_hbal_tree(arr[mid + 1 :])

    return node


# Tests
assert get_hbal_tree([1, 2, 3, 4, 5]).val == 3
assert get_hbal_tree([1, 2, 3, 4, 5, 6]).val == 4

preferences = {
    0: [0, 1, 3, 6],
    1: [1, 4, 7],
    2: [2, 4, 7, 5],
    3: [3, 2, 5],
    4: [5, 8]
}

from typing import Dict, List


def minimize_drinks(drinks, remaining_drinks, remaining_customers, cust_by_drink):
    min_option = drinks

    if not remaining_customers:
        return drinks - remaining_drinks

    for drink in remaining_drinks:
        option = minimize_drinks(
            drinks, remaining_drinks - {drink},
            remaining_customers - cust_by_drink[drink], cust_by_drink)
        if len(option) < len(min_option):
            min_option = option

    return min_option


def get_min_drinks(preferences: Dict[int, List[int]]):
    cust_by_drink = dict()
    for cust in preferences:
        for drink in preferences[cust]:
            if drink not in cust_by_drink:
                cust_by_drink[drink] = set()
            cust_by_drink[drink].add(cust)

    remaining_drinks = set(cust_by_drink.keys())
    remaining_customers = set(preferences.keys())
    min_drinks = minimize_drinks(set(cust_by_drink.keys()), remaining_drinks,
                                 remaining_customers, cust_by_drink)
    return min_drinks


# Tests
preferences = {
    0: [0, 1, 3, 6],
    1: [1, 4, 7],
    2: [2, 4, 7, 5],
    3: [3, 2, 5],
    4: [5, 8]
}
assert get_min_drinks(preferences) == {1, 5}

from typing import List, Dict
from copy import deepcopy


class AppleSet:
    def __init__(self):
        self.apple_types = dict()

    def __repr__(self):
        return str(self.apple_types)

    def add_apple(self, atype: int):
        if atype not in self.apple_types:
            self.apple_types[atype] = 0
        self.apple_types[atype] += 1

    def remove_apple(self, atype: int):
        self.apple_types[atype] -= 1
        if self.apple_types[atype] == 0:
            del self.apple_types[atype]

    def size(self):
        return len(self.apple_types)

    def total(self):
        return sum(x for x in self.apple_types.values())


def get_min_set(apple_set: AppleSet, apples: List[int]):
    if apple_set.size() == 2:
        return apple_set.total()
    if not apples:
        return 0

    first, last = apples[0], apples[-1]

    apple_set_1 = deepcopy(apple_set)
    apple_set_1.remove_apple(first)
    alt_1 = get_min_set(apple_set_1, apples[1:])

    apple_set_2 = deepcopy(apple_set)
    apple_set_2.remove_apple(last)
    alt_2 = get_min_set(apple_set_2, apples[:-1])

    return max(alt_1, alt_2)


def get_longest_portion(apples: List[int]):
    apple_set = AppleSet()
    for atype in apples:
        apple_set.add_apple(atype)

    return get_min_set(apple_set, apples)


# Tests
assert get_longest_portion([2, 1, 2, 3, 3, 1, 3, 5]) == 4
assert get_longest_portion([2, 1, 2, 2, 2, 1, 2, 1]) == 8
assert get_longest_portion([1, 2, 3, 4]) == 2

def connect_houses(pipe_costs, houses, total_cost):
    if not houses:
        return total_cost

    costs = list()
    for start_node in (pipe_costs.keys() - houses):
        for adj_node in (pipe_costs[start_node].keys() & houses):
            cost = connect_houses(pipe_costs, houses - {adj_node},
                                  total_cost + pipe_costs[start_node][adj_node])
            costs.append(cost)

    return min(costs)


def get_min_cost(pipe_costs):
    houses = pipe_costs.keys() - {'plant'}
    return connect_houses(pipe_costs, houses, 0)


# Tests
pipe_costs = {
    'plant': {'A': 1, 'B': 5, 'C': 20},
    'A': {'C': 15},
    'B': {'C': 10},
    'C': {}
}
assert get_min_cost(pipe_costs) == 16

from heapq import heappush, heapify


class VoterFraudException(Exception):
    pass


class Candidate:
    def __init__(self, name: int):
        self.name = name
        self.vote_count = 0

    def __eq__(self, other):
        return self.vote_count == other.vote_count

    def __lt__(self, other):
        return self.vote_count < other.vote_count

    def __gt__(self, other):
        return self.vote_count > other.vote_count

    def __repr__(self):
        return "Candidate: {}, Votes: {}".format(self.name, self.vote_count)


class VotingMachine:
    def __init__(self):
        self.votes = dict()
        self.leaderboard = list()
        self.voters = set()

    def cast_vote(self, candidate: int, voter: int):
        if voter in self.voters:
            raise VoterFraudException(
                "Fraud committed by voter {}".format(voter))
        self.voters.add(voter)

        if not candidate in self.votes:
            cand_obj = Candidate(candidate)
            heappush(self.leaderboard, cand_obj)
            self.votes[candidate] = cand_obj
        cand_obj = self.votes[candidate]
        cand_obj.vote_count += 1

    def get_top_three(self):
        heapify(self.leaderboard)
        return [x.name for x in self.leaderboard[-3:]]


def process_votes(vm, file_contents):
    for (candidate, voter) in file_contents:
        vm.cast_vote(candidate, voter)


# Tests
file_contents = [
    (0, 0),
    (0, 1),
    (1, 2),
    (1, 3),
    (1, 4),
    (1, 5),
    (2, 6)
]
vm = VotingMachine()
process_votes(vm, file_contents)
assert vm.get_top_three() == [2, 0, 1]
process_votes(vm, [(2, 0)])

from hashlib import md5, sha256
from binascii import unhexlify


class BloomFilter:
    def __init__(self):
        self.vector = 0

    def get_hash(self, value):
        return int.from_bytes(
            unhexlify(md5(value.encode("UTF-8")).hexdigest()),
            byteorder='little')

    def add(self, value):
        hashed = self.get_hash(value)
        self.vector |= hashed

    def check(self, value):
        hashed = self.get_hash(value)
        for a, b in zip(bin(hashed)[2:], bin(self.vector)[2:]):
            if bool(int(a)) and not bool(int(b)):
                return False
        return True


# Tests
bf = BloomFilter()
bf.add("test1")
bf.add("test2")
assert bf.check("test1")
assert not bf.check("test3")

\    /
 \  /
  \/

from typing import Set
from random import sample


class Coord:
    def __init__(self, x, y):
        self.x = x
        self.y = y

    def __hash__(self):
        return hash("{}-{}".format(self.x, self.y))

    def __eq__(self, other):
        return self.x == other.x and self.y == other.y

    def __repr__(self):
        return "[x={}, y={}]".format(self.x, self.y)


def explore_region(start: Coord, empty_spaces: Set, nrows: int, ncols: int):
    if start not in empty_spaces:
        return

    empty_spaces.remove(start)
    if start.x > 0:
        explore_region(Coord(start.x - 1, start.y), empty_spaces, nrows, ncols)
    if start.x < nrows - 1:
        explore_region(Coord(start.x + 1, start.y), empty_spaces, nrows, ncols)
    if start.y > 0:
        explore_region(Coord(start.x, start.y - 1), empty_spaces, nrows, ncols)
    if start.y < ncols - 1:
        explore_region(Coord(start.x, start.y + 1), empty_spaces, nrows, ncols)


def get_region_count(text: str):
    matrix = text.splitlines()
    nrows, ncols = len(matrix), len(matrix[0])
    for i in range(nrows):
        matrix[i] = [x for x in matrix[i]]

    empty_spaces = set()
    for row in range(nrows):
        for col in range(ncols):
            if matrix[row][col] == " ":
                empty_spaces.add(Coord(row, col))

    regions = 0
    while empty_spaces:
        start = sample(empty_spaces, 1)[0]
        explore_region(start, empty_spaces, nrows, ncols)
        regions += 1

    return regions


# Tests
matrix = \
    "\\    /\n" + \
    " \\  / \n" + \
    "  \\/  "
assert get_region_count(matrix) == 3

matrix = \
    "     /\n" + \
    " \\  / \n" + \
    "  \\/  "
assert get_region_count(matrix) == 2

matrix = \
    "     /\n" + \
    " \\  / \n" + \
    "  \\   "
assert get_region_count(matrix) == 1

from math import isclose

FLOAT_EQUALITY_TOLERANCE = 0.5


def get_angle_for_hour(hour: int, minute: int):
    minute_offset = minute / 12
    hour_angle = (hour * 30) + minute_offset
    return hour_angle


