




import math

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





def 						__A						(      __lowerCamelCase = 3       ) ->			qiskit.result.counts.Counts:
	if isinstance(lowerCAmelCase_				,     lowerCAmelCase_       ):
		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(lowerCAmelCase_       ) != 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)."""       )

	a									=				QuantumRegister(lowerCAmelCase_				,     """qr"""       )
	a									=				ClassicalRegister(lowerCAmelCase_				,     """cr"""       )

	a									=				QuantumCircuit(lowerCAmelCase_				,     lowerCAmelCase_       )

	a									=				number_of_qubits

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

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

	# measure all the qubits
	quantum_circuit.measure(lowerCAmelCase_				,     lowerCAmelCase_       )
	# simulate with 10000 shots
	a									=				Aer.get_backend("""qasm_simulator"""       )
	a									=				execute(lowerCAmelCase_				,     lowerCAmelCase_				,     shots=1_0000       )

	return job.result().get_counts(lowerCAmelCase_       )


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





def 	_UpperCamelCase					(    lowerCAmelCase_ )    ->Any:
   UpperCAmelCase      					=  0
   UpperCAmelCase      					=  len(lowerCAmelCase_ )

   for i in range(n - 1 ):
      for j in range(i + 1	,    lowerCAmelCase_ ):
         if arr[i] > arr[j]:
            num_inversions += 1

   return num_inversions
def 	_UpperCamelCase					(    lowerCAmelCase_ )    ->Any:
   if len(lowerCAmelCase_ ) <= 1:
      return arr, 0
   UpperCAmelCase      					=  len(lowerCAmelCase_ ) // 2
   UpperCAmelCase      					=  arr[0:mid]
   UpperCAmelCase      					=  arr[mid:]

   UpperCAmelCase					,	UpperCAmelCase      					=  count_inversions_recursive(lowerCAmelCase_ )
   UpperCAmelCase					,	UpperCAmelCase      					=  count_inversions_recursive(lowerCAmelCase_ )
   UpperCAmelCase					,	UpperCAmelCase      					=  _count_cross_inversions(lowerCAmelCase_	,    lowerCAmelCase_ )

   UpperCAmelCase      					=  inversion_p + inversions_q + cross_inversions
   return c, num_inversions
def 	_UpperCamelCase					(    lowerCAmelCase_	,    lowerCAmelCase_ )    ->int:
   UpperCAmelCase      					=  []
   UpperCAmelCase      					=  UpperCAmelCase      					=  UpperCAmelCase      					=  0
   while i < len(lowerCAmelCase_ ) and j < len(lowerCAmelCase_ ):
      if p[i] > q[j]:
         # if P[1] > Q[j], then P[k] > Q[k] for all  i < k <= len(P)
         # These are all inversions. The claim emerges from the
         # property that P is sorted.
         num_inversion += len(lowerCAmelCase_ ) - i
         r.append(q[j] )
         j += 1
      else:
         r.append(p[i] )
         i += 1

   if i < len(lowerCAmelCase_ ):
      r.extend(p[i:] )
   else:
      r.extend(q[j:] )

   return r, num_inversion
def 	_UpperCamelCase					(    )    ->int:
   UpperCAmelCase      					=  [1_0, 2, 1, 5, 5, 2, 1_1]

   # this arr has 8 inversions:
   # (10, 2), (10, 1), (10, 5), (10, 5), (10, 2), (2, 1), (5, 2), (5, 2)

   UpperCAmelCase      					=  count_inversions_bf(lowerCAmelCase_ )
   UpperCAmelCase					,	UpperCAmelCase      					=  count_inversions_recursive(lowerCAmelCase_ )

   assert num_inversions_bf == num_inversions_recursive == 8

   print("""number of inversions = """	,    lowerCAmelCase_ )

   # testing an array with zero inversion (a sorted arr_1)

   arr_a.sort()
   UpperCAmelCase      					=  count_inversions_bf(lowerCAmelCase_ )
   UpperCAmelCase					,	UpperCAmelCase      					=  count_inversions_recursive(lowerCAmelCase_ )

   assert num_inversions_bf == num_inversions_recursive == 0
   print("""number of inversions = """	,    lowerCAmelCase_ )

   # an empty list should also have zero inversions
   UpperCAmelCase      					=  []
   UpperCAmelCase      					=  count_inversions_bf(lowerCAmelCase_ )
   UpperCAmelCase					,	UpperCAmelCase      					=  count_inversions_recursive(lowerCAmelCase_ )

   assert num_inversions_bf == num_inversions_recursive == 0
   print("""number of inversions = """	,    lowerCAmelCase_ )


if __name__ == "__main__":
 main()



