
import heapq



def        UpperCamelCase    (							lowerCAmelCase__		):
					'''simple docstring'''
					lowercase							=						[]

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

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

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


if __name__ == "__main__":
							import doctest

							doctest.testmod()

							lowercase__		:Any   =    {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 math

import numpy as np
import qiskit
from qiskit import Aer, ClassicalRegister, QuantumCircuit, QuantumRegister, execute

def    SCREAMING_SNAKE_CASE_							(							__magic_name__					:  int = 3					)		->			qiskit.result.counts.Counts:






	"""simple docstring"""



	if isinstance(__magic_name__	,			__magic_name__					):
		raise TypeError("""number of qubits must be a integer."""					)
	if number_of_qubits <= 0:
		raise ValueError("""number of qubits must be > 0."""					)
	if math.floor(__magic_name__					) != number_of_qubits:
		raise ValueError("""number of qubits must be exact integer."""					)
	if number_of_qubits > 10:
		raise ValueError("""number of qubits too large to simulate(>10)."""					)

	UpperCamelCase     :int          =	QuantumRegister(__magic_name__	,			"""qr"""					)
	UpperCamelCase     :str          =	ClassicalRegister(__magic_name__	,			"""cr"""					)

	UpperCamelCase     :str          =	QuantumCircuit(__magic_name__	,			__magic_name__					)

	UpperCamelCase     :List[Any]          =	number_of_qubits

	for i in range(__magic_name__					):
		quantum_circuit.h(number_of_qubits - i - 1					)
		counter -= 1
		for j in range(__magic_name__					):
			quantum_circuit.cp(np.pi / 2 ** (counter - j)	,			__magic_name__	,			__magic_name__					)

	for k in range(number_of_qubits // 2					):
		quantum_circuit.swap(__magic_name__	,			number_of_qubits - k - 1					)

	# measure all the qubits
	quantum_circuit.measure(__magic_name__	,			__magic_name__					)
	# simulate with 10000 shots
	UpperCamelCase     :str          =	Aer.get_backend("""qasm_simulator"""					)
	UpperCamelCase     :Dict          =	execute(__magic_name__	,			__magic_name__	,			shots=1_0000					)

	return job.result().get_counts(__magic_name__					)


if __name__ == "__main__":
	print(
	    F'''Total count for quantum fourier transform state is: \
    {quantum_fourier_transform(3)}'''
	)