def get_angle_for_minute(minute: int):
    return minute * 6


def get_angle(hhmm_time: str):
    hour, minute = map(int, hhmm_time.split(":"))
    hour %= 12
    ha = get_angle_for_hour(hour, minute)
    ma = get_angle_for_minute(minute)

    angle = abs(ha - ma)
    return angle if angle < 180 else 360 - angle


# Tests
assert isclose(get_angle("12:20"), 118, abs_tol=FLOAT_EQUALITY_TOLERANCE)
assert isclose(get_angle("12:00"), 0, abs_tol=FLOAT_EQUALITY_TOLERANCE)
assert isclose(get_angle("6:30"), 3, abs_tol=FLOAT_EQUALITY_TOLERANCE)
assert isclose(get_angle("3:45"), 176, abs_tol=FLOAT_EQUALITY_TOLERANCE)

from typing import Set, List


BOARD_SIZE = 8
POSSIBLE_MOVES = 8
CACHE = dict()
KNIGHT_RANGE = [-2, -1, 1, 2]


class Position:
    def __init__(self, x: int, y: int):
        self.x = x
        self.y = y

    def __hash__(self) -> int:
        return hash((self.x, self.y))

    def __eq__(self, other) -> bool:
        return self.x == other.x and self.y == other.y

    def __repr__(self) -> str:
        return "Pos[x={},y={}]".format(self.x, self.y)

    def is_valid(self) -> bool:
        return self.x > 0 and self.x <= BOARD_SIZE and self.y > 0 and self.y <= BOARD_SIZE


def get_valid_moves(start: Position) -> Set[Position]:
    if start in CACHE:
        return CACHE[start]

    candidates = set()
    for hor in KNIGHT_RANGE:
        for ver in KNIGHT_RANGE:
            if abs(hor) + abs(ver) == 3:
                candidates.add(Position(start.x + hor, start.y + ver))
    val_candidates = [pos for pos in candidates if pos.is_valid()]

    CACHE[start] = val_candidates

    return val_candidates


def explore(start: Position, turns: int, counts: List) -> None:
    if not turns:
        return

    valid_moves = get_valid_moves(start)
    counts[0] += POSSIBLE_MOVES
    counts[1] += len(valid_moves)

    for next_pos in valid_moves:
        explore(next_pos, turns - 1, counts)


def get_prob_remain(start: Position, turns: int) -> float:
    global CACHE
    CACHE = dict()

    counts = [0, 0]
    explore(start, turns, counts)

    return counts[1] / counts[0]


# Tests
assert get_prob_remain(Position(4, 4), 1) == 1.0
assert get_prob_remain(Position(1, 1), 3) < 0.66

class Node:
    def __init__(self, x):
        self.val = x
        self.cum = 0
        self.next = None

    def __str__(self):
        string = "["
        node = self
        while node:
            string += "{},{} ->".format(node.val, node.cum)
            node = node.next
        string += "None]"
        return string


def get_nodes(values):
    next_node = None
    for value in values[::-1]:
        node = Node(value)
        node.next = next_node
        next_node = node

    return next_node


def get_list(head):
    node = head
    nodes = list()
    while node:
        nodes.append(node.val)
        node = node.next
    return nodes


def add_cum_sum(head):
    node = head
    cum_sum = 0
    while node:
        node.cum = node.val + cum_sum
        cum_sum = node.cum
        node = node.next


def remove_zero_sum(head):
    add_cum_sum(head)
    dummy_head = Node(None)
    dummy_head.next = head

    seen_totals = dict()
    node = dummy_head
    index = 0
    while node:
        if node.cum in seen_totals:
            seen_totals[node.cum].next = node.next
        seen_totals[node.cum] = node
        index += 1
        node = node.next

    return dummy_head.next


# Tests
llist = get_nodes([3, 4, -7, 5, -6, 6])
assert get_list(remove_zero_sum(llist)) == [5]

def sort_k(arr, k):
    arr = sorted(arr[:k]) + arr[k:]
    for i in range(k, len(arr)):
        start, end = i-k+1, i+1
        p, n = arr[:start], arr[end:]
        sub = sorted(arr[start:end])
        arr = p + sub + n
    return arr


# Test
assert sort_k([1, 0, 2, 4, 3], 2) == [0, 1, 2, 3, 4]

import bisect


class Node:
    def __init__(self, val):
        self.val = val
        self.l = None
        self.r = None


def get_arr(root):
    if not root:
        return list()

    return get_arr(root.l) + [root.val] + get_arr(root.r)


def get_fc(root, val):
    arr = get_arr(root)
    ind = bisect.bisect(arr, val)
    if ind == 0:
        return None, arr[0]
    elif ind == len(arr):
        return arr[-1], None
    elif val == arr[ind-1]:
        return val, val
    else:
        return arr[ind-1], arr[ind]


# Tests
a = Node(4)
b = Node(2)
c = Node(1)
d = Node(3)
b.l = c
b.r = d
e = Node(6)
a.l = b
a.r = e

assert get_fc(a, 2) == (2, 2)
assert get_fc(a, 7) == (6, None)
assert get_fc(a, -1) == (None, 1)
assert get_fc(a, 5) == (4, 6)

SYMBOLS = {'|', '&', '^'}


class Boolean:
    def __init__(self, exp, val, fe, se):
        self.exp = exp
        self.val = val
        self.fe = fe
        self.se = se


def evaluator(arr):
    expr = "".join(arr)
    if len(arr) == 1 or len(arr) == 3:
        return [Boolean(expr, eval(expr), arr[0], arr[2] if len(arr) > 2 else None)]

    groupings = list()
    for i in range(len(arr) // 2):
        pivot = i*2 + 1
        first = arr[:pivot]
        second = arr[pivot + 1:]

        for fe in evaluator(first):
            for se in evaluator(second):
                new_exp = str(fe.val) + arr[pivot] + str(se.val)
                groupings.append(Boolean(
                    new_exp, eval(new_exp), fe, se))

    return groupings


def get_groupings(arr):
    if not arr:
        return []

    for ind in range(len(arr)):
        if arr[ind] == 'F':
            arr[ind] = 'False'
        elif arr[ind] == 'T':
            arr[ind] = 'True'
    groupings = evaluator(arr)
    return groupings


# Tests
assert len(get_groupings(['F', '|', 'T', '&', 'T'])) == 2
assert len(get_groupings(['F', '|', 'T', '&', 'T', '^', 'F'])) == 5

import sys
from itertools import permutations


def get_people_indices(arr):
    return set([x for x, y in enumerate(arr) if y == 1])


def get_min_dist(vacant_spots, available_people):
    min_dist = sys.maxsize
    perms = list(permutations(range(len(vacant_spots))))
    for perm in perms:
        dist = 0
        for i in range(len(vacant_spots)):
            k = perm[i]
            dist += abs(vacant_spots[i] - available_people[k])
        min_dist = min(min_dist, dist)
    return min_dist


def get_lowest_cost(arr):
    num_people = sum(arr)
    ovr_people_indices = set([x for x, y in enumerate(arr) if y == 1])

    lowest_cost = sys.maxsize
    for offset in range(len(arr) - num_people + 1):
        subarr = arr[offset:offset + num_people]
        all_indices = set([offset + x for x in range(num_people)])
        people_indices = set([offset + x for x in get_people_indices(subarr)])

        vacant_indices = list(all_indices - people_indices)
        occupied_ovr_indices = list(ovr_people_indices - people_indices)

        lowest_cost = min(lowest_cost, get_min_dist(
            vacant_indices, occupied_ovr_indices))

    return lowest_cost


# Tests
assert get_lowest_cost([0, 1, 1, 0, 1, 0, 0, 0, 1]) == 5

def get_set_bits(num):
    if not num:
        return 0

    max_pow, max_pow_of_two = 0, 1
    while max_pow_of_two - 1 <= num:
        max_pow_of_two *= 2
        max_pow += 1
    max_pow_of_two //= 2
    max_pow -= 1

    remainder = num - (max_pow_of_two - 1)
    set_bits = ((max_pow * max_pow_of_two) // 2)

    set_bits = set_bits + get_set_bits(remainder)

    return set_bits


# Tests
assert get_set_bits(0) == 0
assert get_set_bits(1) == 1
assert get_set_bits(2) == 2
assert get_set_bits(3) == 4
assert get_set_bits(4) == 5

def find_peak(arr):
    if not arr:
        return None

    mid = len(arr) // 2

    if mid > 0 and arr[mid] > arr[mid - 1] and \
            mid < len(arr) and arr[mid] > arr[mid + 1]:
        return arr[mid]

    if mid > 0 and arr[mid] > arr[mid - 1]:
        return find_peak(arr[:mid])

    return find_peak(arr[mid + 1:])


