



from __future__ import annotations

from pathlib import Path







def 							A     (						__UpperCAmelCase				,   __UpperCAmelCase      )			->			int:



						'''simple docstring'''






						return pointa[0] * pointa[1] - pointa[1] * pointa[0]







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



						'''simple docstring'''






						UpperCAmelCase_					=	(xa, ya)
						UpperCAmelCase_					=	(xa - xa, ya - ya)
						UpperCAmelCase_					=	(xa - xa, ya - ya)
						UpperCAmelCase_					=	-vector_product(__UpperCAmelCase				,   __UpperCAmelCase      ) / vector_product(
						    __UpperCAmelCase				,   __UpperCAmelCase      )
						UpperCAmelCase_					=	+vector_product(__UpperCAmelCase				,   __UpperCAmelCase      ) / vector_product(
						    __UpperCAmelCase				,   __UpperCAmelCase      )

						return a > 0 and b > 0 and a + b < 1







def 							A     (						__UpperCAmelCase = "p102_triangles.txt"      )			->			int:



						'''simple docstring'''






						UpperCAmelCase_					=	Path(__UpperCAmelCase      ).parent.joinpath(__UpperCAmelCase      ).read_text(encoding='''utf-8'''      )

						UpperCAmelCase_					=	[]
						for line in data.strip().split('''\n'''      ):
												triangles.append([int(__UpperCAmelCase      ) for number in line.split(''','''      )]      )

						UpperCAmelCase_					=	0
						UpperCAmelCase_					=	42

						for triangle in triangles:
												ret += contains_origin(*__UpperCAmelCase      )

						return ret


if __name__ == "__main__":
							print(f"{solution() = }")










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)}")





