





"""simple docstring"""



from __future__ import annotations







def 		__lowercase					(       snake_case_  :  list    ,snake_case_  :  int						)       ->List[Any]:



    '''simple docstring'''







    if len(snake_case_						) <= 1 or n <= 1:
        return

    insert_next(snake_case_    ,n - 1						)
    rec_insertion_sort(snake_case_    ,n - 1						)







def 		__lowercase					(       snake_case_  :  list    ,snake_case_  :  int						)       ->Union[str, Any]:



    '''simple docstring'''







    if index >= len(snake_case_						) or collection[index - 1] <= collection[index]:
        return

    # Swaps adjacent elements since they are not in ascending order
    __A			,	__A   :						Union[str, Any]									=					(
        collection[index],
        collection[index - 1],
    )

    insert_next(snake_case_    ,index + 1						)


if __name__ == "__main__":
       a_			=      input("""Enter integers separated by spaces: """)
       a_			=      [int(num) for num in numbers.split()]
       rec_insertion_sort(number_list, len(number_list))
       print(number_list)











"""simple docstring"""



import numpy as np
import qiskit







def 		__lowercase					(       snake_case_  :  int = 8    ,snake_case_  :  int | None = None						)       ->str:



    '''simple docstring'''







    __A   :						str									=					np.random.default_rng(seed=snake_case_						)

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

    # Quantum Circuit to simulate BB84
    __A   :						Dict									=					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.
    __A   :						List[str]									=					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.
    __A   :						List[str]									=					qiskit.execute(snake_case_    ,snake_case_    ,shots=1    ,seed_simulator=snake_case_						)
    # Returns the result of measurement.
    __A   :						Union[str, Any]									=					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.
    __A   :						int									=					''''''.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.
    __A   :						Union[str, Any]									=					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()