# Tests
assert find_peak([0, 2, 4, 5, 3, 1]) == 5

A B B C
A B C C

def get_arrangement_count(free_spaces):
    if not free_spaces:
        return 1
    elif free_spaces < 2:
        return 0

    arrangements = 0
    if free_spaces >= 3:
        arrangements += (2 + get_arrangement_count(free_spaces - 3))
    arrangements += (2 + get_arrangement_count(free_spaces - 2))

    return arrangements


def count_arragements(columns):
    return get_arrangement_count(columns * 2)


# Tests
assert count_arragements(4) == 32

from typing import Set


class Combo:
    def __init__(self, key_1: int, key_2: int, key_3: int):
        self.key_1 = key_1 if key_1 > -1 else key_1 + 10
        self.key_2 = key_2 if key_1 > -1 else key_1 + 10
        self.key_3 = key_3 if key_1 > -1 else key_1 + 10

    def __hash__(self):
        return hash((self.key_1, self.key_2, self.key_3))

    def __eq__(self, other):
        return \
            self.key_1 == other.key_1 and \
            self.key_2 == other.key_2 and \
            self.key_3 == other.key_3

    def __repr__(self):
        return "{}-{}-{}".format(self.key_1, self.key_2, self.key_3)


def get_moves(target: Combo, deadends: Set[Combo],
              start: Combo = Combo(0, 0, 0)):
    if start == target:
        return 0
    elif start in deadends:
        return None

    if start.key_1 != target.key_1:
        k1_moves = list()
        k1_diff = abs(start.key_1 - target.key_1)
        k1_new_start = Combo(target.key_1, start.key_2, start.key_3)
        k1_moves = [
            k1_diff + get_moves(target, deadends, k1_new_start),
            (10 - k1_diff) + get_moves(target, deadends, k1_new_start)
        ]
        k1_moves = [x for x in k1_moves if x]
        if k1_moves:
            return min(k1_moves)

    if start.key_2 != target.key_2:
        k2_moves = list()
        k2_diff = abs(start.key_1 - target.key_1)
        k2_new_start = Combo(start.key_1, target.key_2, start.key_3)
        k2_moves = [
            k2_diff + get_moves(target, deadends, k2_new_start),
            (10 - k2_diff) + get_moves(target, deadends, k2_new_start)
        ]
        k2_moves = [x for x in k2_moves if x]
        if k2_moves:
            return min(k2_moves)

    if start.key_2 != target.key_3:
        k3_moves = list()
        k3_diff = abs(start.key_1 - target.key_1)
        k3_new_start = Combo(start.key_1, start.key_2, target.key_3)
        k3_moves = [
            k3_diff + get_moves(target, deadends, k3_new_start),
            (10 - k3_diff) + get_moves(target, deadends, k3_new_start)
        ]
        k3_moves = [x for x in k3_moves if x]
        if k3_moves:
            return min(k3_moves)

    return None


# Tests
assert get_moves(target=Combo(3, 4, 5), deadends={Combo(6, 6, 6)}) == 13

from typing import List, Set


def get_closest_tower_dist(start: int, end: int, towers: Set[int], dist_so_far: int):
    if start in towers or end in towers:
        return dist_so_far

    return get_closest_tower_dist(start - 1, end + 1, towers, dist_so_far + 1)


def get_max_range(listeners: List[int], towers: List[int]):
    max_dist = 0
    for listener in listeners:
        closest_dist = get_closest_tower_dist(
            listener, listener, set(towers), 0)
        max_dist = max(max_dist, closest_dist)

    return max_dist


# Tests
assert get_max_range([1, 5, 11, 20], [4, 8, 15]) == 5

1 2 3 4 8
5 1 2 3 4
4 5 1 2 3
7 4 5 1 2

def check_diagonal(start, matrix, val, rows, cols):
    if start[0] == rows or start[1] == cols:
        return True

    if matrix[start[0]][start[1]] == val:
        return check_diagonal((start[0] + 1, start[1] + 1), matrix, val, rows, cols)

    return False


def is_toeplitz(matrix):
    rows, cols = len(matrix), len(matrix[0])
    for ind in range(rows):
        val = matrix[ind][0]
        if not check_diagonal((ind + 1, 1), matrix, val, rows, cols):
            return False

    for ind in range(1, cols):
        val = matrix[0][ind]
        if not check_diagonal((1, ind + 1), matrix, val, rows, cols):
            return False

    return True


# Tests
matrix = [[1, 2, 3, 4, 8], [5, 1, 2, 3, 4], [4, 5, 1, 2, 3], [7, 4, 5, 1, 2]]
assert is_toeplitz(matrix)
matrix = [[1, 2, 3, 0, 8], [5, 1, 2, 3, 4], [4, 5, 1, 2, 3], [7, 4, 5, 1, 2]]
assert not is_toeplitz(matrix)

from typing import List


def get_ways_to_produce(num: int, factors: List[int]):
    if not num or num in factors:
        return 1

    ways = 0
    for i, factor in enumerate(factors):
        if num % factor == 0:
            ways += get_ways_to_produce(num // factor, factors[i:])

    return ways


def get_denominators(ways_to_produce: List[int]):
    factors = [i for i, num in enumerate(ways_to_produce)
               if (num == 1 and i > 0)]

    for i, num in enumerate(ways_to_produce):
        if get_ways_to_produce(i, factors) == num - 1:
            factors.append(i)

    return factors


# Tests
assert get_denominators([1, 0, 1, 1, 2]) == [2, 3, 4]

# if there are 2 consecutive numbers, the least significant
# bit will be 0 once, which means the result of an AND on
# the last bit will be zero
from math import log2, ceil


def bitwise_and_slow(start, end):
    result = end
    for num in range(start, end):
        result &= num

    return result


def bitwise_and(start, end):
    diff = end - start + 1
    power_diff = ceil(log2(diff))
    power_end = ceil(log2(end))

    result = start & (2**power_end - 2**power_diff)
    return result


# Tests
assert bitwise_and_slow(5, 6) == 4
assert bitwise_and(5, 6) == 4
assert bitwise_and_slow(126, 127) == 126
assert bitwise_and(126, 127) == 126
assert bitwise_and_slow(129, 215) == 128
assert bitwise_and(193, 215) == 192

import random
from copy import deepcopy


class Node:
    def __init__(self, val):
        self.val = val
        self.prev = None
        self.next = None

    def __hash__(self):
        return hash(self.val)

    def __eq__(self, other):
        return self.val == other.val

    def __repr__(self):
        return str(self.val)


class LRUCache:
    def __init__(self, size):
        self.head = Node(None)
        self.tail = Node(None)
        self.head.next = self.tail
        self.tail.prev = self.head
        self.size = size
        self.recent_nodes = dict()

    def use(self, val):
        if val in self.recent_nodes:
            used_node = self.recent_nodes[val]
            used_node.prev = used_node.next
        elif len(self.recent_nodes) == self.size:
            used_node = Node(val)
            del self.recent_nodes[self.head.next.val]
            self.head.next = self.head.next.next
        else:
            used_node = Node(val)

        before_tail = self.tail.prev
        before_tail.next = used_node
        used_node.next = self.tail
        used_node.prev = before_tail
        self.tail.prev = used_node
        self.recent_nodes[val] = used_node


def count_playlists(song_ids, cache, plays_left):
    if plays_left == 0:
        return 1

    total = 0
    for song_id in song_ids:
        if song_id in cache.recent_nodes:
            continue
        new_cache = deepcopy(cache)
        new_cache.use(song_id)
        total += count_playlists(song_ids, new_cache, plays_left - 1)

    return total


def get_valid_playlists(plays, songs, buffer):
    song_ids = set(range(songs))
    lru_cache = LRUCache(buffer)

    total = count_playlists(song_ids, lru_cache, plays)
    return total


# Tests
assert get_valid_playlists(6, 4, 2) > get_valid_playlists(6, 4, 3)

FINAL_STATE = [
    [1, 2, 3],
    [4, 5, 6],
    [7, 8, None]
]


class Coord:
    def __init__(self, x, y):
        self.x = x
        self.y = y

    def __hash__(self):
        return hash((self.x, self.y))

