77 lines
1.4 KiB
Python
77 lines
1.4 KiB
Python
"""
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函数递归调用 - 函数直接或者间接的调用了自身
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1. 收敛条件
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2. 递归公式
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n! = n * (n-1)!
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f(n) = f(n-1) + f(n-2)
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1 1 2 3 5 8 13 21 34 55 ...
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"""
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from contextlib import contextmanager
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from time import perf_counter
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def fac(num):
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"""求阶乘"""
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assert num >= 0
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if num in (0, 1):
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return 1
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return num * fac(num - 1)
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def fib2(num):
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"""普通函数"""
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a, b = 1, 1
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for _ in range(num - 1):
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a, b = b, a + b
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return a
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def fib3(num):
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"""生成器"""
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a, b = 0, 1
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for _ in range(num):
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a, b = b, a + b
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yield a
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# 动态规划 - 保存可能进行重复运算的中间结果（空间换时间）
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def fib(num, results={}):
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"""斐波拉切数"""
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assert num > 0
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if num in (1, 2):
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return 1
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try:
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return results[num]
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except KeyError:
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results[num] = fib(num - 1) + fib(num - 2)
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return results[num]
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@contextmanager
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def timer():
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try:
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start = perf_counter()
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yield
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finally:
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end = perf_counter()
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print(f'{end - start}秒')
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def main():
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"""主函数"""
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# for val in fib3(20):
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# print(val)
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# gen = fib3(20)
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# for _ in range(10):
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# print(next(gen))
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for num in range(1, 121):
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with timer():
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print(f'{num}: {fib(num)}')
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# print(fac(5))
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# print(fac(-5))
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if __name__ == '__main__':
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main()
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