



def 							A     (						__UpperCAmelCase				,   __UpperCAmelCase				,   __UpperCAmelCase				,   __UpperCAmelCase      )			->			int:



						'''simple docstring'''






						return len_board * len_board_column * row + column







def 							A     (						__UpperCAmelCase				,   __UpperCAmelCase				,   __UpperCAmelCase				,   __UpperCAmelCase				,   __UpperCAmelCase				,   __UpperCAmelCase				,   )			->			bool:



						'''simple docstring'''






						if board[row][column] != word[word_index]:
												return False

						if word_index == len(__UpperCAmelCase      ) - 1:
												return True

						UpperCAmelCase_					=	[(0, 1), (0, -1), (-1, 0), (1, 0)]
						UpperCAmelCase_					=	len(__UpperCAmelCase      )
						UpperCAmelCase_					=	len(board[0]      )
						for direction in traverts_directions:
												UpperCAmelCase_					=	row + direction[0]
												UpperCAmelCase_					=	column + direction[1]
												if not (0 <= next_i < len_board and 0 <= next_j < len_board_column):
																		continue

												UpperCAmelCase_					=	get_point_key(__UpperCAmelCase				,   __UpperCAmelCase				,   __UpperCAmelCase				,   __UpperCAmelCase      )
												if key in visited_points_set:
																		continue

												visited_points_set.add(__UpperCAmelCase      )
												if exits_word(__UpperCAmelCase				,   __UpperCAmelCase				,   __UpperCAmelCase				,   __UpperCAmelCase				,   word_index + 1				,   __UpperCAmelCase      ):
																		return True

												visited_points_set.remove(__UpperCAmelCase      )

						return False







def 							A     (						__UpperCAmelCase				,   __UpperCAmelCase      )			->			bool:



						'''simple docstring'''






						UpperCAmelCase_					=	(
						    '''The board should be a non empty matrix of single chars strings.'''
						)

						UpperCAmelCase_					=	len(__UpperCAmelCase      )
						if not isinstance(__UpperCAmelCase				,   __UpperCAmelCase      ) or len(__UpperCAmelCase      ) == 0:
												raise ValueError(__UpperCAmelCase      )

						for row in board:
												if not isinstance(__UpperCAmelCase				,   __UpperCAmelCase      ) or len(__UpperCAmelCase      ) == 0:
																		raise ValueError(__UpperCAmelCase      )

												for item in row:
																		if not isinstance(__UpperCAmelCase				,   __UpperCAmelCase      ) or len(__UpperCAmelCase      ) != 1:
																								raise ValueError(__UpperCAmelCase      )

    # Validate word
						if not isinstance(__UpperCAmelCase				,   __UpperCAmelCase      ) or len(__UpperCAmelCase      ) == 0:
												raise ValueError(
												    '''The word parameter should be a string of length greater than 0.'''      )

						UpperCAmelCase_					=	len(board[0]      )
						for i in range(__UpperCAmelCase      ):
												for j in range(__UpperCAmelCase      ):
																		if exits_word(
																		    __UpperCAmelCase				,   __UpperCAmelCase				,   __UpperCAmelCase				,   __UpperCAmelCase				,   0				,   {get_point_key(__UpperCAmelCase				,   __UpperCAmelCase				,   __UpperCAmelCase				,   __UpperCAmelCase      )}      ):
																								return True

						return False


if __name__ == "__main__":
							import doctest

							doctest.testmod()










import numpy as np
import qiskit







def 							A     (						__UpperCAmelCase				,   __UpperCAmelCase      )			->			qiskit.QuantumCircuit:



						'''simple docstring'''






						UpperCAmelCase_					=	qiskit.QuantumCircuit(num_qubits + 1      )

						# First, let's deal with the case in which oracle is balanced
						if case == "balanced":
												# First generate a random number that tells us which CNOTs to
												# wrap in X-gates:
												UpperCAmelCase_					=	np.random.randint(1				,   2**num_qubits      )
												# Next, format 'b' as a binary string of length 'n', padded with zeros:
												UpperCAmelCase_					=	format(__UpperCAmelCase				,   f"0{num_qubits}b"      )
												# Next, we place the first X-gates. Each digit in our binary string
												# corresponds to a qubit, if the digit is 0, we do nothing, if it's 1
												# we apply an X-gate to that qubit:
												for index, bit in enumerate(__UpperCAmelCase      ):
																		if bit == "1":
																								oracle_qc.x(__UpperCAmelCase      )
        # Do the controlled-NOT gates for each qubit, using the output qubit
        # as the target:
												for index in range(__UpperCAmelCase      ):
																		oracle_qc.cx(__UpperCAmelCase				,   __UpperCAmelCase      )
												# Next, place the final X-gates
												for index, bit in enumerate(__UpperCAmelCase      ):
																		if bit == "1":
																								oracle_qc.x(__UpperCAmelCase      )

    # Case in which oracle is constant
						if case == "constant":
												# First decide what the fixed output of the oracle will be
												# (either always 0 or always 1)
												UpperCAmelCase_					=	np.random.randint(2      )
												if output == 1:
																		oracle_qc.x(__UpperCAmelCase      )

						UpperCAmelCase_					=	oracle_qc.to_gate()
						UpperCAmelCase_					=	'''Oracle'''  # To show when we display the circuit
						return oracle_gate







def 							A     (						__UpperCAmelCase				,   __UpperCAmelCase      )			->			qiskit.QuantumCircuit:



						'''simple docstring'''






						UpperCAmelCase_					=	qiskit.QuantumCircuit(num_qubits + 1				,   __UpperCAmelCase      )
						# Set up the output qubit:
						dj_circuit.x(__UpperCAmelCase      )
						dj_circuit.h(__UpperCAmelCase      )
						# And set up the input register:
						for qubit in range(__UpperCAmelCase      ):
												dj_circuit.h(__UpperCAmelCase      )
						# Let's append the oracle gate to our circuit:
						dj_circuit.append(__UpperCAmelCase				,   range(num_qubits + 1      )      )
						# Finally, perform the H-gates again and measure:
						for qubit in range(__UpperCAmelCase      ):
												dj_circuit.h(__UpperCAmelCase      )

						for i in range(__UpperCAmelCase      ):
												dj_circuit.measure(__UpperCAmelCase				,   __UpperCAmelCase      )

						return dj_circuit







def 							A     (						__UpperCAmelCase				,   __UpperCAmelCase      )			->			qiskit.result.counts.Counts:



						'''simple docstring'''






						UpperCAmelCase_					=	qiskit.Aer.get_backend('''aer_simulator'''      )

						UpperCAmelCase_					=	dj_oracle(__UpperCAmelCase				,   __UpperCAmelCase      )
						UpperCAmelCase_					=	dj_algorithm(__UpperCAmelCase				,   __UpperCAmelCase      )

						# Execute the circuit on the simulator
						UpperCAmelCase_					=	qiskit.execute(__UpperCAmelCase				,   __UpperCAmelCase				,   shots=1000      )

						# Return the histogram data of the results of the experiment.
						return job.result().get_counts(__UpperCAmelCase      )


if __name__ == "__main__":
							print(f"Deutsch Jozsa - Constant Oracle: {deutsch_jozsa('constant', 3)}")
							print(f"Deutsch Jozsa - Balanced Oracle: {deutsch_jozsa('balanced', 3)}")





