

'''simple docstring'''





import heapq







def   _UpperCamelCase	(		__UpperCamelCase	)       ->			List[Any]:
					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(__UpperCamelCase    ,[-1 * len(__UpperCamelCase	), (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(__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]:
																				lowerCamelCase_  				=      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)}''')









'''simple docstring'''


from __future__ import annotations

import math
def 						lowerCamelCase__   (				a    ,	a							):
						__snake_case						 =   u
						for i in range(1    ,	a							):
												__snake_case						 =   temp * (u - i)
						return temp
def 						lowerCamelCase__   (				):
						__snake_case						 =   int(input('enter the numbers of values: '							)							)
						__snake_case						 =   []
						for _ in range(a							):
												y.append([]							)
						for i in range(a							):
												for j in range(a							):
																		y[i].append(a							)
																		__snake_case						 =   0

						print('enter the values of parameters in a list: '							)
						__snake_case						 =   list(map(a    ,	input().split()							)							)

						print('enter the values of corresponding parameters: '							)
						for i in range(a							):
												__snake_case						 =   float(input()							)

						__snake_case						 =   int(input('enter the value to interpolate: '							)							)
						__snake_case						 =   (value - x[0]) / (x[1] - x[0])

						# for calculating forward difference table

						for i in range(1    ,	a							):
												for j in range(n - i							):
																		__snake_case						 =   y[j + 1][i - 1] - y[j][i - 1]

						__snake_case						 =   y[0][0]
						for i in range(1    ,	a							):
												summ += (ucal(a    ,	a							) * y[0][i]) / math.factorial(a							)

						print(f'the value at {value} is {summ}'							)


if __name__ == "__main__":
	main()