    def __eq__(self, other):
        return self.x == other.x and self.y == other.y

    def __repr__(self):
        return "({}, {})".format(self.x, self.y)


def get_adj_nums(empty_pos, num_rows, num_cols):
    adj_nums = set()
    if empty_pos.x > 0:
        if empty_pos.y > 0:
            adj_nums.add(Coord(empty_pos.x - 1, empty_pos.y - 1))
        if empty_pos.y < num_cols - 1:
            adj_nums.add(Coord(empty_pos.x - 1, empty_pos.y + 1))
    if empty_pos.y < num_rows - 1:
        if empty_pos.y > 0:
            adj_nums.add(Coord(empty_pos.x + 1, empty_pos.y - 1))
        if empty_pos.y < num_cols - 1:
            adj_nums.add(Coord(empty_pos.x + 1, empty_pos.y + 1))

    return adj_nums


def play(grid, empty_pos, num_rows, num_cols):
    if grid == FINAL_STATE:
        return

    adj_nums = get_adj_nums(empty_pos, num_rows, num_cols)
    for adj_num in adj_nums:
        new_grid = grid.copy()
        new_grid[empty_pos.x][empty_pos.y] = grid[adj_num.x][adj_num.y]
        new_grid[adj_num.x][adj_num.y] = None
        return play(new_grid, adj_num, num_rows, num_cols)


def win_game(grid):
    empty_pos = None
    for x, row in enumerate(grid):
        for y, val in enumerate(row):
            if not val:
                empty_pos = Coord(x, y)

    play(grid, empty_pos, len(start), len(start[0]))


# Tests
start = [
    [1, 2, 3],
    [4, 5, None],
    [7, 8, 6]
]
assert win_game(start)

from sys import maxsize


def check_string(string, start, end, unique_chars):
    substr = string[start:end]
    if start == end or len(set(substr)) < unique_chars:
        return maxsize

    can_1 = check_string(string, start, end - 1, unique_chars)
    can_2 = check_string(string, start + 1, end, unique_chars)

    return min(len(substr), min(can_1, can_2))


def get_longest_distinct_window(string):
    if not string:
        return 0

    return check_string(string, 0, len(string), len(set(string)))


# Tests
assert get_longest_distinct_window("jiujitsu") == 5
assert get_longest_distinct_window("jiujiuuts") == 6

def get_closest_factors(num):
    a, b = 1, num
    pa, pb = 1, 1
    while b > a:
        if num % a == 0:
            pa, pb = a, num // a
        b = num / a
        a += 1

    return (pa, pb)


def reduce(num):
    if num == 1:
        return [1]

    # permitted step 1
    next_steps = reduce(num - 1)

    # permitted step 2
    _, large_factor = get_closest_factors(num)
    if large_factor < num:
        # only consider this option if the number is not a prime
        alt_2 = reduce(large_factor)
        if len(next_steps) > len(alt_2):
            # if it's a better option that decrementing by 1, use it
            next_steps = alt_2

    return [num] + next_steps


# Tests
assert reduce(100) == [100, 10, 9, 3, 2, 1]
assert reduce(50) == [50, 10, 9, 3, 2, 1]
assert reduce(64) == [64, 8, 4, 2, 1]
assert reduce(31) == [31, 30, 6, 3, 2, 1]

def jump_to_target(num):
    abs_num = abs(num)
    if abs_num < 2:
        return abs_num

    point, new_point = None, 0
    jump = 1
    while new_point <= abs_num:
        point = new_point
        new_point += jump
        jump += 1
    jump -= 2

    return (2 * (abs_num - point)) + jump


# Tests
assert jump_to_target(0) == 0
assert jump_to_target(1) == 1
assert jump_to_target(2) == 3
assert jump_to_target(3) == 2
assert jump_to_target(-3) == 2
assert jump_to_target(10) == 4
assert jump_to_target(11) == 6

from heapq import heappush
from random import randint


def approx_median(arr):
    if not arr:
        return None

    sarr = list()
    for _ in range(len(arr)//2):
        rand = randint(0, len(arr) - 1)
    heappush(sarr, arr[rand])

    return sarr[len(sarr)//2]


# Tests
print(approx_median([3, 4, 3, 2, 4, 3, 1, 4, 3,
                     4, 2, 3, 4, 3, 0, 4, 0, 0, 1, 1, 0, 1, 2]))

import sys


def get_min_steps(mice, holes, largest_step=-sys.maxsize):
    if not mice:
        return largest_step

    mouse = mice[0]
    min_steps = list()
    for hole in holes:
        diff = abs(mouse - hole)
        min_steps.append(
            get_min_steps(mice[1:], holes - {hole}, max(largest_step, diff))
        )

    return min(min_steps)


# Tests
assert get_min_steps(mice=[1, 4, 9, 15], holes={10, -5, 0, 16}) == 6

class UnitConverter:
    def __init__(self):
        self.conv_unit = None
        self.units = dict()

    def add_unit(self, unit_tuple, quantities):
        (known_unit, new_unit) = unit_tuple
        if not self.conv_unit:
            self.conv_unit = known_unit
            self.units[known_unit] = 1

        assert known_unit in self.units or unit_tuple[1] in self.units
        self.units[new_unit] = \
            (quantities[1] / quantities[0]) * \
            self.units[known_unit]

    def convert(self, source_unit, source_quantity, target_unit):
        assert source_unit in self.units and target_unit in self.units
        source_conv = source_quantity / self.units[source_unit]
        return round(source_conv * self.units[target_unit], 2)


# Tests
uc = UnitConverter()
uc.add_unit(("inch", "foot"), (12, 1))
uc.add_unit(("foot", "yard"), (3, 1))
uc.add_unit(("yard", "chain"), (22, 1))
assert uc.convert("inch", 24, "foot") == 2.0
assert uc.convert("inch", 36, "yard") == 1
assert uc.convert("inch", 48, "yard") == 1.33
assert uc.convert("foot", 4, "yard") == 1.33
assert uc.convert("chain", 2, "inch") == 1584.0
assert uc.convert("chain", 3, "foot") == 198.0

      1
    /   \   
  2       9
 / \
3   6

from typing import List


class Node:
    def __init__(self, val: int):
        self.val = val
        self.l = None
        self.r = None

    def __repr__(self):
        return "{}=[l->{}, r->{}]".format(self.val, self.l, self.r)


def make_cartree(arr: List[int], last: Node, root: Node):
    if not arr:
        return root

    node = Node(arr[0])
    if not last:
        return make_cartree(arr[1:], node, node)

    if last.val > node.val:
        node.l = last
        return make_cartree(arr[1:], node, node)

    last.r = node
    return make_cartree(arr[1:], last, last)


# Tests
cartree = make_cartree([3, 2, 6, 1, 9], None, None)
assert str(cartree) == \
    "1=[l->2=[l->3=[l->None, r->None], " + \
    "r->6=[l->None, r->None]], " + \
    "r->9=[l->None, r->None]]"

class Node:
    def __init__(self, val):
        self.val = val
        self.l = None
        self.r = None

    def __repr__(self):
        return "{}".format(self.val)


def merge(t1, t2, final_prev, left):
    if not t1 and not t2:
        return

    if t1 and t2:
        final_node = Node(t1.val + t2.val)
        if left:
            final_prev.l = final_node
        else:
            final_prev.r = final_node
        merge(t1.l, t2.l, final_node, True)
        merge(t1.r, t2.r, final_node, False)
        return

    only_node = t1 if t1 else t2
    if left:
        final_prev.l = only_node
    else:
        final_prev.r = only_node


# Tests
root_1 = Node(1)
root_1.l = Node(2)
root_1.r = Node(3)
root_1.l.l = Node(4)

root_2 = Node(2)

final_root = Node(0)
merge(root_1, root_2, final_root, True)
assert final_root.l.val == 3

class EloRatings:
    START_RATING = 1000

    def __init__(self):
        self.ratings = dict()

    def add_player(self, name):
        self.ratings[name] = EloRatings.START_RATING

    def add_result(self, p1, p2, winner):
        if p1 not in self.ratings:
            self.add_player(p1)
        if p2 not in self.ratings:
            self.add_player(p2)

        if not winner:
            if self.ratings[p1] == self.ratings[p2]:
                return

            diff = self.ratings[p1] // 20 \
                if self.ratings[p1] > self.ratings[p2] \
                else -self.ratings[p2] // 20

            self.ratings[p1] -= diff
            self.ratings[p2] += diff
        else:
            loser = p2 if winner == p1 else p1
            diff = self.ratings[loser] // 10
            self.ratings[loser] -= diff
            self.ratings[winner] += diff


