33 lines
737 B
Python
33 lines
737 B
Python
"""
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性能对比：循环累加 vs 高斯求和公式
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比较两种算法计算 1+2+...+n 的耗时差异
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"""
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import time
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def sum_by_loop(n):
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"""循环累加 O(n)"""
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total = 0
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for i in range(1, n + 1):
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total += i
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return total
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def sum_by_gauss(n):
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"""高斯求和公式 O(1)"""
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return n * (n + 1) // 2
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# 测试不同规模
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for n in [1000, 10000, 100000, 1000000]:
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print(f"\n--- n = {n} ---")
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start = time.time()
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r1 = sum_by_loop(n)
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t1 = time.time() - start
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start = time.time()
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r2 = sum_by_gauss(n)
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t2 = time.time() - start
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print(f"循环累加: {t1:.6f} 秒, 结果 = {r1}")
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print(f"高斯公式: {t2:.6f} 秒, 结果 = {r2}")
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print(f"加速比: {t1/t2:.2f}x")
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