



'''simple docstring'''


import heapq






def  UpperCAmelCase_       (		lowercase__       ):


					'''simple docstring'''







					a_       		=[]

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

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

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


if __name__ == "__main__":
		import doctest

		doctest.testmod()

		lowercase							       =			{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)}""")







'''simple docstring'''


from __future__ import annotations






def  UpperCAmelCase_       (		lowercase__       ):


     '''simple docstring'''







     a_       		=str(lowercase__       )
     return len(lowercase__       ) == 9 and set(lowercase__       ) == set("123456789"       )






def  UpperCAmelCase_       (		):


     '''simple docstring'''







     for base_num in range(9_9_9_9       ,	4_9_9_9       ,	-1       ):
          a_       		=1_0_0_0_0_2 * base_num
          if is_9_pandigital(lowercase__       ):
               return candidate

     for base_num in range(3_3_3       ,	9_9       ,	-1       ):
          a_       		=1_0_0_2_0_0_3 * base_num
          if is_9_pandigital(lowercase__       ):
               return candidate

     return None


if __name__ == "__main__":
  print(F"""{solution() = }""")