# Tests
elo = EloRatings()
elo.add_player("a")
elo.add_player("b")
elo.add_player("c")
elo.add_result("a", "b", "a")
elo.add_result("a", "b", "b")
elo.add_result("a", "b", None)

guy_preferences = {
    'andrew': ['caroline', 'abigail', 'betty'],
    'bill': ['caroline', 'betty', 'abigail'],
    'chester': ['betty', 'caroline', 'abigail'],
}
gal_preferences = {
    'abigail': ['andrew', 'bill', 'chester'],
    'betty': ['bill', 'andrew', 'chester'],
    'caroline': ['bill', 'chester', 'andrew']
}

def find_matches(guy_pref, gal_pref):
    if not guy_pref:
        return []

    matches = list()
    taken_guys, taken_gals = set(), set()
    for guy in guy_preferences:
        gal = guy_pref[guy][0]
        pref_guy = gal_pref[gal][0]
        if pref_guy == guy:
            matches.append((guy, gal))
            taken_guys.add(guy)
            taken_gals.add(gal)

    if not matches:
        for guy in guy_preferences:
            gal = guy_pref[guy][0]
            matches.append((guy, gal))
        return matches

    for (guy, gal) in matches:
        del guy_pref[guy]
        del gal_pref[gal]

        for rguy in guy_pref:
            guy_pref[rguy] = [x for x in guy_pref[rguy] if x not in taken_gals]
        for rgal in gal_pref:
            gal_pref[rgal] = [x for x in gal_pref[rgal] if x not in taken_guys]

    return matches + find_matches(guy_pref, gal_pref)


# Tests
guy_preferences = {
    'andrew': ['caroline', 'abigail', 'betty'],
    'bill': ['caroline', 'betty', 'abigail'],
    'chester': ['betty', 'caroline', 'abigail'],
}
gal_preferences = {
    'abigail': ['andrew', 'bill', 'chester'],
    'betty': ['bill', 'andrew', 'chester'],
    'caroline': ['bill', 'chester', 'andrew']
}
assert find_matches(guy_preferences, gal_preferences) == \
    [('bill', 'caroline'), ('andrew', 'abigail'), ('chester', 'betty')]

(¬c OR b) AND (b OR c) AND (¬b OR c) AND (¬c OR ¬a)

NOT_SYMBOL = "¬"
OR_SYMBOL = "OR"
AND_SYMBOL = "AND"


def get_solution(string, symbols):
    power = len(symbols)
    count_sol = 2 ** power

    sol = None
    for solution in range(count_sol):
        bin_rep = format(solution, '0' + str(power) + 'b')

        new_str = string[:]
        for i in range(power):
            val = str(bool(int(bin_rep[i])))
            new_str = new_str.replace(symbols[i], val)
            new_str = new_str.replace(NOT_SYMBOL, "not ")
            new_str = new_str.replace(OR_SYMBOL, "or")
            new_str = new_str.replace(AND_SYMBOL, "and ")

        if eval(new_str) == True:
            sol = bin_rep
            break

    if not sol:
        return None

    solution_map = dict()
    for i in range(power):
        solution_map[symbols[i]] = bool(int(sol[i]))
    return solution_map


# Tests
assert get_solution(
    "(¬c OR b) AND (b OR c) AND (¬b OR c) AND (¬c OR ¬a)",
    ['a', 'b', 'c']
) == {'a': False, 'b': True, 'c': True}

def get_flip_count(string):
    strlen = len(string)

    last_x_pos, first_y_pos = strlen, -1
    for i in range(strlen):
        if string[i] == 'y':
            first_y_pos = i
            break
    for i in range(strlen):
        index = strlen - i - 1
        if string[index] == 'x':
            last_x_pos = index
            break

    x_count, y_count = 0, 0
    for i in range(last_x_pos):
        if string[i] == 'y':
            y_count += 1
    for i in range(first_y_pos + 1, strlen):
        if string[i] == 'x':
            x_count += 1

    return min(x_count, y_count)


# Tests
assert get_flip_count("xyxxxyxyy") == 2

a + b = M
a XOR b = N

def get_variables(m, n):
    candidates = list()
    for a in range(m // 2 + 1):
        b = m - a
        if a ^ b == n:
            candidates.append((a, b))

    return candidates


# Tests
assert get_variables(100, 4) == [(48, 52)]

import random


def knows(known, a, b):
    return b in known[a]


def get_celeb(known):
    celeb_candidates = set(known.keys())

    while celeb_candidates:
        sample = next(iter(celeb_candidates))
        celeb_candidates.remove(sample)
        count = len(celeb_candidates)
        for other in celeb_candidates:
            if not knows(known, sample, other):
                count -= 1
        if count == 0:
            return sample


# Tests
known = {
    'a': {'b', 'c'},
    'b': set(),
    'c': {'b'}
}
assert knows(known, 'a', 'b')
assert not knows(known, 'b', 'a')
assert knows(known, 'c', 'b')
assert get_celeb(known) == 'b'

OPERATORS = {'+', '-', '*', '/'}
TARGET = 24


def possible(arr):
    if len(arr) == 1:
        return arr[0] == TARGET

    new_possibilities = list()
    for si in range(len(arr) - 1):
        for operator in OPERATORS:
            num_1 = arr[si]
            num_2 = arr[si + 1]
            try:
                possibility = \
                    arr[:si] + \
                    [eval("{}{}{}".format(num_1, operator, num_2))] + \
                    arr[si + 2:]
                new_possibilities.append(possibility)
            except Exception:
                pass

    return any([possible(x) for x in new_possibilities])


# Tests
assert possible([5, 2, 7, 8])
assert not possible([10, 10, 10, 10])

score(Sj) = (1 - d) / N + d * (score(Sx) / Cx+ score(Sy) / Cy+ ... + score(Sz) / Cz))

from typing import Set, Dict

DAMPING = 0.85


class Graph:
    def __init__(self):
        self.edges = dict()

    def __repr__(self):
        return str(self.edges)

    def add_edge(self, src, tgt):
        if not src in self.edges:
            self.edges[src] = set()
        if not tgt in self.edges:
            self.edges[tgt] = set()

        self.edges[src].add(tgt)


def calculate_score(node: str, g: Graph, page_scores: Dict):
    agg_score = 0
    for other in g.edges:
        if node in g.edges[other]:
            agg_score += page_scores[other] / len(g.edges[other])

    score = ((1 - DAMPING) / len(g.edges)) + (DAMPING * agg_score)
    return score


def rank_pages(g: Graph):
    page_scores = dict()
    start_prob = 1 / len(g.edges)
    for node in g.edges.keys():
        page_scores[node] = start_prob

    for node in g.edges.keys():
        page_scores[node] = calculate_score(node, g, page_scores)

    return page_scores


# Tests
g = Graph()
g.add_edge('a', 'b')
g.add_edge('a', 'c')
g.add_edge('b', 'c')
print(rank_pages(g))

  3      3
 / \    / \
1   2  2   1

class Node:
    def __init__(self, val):
        self.val = val
        self.l, self.r = None, None


def get_distinct_ways(node):
    if node and node.l and node.r:
        return 2 * get_distinct_ways(node.l) * get_distinct_ways(node.r)

    return 1


# Tests
a = Node(3)
b = Node(2)
c = Node(1)
a.l = b
a.r = c
assert get_distinct_ways(a) == 2

from random import shuffle


class Node:
    def __init__(self, x):
        self.val = x
        self.next = None

    def __str__(self):
        string = "["
        node = self
        while node:
            string += "{} ->".format(node.val)
            node = node.next
        string += "None]"
        return string


def get_nodes(values):
    next_node = None
    for value in values[::-1]:
        node = Node(value)
        node.next = next_node
        next_node = node

    return next_node


def get_list(head):
    node = head
    nodes = list()
    while node:
        nodes.append(node.val)
        node = node.next
    return nodes


def unishuffle(llist):
    length = 0
    node = ll
    node_list = list()
    while node:
        node_list.append(node)
        node = node.next
        length += 1

    shuffle(node_list)

    dummy = Node(None)
    for node in node_list:
        node.next = dummy.next
        dummy.next = node

    return dummy.next


# Tests
ll = get_nodes([1, 2, 3, 4, 5])
print(unishuffle(ll))

def get_ones(num: int):
    binary = str(bin(num))
    count = 0
    for ch in binary:
        if ch == '1':
            count += 1

    return count


def get_next(num: int):
    inc = 1
    base_count = get_ones(num)
    while True:
        next_num = num + inc
        new_count = get_ones(next_num)
        if base_count == new_count:
            return next_num
        inc += 1


