def one_iteration(marked, apply_oracle=True):
    if marked not in range(4) or type(apply_oracle) is not bool:
        raise ValueError("marked must be a four-item oracle index")
    amplitudes = [0.5] * 4
    if apply_oracle:
        amplitudes[marked] *= -1
    assert abs(sum(a*a for a in amplitudes) - 1.0) < 1e-12
    mean = sum(amplitudes) / 4
    amplitudes = [2*mean - a for a in amplitudes]
    assert abs(sum(a*a for a in amplitudes) - 1.0) < 1e-12
    return amplitudes
baseline = one_iteration(2)
alternate = one_iteration(0)
oracle_omitted = one_iteration(2, False)
for marked in range(4):
    result = one_iteration(marked)
    assert result[marked] == 1.0 and sum(abs(a) for i, a in enumerate(result) if i != marked) == 0
assert baseline == [0.0, 0.0, 1.0, 0.0] and alternate == [1.0, 0.0, 0.0, 0.0]
assert oracle_omitted == [0.5, 0.5, 0.5, 0.5]
print(f"PASS: 83 full-stack Grover baseline={baseline} alternate={alternate} no_oracle_success={oracle_omitted[2]**2:.2f}")