






'''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   UpperCamelCase  (       snake_case__     :   int	,snake_case__     :   List[Any]	,snake_case__     :   Dict	,snake_case__     :   Optional[int]  ):




     '''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   UpperCamelCase  (       snake_case__     :   List[Any]  ):




     '''simple docstring'''






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






def   UpperCamelCase  (       snake_case__     :   int  ):




     '''simple docstring'''






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

     for digit in range(1	,10  ):
          if is_safe(snake_case__	,snake_case__	,snake_case__	,snake_case__  ):
               __snake_case			:Any          =						digit

               if sudoku(snake_case__  ) is not None:
                    return grid

               __snake_case			:Optional[Any]          =						0

     return None






def   UpperCamelCase  (       snake_case__     :   Optional[Any]  ):




     '''simple docstring'''






     for row in grid:
          for cell in row:
               print(snake_case__	,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 numpy as np
import qiskit






def   UpperCamelCase  (       snake_case__     :   int = 8	,snake_case__     :   int | None = None  ):




     '''simple docstring'''






     __snake_case			:Tuple          =						np.random.default_rng(seed=snake_case__  )

     # Roughly 25% of the qubits will contribute to the key.
     # So we take more than we need.
     __snake_case			:Union[str, Any]          =						6 * key_len
     # Measurement basis for Alice's qubits.
     __snake_case			:int          =						rng.integers(2	,size=snake_case__  )
     # The set of states Alice will prepare.
     __snake_case			:Dict          =						rng.integers(2	,size=snake_case__  )
     # Measurement basis for Bob's qubits.
     __snake_case			:str          =						rng.integers(2	,size=snake_case__  )

     # Quantum Circuit to simulate BB84
     __snake_case			:Optional[int]          =						qiskit.QuantumCircuit(snake_case__	,name="""BB84"""  )

     # Alice prepares her qubits according to rules above.
     for index, _ in enumerate(snake_case__  ):
          if alice_state[index] == 1:
               bbaa_circ.x(snake_case__  )
          if alice_basis[index] == 1:
               bbaa_circ.h(snake_case__  )
     bbaa_circ.barrier()

     # Bob measures the received qubits according to rules above.
     for index, _ in enumerate(snake_case__  ):
          if bob_basis[index] == 1:
               bbaa_circ.h(snake_case__  )

     bbaa_circ.barrier()
     bbaa_circ.measure_all()

     # Simulate the quantum circuit.
     __snake_case			:Optional[int]          =						qiskit.Aer.get_backend("""aer_simulator"""  )
     # We only need to run one shot because the key is unique.
     # Multiple shots will produce the same key.
     __snake_case			:List[Any]          =						qiskit.execute(snake_case__	,snake_case__	,shots=1	,seed_simulator=snake_case__  )
     # Returns the result of measurement.
     __snake_case			:Tuple          =						job.result().get_counts(snake_case__  ).most_frequent()

     # Extracting the generated key from the simulation results.
     # Only keep measurement results where Alice and Bob chose the same basis.
     __snake_case			:Any          =						"""""".join(
         [
             result_bit
             for alice_basis_bit, bob_basis_bit, result_bit in zip(
                 snake_case__	,snake_case__	,snake_case__  )
             if alice_basis_bit == bob_basis_bit
         ]  )

     # Get final key. Pad with 0 if too short, otherwise truncate.
     __snake_case			:Dict          =						gen_key[:key_len] if len(snake_case__  ) >= key_len else gen_key.ljust(snake_case__	,"""0"""  )
     return key


if __name__ == "__main__":
     print(f'''The generated key is : {bbaa(8, seed=0)}''')
     from doctest import testmod

     testmod()