# Tests
assert get_next(6) == 9

def get_twos_sum(result, arr):
    i, k = 0, len(arr) - 1
    while i < k:
        a, b = arr[i], arr[k]
        res = a + b
        if res == result:
            return (a, b)
        elif res < result:
            i += 1
        else:
            k -= 1


def get_threes_sum(result, arr):
    arr.sort()
    for i in range(len(arr)):
        c = arr[i]
        if c > result:
            continue
        twos = get_twos_sum(result - c, arr[:i] + arr[i+1:])
        if twos:
            return True

    return get_twos_sum(result, arr)


# Tests
assert get_threes_sum(49, [20, 303, 3, 4, 25])
assert not get_threes_sum(50, [20, 303, 3, 4, 25])

import sys


class Point:
    def __init__(self, x, y):
        self.x = x
        self.y = y

    def __repr__(self):
        return "[x={},y={}]".format(self.x, self.y)


def get_distance(p1, p2):
    return ((p1.x - p2.x) ** 2 + (p1.y - p2.y) ** 2) ** 0.5


def get_closest(point_tuples):
    points = [Point(x, y) for (x, y) in point_tuples]
    min_dist, min_dist_pts = sys.maxsize, None
    for i in range(len(points) - 1):
        for j in range(i + 1, len(points)):
            dist = get_distance(points[i], points[j])
            if dist < min_dist:
                min_dist = dist
                min_dist_pts = ((points[i].x, points[i].y),
                                (points[j].x, points[j].y))

    return min_dist_pts


# Tests
assert get_closest([(1, 1), (-1, -1), (3, 4), (6, 1), (-1, -6), (-4, -3)]) == \
    ((1, 1), (-1, -1))

{ 'eat', 'rain', 'in', 'rat' }

[['e', 'a', 'n'],
 ['t', 't', 'i'],
 ['a', 'r', 'a']]

import itertools


class Cell:
    def __init__(self, x, y):
        self.x = x
        self.y = y

    def __hash__(self):
        return hash((self.x, self.y))

    def __eq__(self, other):
        return self.x == other.x and self.y == other.y

    def __repr__(self):
        return "[Cell(x={},y={})]".format(self.x, self.y)


def get_adj_options(matrix, size, row, col, seen):
    adj_options = list()
    if row > 0:
        adj_options.append(Cell(row - 1, col))
    if row < size - 1:
        adj_options.append(Cell(row + 1, col))
    if col > 0:
        adj_options.append(Cell(row, col - 1))
    if col < size - 1:
        adj_options.append(Cell(row, col + 1))

    adj_options = [x for x in adj_options if x not in seen]
    return adj_options


def consume_word(start, word, matrix, size, seen_cells):
    # print("Consuming. start:{}, word:{}, seen:{}".format(start, word, seen_cells))
    if not word:
        return [(True, seen_cells)]
    if matrix[start.x][start.y] != word[0]:
        return [(False, set())]

    seen = seen_cells | {start}
    adj_cells = get_adj_options(matrix, size, start.x, start.y, seen)

    results = list()
    for adj_cell in adj_cells:
        result = consume_word(adj_cell, word[1:], matrix, size, seen)
        results.extend(result)

    return results


def get_max_packed(matrix, dictionary, size, seen, packed):
    cell_occ = dict()
    for word in dictionary:
        cell_occ[word] = list()
        for i in range(size):
            for k in range(size):
                possibilities = consume_word(
                    Cell(i, k), word, matrix, size, set())
                consumed = [y for (x, y) in possibilities if x]
                if consumed:
                    cell_occ[word].extend(consumed)

    max_perm_length = len(dictionary)
    while max_perm_length > 0:
        all_seen = set()
        perms = itertools.combinations(dictionary, max_perm_length)
        for perm in perms:
            count_words = 0
            for word in perm:
                independent, val = False, None
                for poss in cell_occ[word]:
                    if poss & all_seen:
                        continue
                    independent, val = True, poss
                if independent:
                    all_seen |= val
                    count_words += 1
            if count_words == max_perm_length:
                return max_perm_length

        max_perm_length -= 1

    return 1


def get_max_packed_helper(matrix, dictionary):
    print(get_max_packed(matrix, dictionary, len(matrix), set(), set()))


# Tests
matrix = \
    [
        ['e', 'a', 'n'],
        ['t', 't', 'i'],
        ['a', 'r', 'a']
    ]
dictionary = {'eat', 'rain', 'in', 'rat'}
get_max_packed_helper(matrix, dictionary)

def reduce(lst, f, init):
    res = init
    for x in lst:
        res = f(res, x)
    return res


def add(a, b):
    return a + b


def multiply(a, b):
    return a * b


def custom_sum(lst):
    return reduce(lst, add, 0)


def custom_prod(lst):
    return reduce(lst, multiply, 1)


# Tests
assert custom_sum([1, 2, 3, 4]) == 10
assert custom_prod([1, 2, 3, 4]) == 24

    5
   / \
  3   8
 / \ / \
2  4 6  10

class Node:
    def __init__(self, val):
        self.val = val
        self.l = None
        self.r = None


def sum_range(node, lo, hi):
    if not node:
        return 0
    elif node.val < lo:
        return sum_range(node.r, lo, hi)
    elif node.val > hi:
        return sum_range(node.l, lo, hi)

    return node.val + sum_range(node.l, lo, hi) + sum_range(node.r, lo, hi)


# Tests
a = Node(5)
b = Node(3)
c = Node(8)
d = Node(2)
e = Node(4)
f = Node(6)
g = Node(10)
a.l = b
a.r = c
b.l = d
b.r = e
c.l = f
c.r = g
assert sum_range(a, 4, 9) == 23

   1
  / \ 
 2   3
    / \ 
   4   5
 / | \
6  7  8

class Node:
    def __init__(self, val):
        self.val = val
        self.ch = set()
        self.par = None

    def size(self):
        if not self.ch:
            return 1

        return 1 + sum([x.size() for x in self.ch])


def split(node):
    results = list()
    for child in node.ch:
        if child.size() % 2 == 0:
            new_children = [x for x in node.ch if x != child]
            node.ch = new_children
            return [node, child]
        else:
            results.extend(split(child))
    return results


def segment(nodes):
    new_nodes = list()
    count = len(nodes)
    for node in nodes:
        new_nodes = split(node)

    if len(new_nodes) == count:
        return count

    return segment(new_nodes)


# Tests
a = Node(1)
b = Node(2)
c = Node(3)
d = Node(4)
e = Node(5)
f = Node(6)
g = Node(7)
h = Node(8)
d.ch = [f, g, h]
c.ch = [d, e]
a.ch = [b, c]
assert segment([a]) == 2

def get_synonyms(pairs):
    synonyms = dict()
    for pair in pairs:
        default = min(pair)
        synonyms[pair[0]] = default
        synonyms[pair[1]] = default

    return synonyms


def are_equal(s1, s2, synonyms):
    words_1, words_2 = s1.split(), s2.split()
    if len(words_1) != len(words_2):
        return False

    def lookup(word):
        return synonyms[word] if word in synonyms else word

    for (w1, w2) in zip(words_1, words_2):
        a1 = lookup(w1)
        a2 = lookup(w2)
        if a1 != a2:
            return False

    return True


# Tests
synonyms = get_synonyms([("big", "large"), ("eat", "consume")])
assert are_equal("He wants to eat food.",
                 "He wants to consume food.",
                 synonyms)
assert not are_equal("He wants to large food.",
                     "He wants to consume food.",
                     synonyms)

[
    ('JFK', 'ATL', 150),
    ('ATL', 'SFO', 400),
    ('ORD', 'LAX', 200),
    ('LAX', 'DFW', 80),
    ('JFK', 'HKG', 800),
    ('ATL', 'ORD', 90),
    ('JFK', 'LAX', 500),
]

import sys


def get_city_map(flights):
    city_map = dict()
    for src, dst, fare in flights:
        if dst not in city_map:
            city_map[dst] = list()
        city_map[dst].append((src, fare))

    return city_map


def get_cheapest_fare(src, tgt, max_stops, city_map, total=0, stops=0):
    if stops > max_stops:
        return sys.maxsize

    if src == tgt:
        return total

    new_tgt_fares = city_map[tgt]
    possibilities = list()
    for new_tgt, fare in new_tgt_fares:
        poss = get_cheapest_fare(
            src, new_tgt, max_stops, city_map, total + fare, stops + 1)
        possibilities.append(poss)

    return min(possibilities)


