


from __future__ import annotations

import math




def        snake_case_					(  snake_case      ,							snake_case      ,							snake_case      ,							snake_case      ,							snake_case					)  ->    int:


       if depth < 0:
              raise ValueError('Depth cannot be less than 0'					)

       if not scores:
              raise ValueError('Scores cannot be empty'					)

       if depth == height:
              return scores[node_index]

       return (
           max(
               minimax(depth + 1      ,							node_index * 2      ,							_snake_case      ,							_snake_case      ,							_snake_case					)      ,							minimax(depth + 1      ,							node_index * 2 + 1      ,							_snake_case      ,							_snake_case      ,							_snake_case					)      ,							)
           if is_max
           else min(
               minimax(depth + 1      ,							node_index * 2      ,							_snake_case      ,							_snake_case      ,							_snake_case					)      ,							minimax(depth + 1      ,							node_index * 2 + 1      ,							_snake_case      ,							_snake_case      ,							_snake_case					)      ,							)
       )




def        snake_case_					(  )  ->    None:
       lowercase__:       int        =       [90, 23, 6, 33, 21, 65, 1_23, 3_44_23]
       lowercase__:       int        =       math.log(len(_snake_case					)      ,							2					)
       print(f'Optimal value : {minimax(0      ,							0      ,							_snake_case      ,							_snake_case      ,							_snake_case					)}'					)


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 main()








import math

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




def        snake_case_					(  snake_case = 3					)  ->    qiskit.result.counts.Counts:
       if isinstance(snake_case      ,							snake_case					):
              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(snake_case					) != 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).'					)

       lowercase__:       str        =       QuantumRegister(snake_case      ,							'qr'					)
       lowercase__:       str        =       ClassicalRegister(snake_case      ,							'cr'					)

       lowercase__:       List[Any]        =       QuantumCircuit(snake_case      ,							snake_case					)

       lowercase__:       int        =       number_of_qubits

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

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

       # measure all the qubits
       quantum_circuit.measure(snake_case      ,							snake_case					)
       # simulate with 10000 shots
       lowercase__:       str        =       Aer.get_backend('qasm_simulator'					)
       lowercase__:       Union[str, Any]        =       execute(snake_case      ,							snake_case      ,							shots=1_00_00					)

       return job.result().get_counts(snake_case					)


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


