


from math import factorial




def        snake_case_					(  snake_case      ,							snake_case					)  ->    int:

       # If either of the conditions are true, the function is being asked
       # to calculate a factorial of a negative number, which is not possible
       if n < k or k < 0:
              raise ValueError('Please enter positive integers for n and k where n >= k'					)
       return factorial(snake_case					) // (factorial(snake_case					) * factorial(n - k					))


if __name__ == "__main__":
 print(
     '''The number of five-card hands possible from a standard''',
     F'''fifty-two card deck is: {combinations(52, 5)}\n''',
 )

 print(
     '''If a class of 40 students must be arranged into groups of''',
     F'''4 for group projects, there are {combinations(40, 4)} ways''',
     '''to arrange them.\n''',
 )

 print(
     '''If 10 teams are competing in a Formula One race, there''',
     F'''are {combinations(10, 3)} ways that first, second and''',
     '''third place can be awarded.''',
 )






import math

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




def        snake_case_					(  snake_case = 3					)  ->    qiskit.result.counts.Counts:
       if isinstance(snake_case      ,							snake_case					):
              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(snake_case					) != 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).'					)

       lowercase__:       str        =       QuantumRegister(snake_case      ,							'qr'					)
       lowercase__:       str        =       ClassicalRegister(snake_case      ,							'cr'					)

       lowercase__:       List[Any]        =       QuantumCircuit(snake_case      ,							snake_case					)

       lowercase__:       int        =       number_of_qubits

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

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

       # measure all the qubits
       quantum_circuit.measure(snake_case      ,							snake_case					)
       # simulate with 10000 shots
       lowercase__:       str        =       Aer.get_backend('qasm_simulator'					)
       lowercase__:       Union[str, Any]        =       execute(snake_case      ,							snake_case      ,							shots=1_00_00					)

       return job.result().get_counts(snake_case					)


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