# Tests
flights = [
    ('JFK', 'ATL', 150),
    ('ATL', 'SFO', 400),
    ('ORD', 'LAX', 200),
    ('LAX', 'DFW', 80),
    ('JFK', 'HKG', 800),
    ('ATL', 'ORD', 90),
    ('JFK', 'LAX', 500),
]
city_map = get_city_map(flights)
assert get_cheapest_fare("JFK", "LAX", 3, city_map) == 440
assert get_cheapest_fare("JFK", "LAX", 0, city_map) == sys.maxsize

def lex_mod(string, k):
    if k > 1:
        return "".join(sorted(string))

    min_ch = min(string)
    joined = string + string
    for i, ch in enumerate(joined):
        if ch == min_ch:
            return joined[i:i + len(string)]


# Tests
assert lex_mod("daily", 2) == "adily"
assert lex_mod("daily", 1) == "ailyd"

       c
    /  |  \
   b   o   w
 / |   |   |
a  e   d   a
|    / |   | \ 
x   b  e   r  e

class TernaryTree:
    def __init__(self):
        self.ch = None
        self.l = None
        self.m = None
        self.r = None

    def __repr__(self):
        return "{}->[{}-{}-{}]".format(
            self.ch if self.ch else "",
            self.m if self.m else "",
            self.l if self.l else "",
            self.r if self.r else "")

    @staticmethod
    def add_tree(loc, word):
        if not loc:
            loc = TernaryTree()
        loc.add_word(word)
        return loc

    def add_word(self, word):
        if not word:
            return
        fch = word[0]
        rem_word = word[1:]

        if not self.ch:
            self.ch = fch
            self.m = TernaryTree.add_tree(self.m, rem_word)
        elif self.ch == fch:
            self.m = TernaryTree.add_tree(self.m, rem_word)
        elif self.ch < fch:
            self.l = TernaryTree.add_tree(self.l, word)
        else:
            self.r = TernaryTree.add_tree(self.l, word)

    def search_word(self, word):
        fch = word[0]
        rem_word = word[1:]

        if fch == self.ch:
            if not rem_word and not self.m.ch:
                return True
            return self.m.search_word(rem_word)
        elif fch < self.ch:
            if not self.l:
                return False
            return self.l.search_word(word)
        else:
            if not self.r:
                return False
            return self.r.search_word(word)


# Tests
tt = TernaryTree()
tt.add_word("code")
tt.add_word("cob")
tt.add_word("be")
tt.add_word("ax")
tt.add_word("war")
tt.add_word("we")

assert tt.search_word("code")
assert not tt.search_word("cow")

cons_repl = [
    (["b", "f", "p", "v"], 1),
    (["c", "g", "j", "k", "q", "s", "x", "z"], 2),
    (["d", "t"], 3),
    (["m", "n"], 5),
    (["l"], 4),
    (["r"], 6),
]
sim_cons = [
    {"c", "k", "s"}
]
vowel_like = {"a", "e", "i", "o", "u", "y", "w", "h"}


def build_cons_repl_map(cons_repl):
    cons_repl_map = dict()
    for chars, num in cons_repl:
        for char in chars:
            cons_repl_map[char] = num
    return cons_repl_map


def build_cons_like_map(sim_cons):
    cons_like_map = dict()
    for group in sim_cons:
        elect = min(group)
        for char in group:
            cons_like_map[char] = elect

    return cons_like_map


def soundexify(word, cons_repl_map, cons_like_map):
    word = word.lower()

    # deduplicate similar sounding consonants
    w1 = ""
    for char in word:
        if char in cons_like_map:
            char = cons_like_map[char]
        if w1 and char == w1[-1]:
            continue
        w1 += char

    # remove vowel like characters
    w2 = ""
    for char in w1[1:]:
        if char not in vowel_like:
            w2 += char
    w3 = ""

    # replace consonants with numbers
    for char in w2:
        w3 += str(cons_repl_map[char])

    # massage into final format
    w3 += "000"
    w3 = w3[:3]
    final = w1[0] + w3

    return final


# Test
cons_repl_map = build_cons_repl_map(cons_repl)
cons_like_map = build_cons_like_map(sim_cons)
c1 = soundexify("Jackson", cons_repl_map, cons_like_map)
c2 = soundexify("Jaxen", cons_repl_map, cons_like_map)
assert c1 == c2
assert c1 == "j250"

import sys


def get_sum_sq(target, squares):
    if target == 0:
        return 0
    elif not squares:
        return sys.maxsize

    original_tgt = target
    biggest_sq = squares.pop()
    tally = 0
    while target >= biggest_sq:
        tally += 1
        target -= biggest_sq

    if tally:
        return min(
            tally + get_sum_sq(target, squares.copy()),
            get_sum_sq(original_tgt, squares.copy())
        )
    else:
        return get_sum_sq(original_tgt, squares.copy())


def get_min_squares(target):
    num, sq = 1, 1
    squares = list()
    while sq <= target:
        squares.append(sq)
        num += 1
        sq = num * num

    return get_sum_sq(target, squares)


# Tests
assert get_min_squares(4) == 1
assert get_min_squares(17) == 2
assert get_min_squares(18) == 2

{
    "word_1": ["meaning one", "meaning two", ...],
    ...
    "word_n": ["meaning one", "meaning two", ...]
}

- Problem definition is incomplete
- We also need a source for which word appears in which context, to be able to infer this in the actual sentences.
- Once we have a set of strongly correlated words with each word-sense, we can search the context of a word in the target sentence.
- If there is a high overlap of those words with the already correlated words for a particular word sense, we can guess that that is the answer

# Skipping implementation since no unit tests are provided.

## Steps
- For a white square, if the previous row/column was black/before the start of the grid
  - Check if next 2 squares to the right are white (if column). Ditto for the next 2 squares below (if row). If not for either case, the crossword is invalid.
- Enumerate set of white squres.
- Start at the first white square and do a BFS until there are no more adjacent white squares to be seen. 
  - If the set difference of all white squares and seen white squares from this process if non-empty, then the crossword is invalid.

      x
      x  
  x   x
  x x x
x x x x

def get_max_hist_area(arr, start, end):
    if start == end:
        return 0

    curr_area = (end - start) * min(arr[start:end])
    opt_1 = get_max_hist_area(arr, start, end - 1)
    opt_2 = get_max_hist_area(arr, start + 1, end)

    return max(curr_area, opt_1, opt_2)


def get_max_hist_area_helper(arr):
    return get_max_hist_area(arr, 0, len(arr))


# Tests
assert get_max_hist_area_helper([1, 3, 2, 5]) == 6

# Wikipedia Crawler

## System
- Use the main page to generate a queue of links that is to be processed by the server.
- Each link is put into a queue that is processed on the server.
- The processing involves just monitoring and sending each link to a client.
- The client downloads and parses the page, stores them in the DB and adds new URLs to the queue if the last update date is greater that the date the item was stored in a distributed cache.

## Questions
- How will you reach as many pages as possible? 
  - Parse all URLs on each page and add them back to the queue.
- How can you keep track of pages that have already been visited?
  - Distributed cache
- How will you deal with your client machines being blacklisted?
  - Maybe EC2 instance provisioning once `x` amount of requests get an error code response.
- How can you update your database when Wikipedia pages are added or updated?
  - Handled by the current mechanism of distributed cache checking.

import sys
import math


def round_list(fl_arr, int_arr, rsum, diff):
    if not fl_arr:
        return (diff, int_arr) if sum(int_arr) == rsum else (sys.maxsize, list())

    num = fl_arr[0]

    op_1 = int(math.ceil(num))
    diff_1, int_arr_1 = round_list(
        fl_arr[1:], int_arr + [op_1], rsum, diff + abs(op_1 - num))

    op_2 = int(math.floor(num))
    diff_2, int_arr_2 = round_list(
        fl_arr[1:], int_arr + [op_2], rsum, diff + abs(op_2 - num))

    return (diff_1, int_arr_1) if diff_1 < diff_2 else (diff_2, int_arr_2)


def round_list_helper(arr):
    rounded_sum = int(round(sum(arr), 0))
    return round_list(arr, list(), rounded_sum, 0)[1]


