





"""simple docstring"""





from __future__ import annotations

lowerCAmelCase__   	=	list[list[int]]

# assigning initial values to the grid
lowerCAmelCase__   	=	[
    [3, 0, 6, 5, 0, 8, 4, 0, 0],
    [5, 2, 0, 0, 0, 0, 0, 0, 0],
    [0, 8, 7, 0, 0, 0, 0, 3, 1],
    [0, 0, 3, 0, 1, 0, 0, 8, 0],
    [9, 0, 0, 8, 6, 3, 0, 0, 5],
    [0, 5, 0, 0, 9, 0, 6, 0, 0],
    [1, 3, 0, 0, 0, 0, 2, 5, 0],
    [0, 0, 0, 0, 0, 0, 0, 7, 4],
    [0, 0, 5, 2, 0, 6, 3, 0, 0],
]

# a grid with no solution
lowerCAmelCase__   	=	[
    [5, 0, 6, 5, 0, 8, 4, 0, 3],
    [5, 2, 0, 0, 0, 0, 0, 0, 2],
    [1, 8, 7, 0, 0, 0, 0, 3, 1],
    [0, 0, 3, 0, 1, 0, 0, 8, 0],
    [9, 0, 0, 8, 6, 3, 0, 0, 5],
    [0, 5, 0, 0, 9, 0, 6, 0, 0],
    [1, 3, 0, 0, 0, 0, 2, 5, 0],
    [0, 0, 0, 0, 0, 0, 0, 7, 4],
    [0, 0, 5, 2, 0, 6, 3, 0, 0],
]


def 					a__    (    _SCREAMING_SNAKE_CASE     ,		_SCREAMING_SNAKE_CASE     ,		_SCREAMING_SNAKE_CASE     ,		_SCREAMING_SNAKE_CASE			):




		"""simple docstring"""


		for i in range(9			):
				if grid[row][i] == n or grid[i][column] == n:
						return False

		for i in range(3			):
				for j in range(3			):
						if grid[(row - row % 3) + i][(column - column % 3) + j] == n:
								return False

		return True


def 					a__    (    _SCREAMING_SNAKE_CASE			):




		"""simple docstring"""


		for i in range(9			):
				for j in range(9			):
						if grid[i][j] == 0:
								return i, j
		return None


def 					a__    (    _SCREAMING_SNAKE_CASE			):




		"""simple docstring"""


		if location := find_empty_location(_A			):
				UpperCamelCase      , UpperCamelCase      =		location
		else:
				# If the location is ``None``, then the grid is solved.
				return grid

		for digit in range(1     ,		10			):
				if is_safe(_A     ,		_A     ,		_A     ,		_A			):
						UpperCamelCase      =		digit

						if sudoku(_A			) is not None:
								return grid

						UpperCamelCase      =		0

		return None


def 					a__    (    _SCREAMING_SNAKE_CASE			):




		"""simple docstring"""


		for row in grid:
				for cell in row:
						print(_A     ,		end=" "			)
				print()


if __name__ == "__main__":
						# make a copy of grid so that you can compare with the unmodified grid
						for example_grid in (initial_grid, no_solution):
												print('''\nExample grid:\n''' + '''=''' * 20)
												print_solution(example_grid)
												print('''\nExample grid solution:''')
												lowerCAmelCase__   	=	sudoku(example_grid)
												if solution is not None:
																		print_solution(solution)
												else:
																		print('''Cannot find a solution.''')









import math

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




def 			UpperCAmelCase__				(			_A      : int = 3							):





  '''simple docstring'''







  if isinstance(_A	,      _A							):
    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(_A							) != 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(_A	,      '''qr'''							)
  a__  =ClassicalRegister(_A	,      '''cr'''							)

  a__  =QuantumCircuit(_A	,      _A							)

  a__  =number_of_qubits

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

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

  # measure all the qubits
  quantum_circuit.measure(_A	,      _A							)
  # simulate with 10000 shots
  a__  =Aer.get_backend('''qasm_simulator'''							)
  a__  =execute(_A	,      _A	,      shots=1_00_00							)

  return job.result().get_counts(_A							)


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