

import heapq



def 				snake_case_(_UpperCamelCase					)							->     set[int]:



  """simple docstring"""






  _snake_case						=							[]

  # for each node and his adjacency list add them and the rank of the node to queue
  # using heapq module the queue will be filled like a Priority Queue
  # heapq works with a min priority queue, so I used -1*len(v) to build it
  for key, value in graph.items():
    # O(log(n))
    heapq.heappush(_UpperCamelCase			,	[-1 * len(_UpperCamelCase					), (key, value)]					)

  # chosen_vertices = set of chosen vertices
  _snake_case						=							set()

  # while queue isn't empty and there are still edges
  #   (queue[0][0] is the rank of the node with max rank)
  while queue and queue[0][0] != 0:
    # extract vertex with max rank from queue and add it to chosen_vertices
    _snake_case						=							heapq.heappop(_UpperCamelCase					)[1][0]
    chosen_vertices.add(_UpperCamelCase					)

    # Remove all arcs adjacent to argmax
    for elem in queue:
      # if v haven't adjacent node, skip
      if elem[0] == 0:
        continue
      # if argmax is reachable from elem
      # remove argmax from elem's adjacent list and update his rank
      if argmax in elem[1][1]:
        _snake_case						=							elem[1][1].index(_UpperCamelCase					)
        del elem[1][1][index]
        elem[0] += 1
        # re-order the queue
    heapq.heapify(_UpperCamelCase					)
  return chosen_vertices


if __name__ == "__main__":
 import doctest

 doctest.testmod()

 __A      		=     {0: [1, 3], 1: [0, 3], 2: [0, 3, 4], 3: [0, 1, 2], 4: [2, 3]}
 print(f'''Minimum vertex cover:\n{greedy_min_vertex_cover(graph)}''')




from __future__ import annotations



def 				snake_case_(_UpperCamelCase			,	_UpperCamelCase					)							->     bool:



  """simple docstring"""






  _snake_case						=							get_failure_array(_UpperCamelCase					)

  # 2) Step through text searching for pattern
  _snake_case,					_snake_case						=							0, 0  # index into text, pattern
  while i < len(_UpperCamelCase					):
    if pattern[j] == text[i]:
      if j == (len(_UpperCamelCase					) - 1):
        return True
      j += 1

    # if this is a prefix in our pattern
    # just go back far enough to continue
    elif j > 0:
      _snake_case						=							failure[j - 1]
      continue
    i += 1
  return False



def 				snake_case_(_UpperCamelCase					)							->     list[int]:



  """simple docstring"""






  _snake_case						=							[0]
  _snake_case						=							0
  _snake_case						=							1
  while j < len(_UpperCamelCase					):
    if pattern[i] == pattern[j]:
      i += 1
    elif i > 0:
      _snake_case						=							failure[i - 1]
      continue
    j += 1
    failure.append(_UpperCamelCase					)
  return failure


if __name__ == "__main__":
 # Test 1)
 __A      		=     '''abc1abc12'''
 __A      		=     '''alskfjaldsabc1abc1abc12k23adsfabcabc'''
 __A      		=     '''alskfjaldsk23adsfabcabc'''
 assert kmp(pattern, texta) and not kmp(pattern, texta)

 # Test 2)
 __A      		=     '''ABABX'''
 __A      		=     '''ABABZABABYABABX'''
 assert kmp(pattern, text)

 # Test 3)
 __A      		=     '''AAAB'''
 __A      		=     '''ABAAAAAB'''
 assert kmp(pattern, text)

 # Test 4)
 __A      		=     '''abcdabcy'''
 __A      		=     '''abcxabcdabxabcdabcdabcy'''
 assert kmp(pattern, text)

 # Test 5)
 __A      		=     '''aabaabaaa'''
 assert get_failure_array(pattern) == [0, 1, 0, 1, 2, 3, 4, 5, 2]

