


import heapq






def      __lowerCamelCase		(				lowerCamelCase__						:		dict	):





			'''simple docstring'''




			lowerCamelCase  						=   []

			# 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(__snake_case   ,				[-1 * len(__snake_case	), (key, value)]	)

			# chosen_vertices = set of chosen vertices
			lowerCamelCase  						=   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
						lowerCamelCase  						=   heapq.heappop(__snake_case	)[1][0]
						chosen_vertices.add(__snake_case	)

						# 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]:
												lowerCamelCase  						=   elem[1][1].index(__snake_case	)
												del elem[1][1][index]
												elem[0] += 1
        # re-order the queue
						heapq.heapify(__snake_case	)
			return chosen_vertices


if __name__ == "__main__":
		import doctest

		doctest.testmod()

		UpperCAmelCase					:  str			=						{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)}""")









import os

# Precomputes a list of the 100 first triangular numbers
__UpperCAmelCase								=						[int(0.5 * n * (n + 1)) for n in range(1, 101)]




def      lowercase__      (     ):


					'''simple docstring'''


					UpperCAmelCase_    :      Any            =						os.path.dirname(os.path.realpath(__snake_case  )  )
					UpperCAmelCase_    :      Optional[Any]            =						os.path.join(__snake_case     ,       'words.txt'  )

					UpperCAmelCase_    :      Union[str, Any]            =						''
					with open(__snake_case  ) as f:
										UpperCAmelCase_    :      List[Any]            =						f.readline()

					UpperCAmelCase_    :      Optional[int]            =						[word.strip('"'  ) for word in words.strip('\r\n'  ).split(','  )]
					UpperCAmelCase_    :      Optional[int]            =						[
					    word
					    for word in [sum(ord(__snake_case  ) - 64 for x in word  ) for word in words]
					    if word in TRIANGULAR_NUMBERS
					]
					return len(__snake_case  )


if __name__ == "__main__":
		print(solution())






