




"""simple docstring"""



import math







def     _SCREAMING_SNAKE_CASE  (				lowercase_		)		->						list:
 if n <= 0:
  raise ValueError("Only positive integers have prime factors"		)
 A__			=							[]
 while n % 2 == 0:
  pf.append(2		)
  A__			=							int(n / 2		)
 for i in range(3     ,					int(math.sqrt(lowercase_		)		) + 1     ,					2		):
  while n % i == 0:
   pf.append(lowercase_		)
   A__			=							int(n / i		)
 if n > 2:
  pf.append(lowercase_		)
 return pf







def     _SCREAMING_SNAKE_CASE  (				lowercase_		)		->						int:
 if n <= 0:
  raise ValueError("Only positive numbers are accepted"		)
 A__			=							1
 A__			=							1
 while n % 2 == 0:
  temp += 1
  A__			=							int(n / 2		)
 div *= temp
 for i in range(3     ,					int(math.sqrt(lowercase_		)		) + 1     ,					2		):
  A__			=							1
  while n % i == 0:
   temp += 1
   A__			=							int(n / i		)
  div *= temp
 if n > 1:
  div *= 2
 return div







def     _SCREAMING_SNAKE_CASE  (				lowercase_		)		->						int:
 if n <= 0:
  raise ValueError("Only positive numbers are accepted"		)
 A__			=							1
 A__			=							1
 while n % 2 == 0:
  temp += 1
  A__			=							int(n / 2		)
 if temp > 1:
  s *= (2**temp - 1) / (2 - 1)
 for i in range(3     ,					int(math.sqrt(lowercase_		)		) + 1     ,					2		):
  A__			=							1
  while n % i == 0:
   temp += 1
   A__			=							int(n / i		)
  if temp > 1:
   s *= (i**temp - 1) / (i - 1)
 return int(lowercase_		)







def     _SCREAMING_SNAKE_CASE  (				lowercase_		)		->						int:
 A__			=							n
 for x in set(prime_factors(lowercase_		)		):
  s *= (x - 1) / x
 return int(lowercase_		)


if __name__ == "__main__":
      import doctest

      doctest.testmod()











"""simple docstring"""



import numpy as np
import qiskit







def     _SCREAMING_SNAKE_CASE  (				lowercase_     ,					lowercase_		)		->						qiskit.QuantumCircuit:
 A__			=							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:
  A__			=							np.random.randint(1     ,					2**num_qubits		)
  # Next, format 'b' as a binary string of length 'n', padded with zeros:
  A__			=							format(lowercase_     ,					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(lowercase_		):
   if bit == "1":
    oracle_qc.x(lowercase_		)
        # Do the controlled-NOT gates for each qubit, using the output qubit
        # as the target:
  for index in range(lowercase_		):
   oracle_qc.cx(lowercase_     ,					lowercase_		)
  # Next, place the final X-gates
  for index, bit in enumerate(lowercase_		):
   if bit == "1":
    oracle_qc.x(lowercase_		)

    # 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)
  A__			=							np.random.randint(2		)
  if output == 1:
   oracle_qc.x(lowercase_		)

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







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

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

 return dj_circuit







def     _SCREAMING_SNAKE_CASE  (				lowercase_     ,					lowercase_		)		->						qiskit.result.counts.Counts:
 A__			=							qiskit.Aer.get_backend("aer_simulator"		)

 A__			=							dj_oracle(lowercase_     ,					lowercase_		)
 A__			=							dj_algorithm(lowercase_     ,					lowercase_		)

 # Execute the circuit on the simulator
 A__			=							qiskit.execute(lowercase_     ,					lowercase_     ,					shots=10_00		)

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


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





