خوارزمية غروفر للبحث

import numpy as np

N = 8
target = 5

def oracle(state, marked):
    out = state.copy()
    out[marked] = -out[marked]
    return out

def diffusion(state):
    mean = np.mean(state)
    return 2 * mean - state

state = np.ones(N) / np.sqrt(N)
print("الاتساع الابتدائي لكل حالة:", round(float(state[0]), 4))
print("احتمال الحل قبل البدء:", round(float(state[target] ** 2), 4))

import numpy as np

N = 8
target = 5
state = np.ones(N) / np.sqrt(N)

for step in range(1, 7):
    state[target] = -state[target]
    state = 2 * np.mean(state) - state
    probability = float(state[target] ** 2)
    print(f"بعد {step} تكرار: احتمال الحل = {probability:.4f}")

optimal = int(np.floor(np.pi / 4 * np.sqrt(N)))
print("العدد الأمثل نظرياً:", optimal)

import numpy as np
import matplotlib.pyplot as plt

N = 8
target = 5
state = np.ones(N) / np.sqrt(N)
probabilities = [float(state[target] ** 2)]

for _ in range(10):
    state[target] = -state[target]
    state = 2 * np.mean(state) - state
    probabilities.append(float(state[target] ** 2))

fig, ax = plt.subplots(figsize=(5, 3.2))
ax.plot(range(len(probabilities)), probabilities, marker="o", color="#0D5C43")
ax.axvline(np.pi / 4 * np.sqrt(N), color="#22C55E", linestyle="--", label="optimal k")
ax.set_xlabel("iterations")
ax.set_ylabel("success probability")
ax.set_ylim(0, 1.05)
ax.grid(alpha=0.3)
ax.legend()
plt.show()