# Tests
assert round_list_helper([1.3, 2.3, 4.4]) == [1, 2, 5]

# Not sure how a set of arrays provides advantages over a single array
# Regardless, their indices can be combined to act as a single large array


class Queue:
    def __init__(self, arr_size):
        self.flarr = [None for _ in range(arr_size)]
        self.start, self.end = 0, 0
        self.size = 0
        self.max_size = arr_size

    def enqueue(self, val):
        if self.size == self.max_size:
            # No more space
            return

        new_end = (self.end + 1) % self.max_size
        self.flarr[self.end] = val
        self.end = new_end
        self.size += 1

    def dequeue(self):
        if self.size == 0:
            # Nothing to dequeue
            return None

        new_start = (self.start + 1) % self.max_size
        val = self.flarr[self.start]
        self.flarr[self.start] = None
        self.start = new_start
        self.size -= 1

        return val

    def get_size(self):
        return self.size


# Tests
q = Queue(5)
assert not q.dequeue()

q.enqueue(1)
q.enqueue(2)
q.enqueue(3)
assert q.get_size() == 3
assert q.flarr == [1, 2, 3, None, None]

assert q.dequeue() == 1
assert q.dequeue() == 2

q.enqueue(4)
q.enqueue(5)
assert q.get_size() == 3
assert q.flarr == [None, None, 3, 4, 5]

q.enqueue(6)
q.enqueue(7)
assert q.flarr == [6, 7, 3, 4, 5]

q.enqueue(8)
# no new value added
assert q.flarr == [6, 7, 3, 4, 5]
assert q.dequeue() == 3
assert q.dequeue() == 4
assert q.dequeue() == 5
assert q.dequeue() == 6

def get_continuous_count(string, char):
    count, max_count = 1, 1
    for i in range(1, len(string)):
        if string[i] == string[i-1]:
            count += 1
        else:
            count = 0
        max_count = max(max_count, count)
    return max_count - 1


def get_tree_depth(string):
    c1 = get_continuous_count(string, "(")
    c2 = get_continuous_count(string, ")")
    return max(c1, c2)


# Tests
assert get_tree_depth("(00)") == 0
assert get_tree_depth("((00)(00))") == 1
assert get_tree_depth("((((00)0)0)0)") == 3

import sys


class ValueSet:
    def __init__(self):
        self.keys = set()
        self.prev = None
        self.next = None


class MagicStruct:
    def __init__(self):
        self.keys = dict()
        self.values = dict()
        self.values[0] = ValueSet()
        self.values[sys.maxsize] = ValueSet()
        self.values[0].next = self.values[sys.maxsize]
        self.values[sys.maxsize].prev = self.values[0]
        self.vhead = self.values[0]
        self.vtail = self.values[sys.maxsize]

    def plus(self, k):
        vs = None
        if k not in self.keys:
            self.keys[k] = 0
            vs = ValueSet()
            prev_vs = self.vhead
            next_vs = self.vhead.next

        v = self.keys[k] + 1
        self.keys[k] = v

        if v in self.values:
            vs = self.values[v]
            prev_vs = self.values[v].prev
        vs.keys.add(k)
        next_vs = prev_vs.next

        vs.prev = prev_vs
        vs.next = next_vs

        if v-1 in self.values:
            old_vs = self.values[v-1]
            if not old_vs.keys:
                oprev = old_vs.prev
                onext = old_vs.next
                oprev.next = onext
                onext.prev = oprev

    def minus(self, k):
        if k not in self.keys:
            return

        vs = self.keys[k]
        prev_vs = vs.prev
        next_vs = vs.next
        v = self.keys[k] - 1

        if not v:
            prev_vs.next = next_vs
            next_vs.prev = prev_vs

    def get_max(self):
        pass

    def get_min(self):
        pass


# Tests
ms = MagicStruct()
ms.plus("a")
ms.plus("b")
ms.plus("a")
ms.plus("a")
print(ms.keys, ms.values)
ms.minus("a")
print(ms.keys, ms.values)
ms.minus("b")
print(ms.keys, ms.values)
print(ms.get_max())

WORD_MAP = {
    0: "zero",
    1: "one",
    2: "two",
    3: "three",
    4: "four",
    5: "five",
    6: "six",
    7: "seven",
    8: "eight",
    9: "nine",
}


def get_char_count_dict(string):
    letter_dict = dict()
    for char in string:
        if char not in letter_dict:
            letter_dict[char] = 0
        letter_dict[char] += 1

    return letter_dict


def use_digit(letter_dict, word_dict, digit):
    for char in word_dict:
        if char not in letter_dict or word_dict[char] > letter_dict[char]:
            return letter_dict, 0

    for char in word_dict:
        letter_dict[char] -= word_dict[char]

    letter_dict, uses = use_digit(letter_dict, word_dict, digit)
    return letter_dict, uses + 1


def get_sorted_nums(string):
    letter_dict = get_char_count_dict(string)

    result = 0
    for i in range(10):
        word = WORD_MAP[i]
        word_dict = get_char_count_dict(word)
        letter_dict, uses = use_digit(letter_dict, word_dict, i)

        while uses > 0:
            result = result * 10 + i
            uses -= 1

    return result


# Tests
assert get_sorted_nums("niesevehrtfeev") == 357
assert get_sorted_nums("nienienn") == 99
assert get_sorted_nums("enieniennon") == 199

from heapq import heappush, heappop


def interleave_playlist(ranked_listings):
    scores = dict()
    for listing in ranked_listings:
        num_songs = len(listing)
        total_points = ((num_songs + 1) * num_songs) // 2
        for rank, song in enumerate(listing):
            if song not in scores:
                scores[song] = 0
            scores[song] += total_points / (rank + 1)

    sorted_scored_tuples = list()
    for song, score in scores.items():
        heappush(sorted_scored_tuples, (score, song))

    interleaved = list()
    while sorted_scored_tuples:
        _, song = heappop(sorted_scored_tuples)
        interleaved.append(song)

    return interleaved[::-1]


# Tests
ranked_listings = [
    [1, 7, 3],
    [2, 1, 6, 7, 9],
    [3, 9, 5]
]
assert interleave_playlist(ranked_listings) == [2, 1, 3, 7, 9, 6, 5]

def does_code_match_guess(code, guess, matches):
    count = 0
    for c_char, g_char in zip(code, guess):
        if c_char == g_char:
            count += 1

    return count == matches


def is_valid_code(guess_scores):
    for i in range(1000000):
        code = str(i)
        code = ("0" * (6 - len(code))) + code

        success = True
        for guess, matches in guess_scores.items():
            success = success & does_code_match_guess(
                code, str(guess), matches)

        if success:
            return True

    return False


# Tests
assert is_valid_code({175286: 2, 293416: 3, 654321: 0})
assert not is_valid_code({123456: 4, 345678: 4, 567890: 4})

def get_strob_numbers(num_digits):
    if not num_digits:
        return [""]
    elif num_digits == 1:
        return ["0", "1", "8"]

    smaller_strob_numbers = get_strob_numbers(num_digits - 2)
    strob_numbers = list()
    for x in smaller_strob_numbers:
        strob_numbers.extend([
            "1" + x + "1",
            "6" + x + "9",
            "9" + x + "6",
            "8" + x + "8",
        ])

    return strob_numbers


# Tests
assert get_strob_numbers(1) == ['0', '1', '8']
assert get_strob_numbers(2) == ['11', '69', '96', '88']
assert get_strob_numbers(3) == ['101', '609', '906', '808', '111', '619',
                                '916', '818', '181', '689', '986', '888']

add_subtract(7) -> 7
add_subtract(1)(2)(3) -> 1 + 2 - 3 -> 0
add_subtract(-5)(10)(3)(9) -> -5 + 10 - 3 + 9 -> 11

def add(x, y=1):
    return lambda z: add(x+(y*z), (-1*y)) if z else x


# Tests
assert add(7)(None) == 7
assert add(1)(2)(3)(None) == 0
assert add(-5)(10)(3)(9)(None) == 11

def get_longest_inc_subsq(arr):
    longest = []
    start = 0
    for i in range(len(arr)):
        if arr[i] < arr[i - 1]:
            start = i
        end = i + 1

        if end - start > len(longest):
            longest = arr[start:end]

    return longest


# Tests
assert get_longest_inc_subsq([1, 2, 3, 5, 4]) == [1, 2, 3, 5]
assert get_longest_inc_subsq([5, 4, 3, 2, 1]) == [5]

# no idea how to implement it using 3 stacks
# the time complexity constraints can be satisfied
# using a deque instead

from collections import deque

# Tests
dq = deque()
dq.appendleft(1)
dq.appendleft(2)
dq.appendleft(3)
dq.appendleft(4)
dq.appendleft(5)
assert dq.pop() == 1
assert dq.popleft() == 5