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70 lines
1.5 KiB
70 lines
1.5 KiB
"""
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File: recursion.py
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Created Time: 2023-08-24
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Author: krahets (krahets@163.com)
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"""
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def recur(n: int) -> int:
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"""遞迴"""
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# 終止條件
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if n == 1:
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return 1
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# 遞：遞迴呼叫
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res = recur(n - 1)
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# 迴：返回結果
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return n + res
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def for_loop_recur(n: int) -> int:
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"""使用迭代模擬遞迴"""
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# 使用一個顯式的堆疊來模擬系統呼叫堆疊
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stack = []
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res = 0
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# 遞：遞迴呼叫
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for i in range(n, 0, -1):
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# 透過“入堆疊操作”模擬“遞”
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stack.append(i)
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# 迴：返回結果
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while stack:
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# 透過“出堆疊操作”模擬“迴”
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res += stack.pop()
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# res = 1+2+3+...+n
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return res
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def tail_recur(n, res):
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"""尾遞迴"""
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# 終止條件
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if n == 0:
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return res
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# 尾遞迴呼叫
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return tail_recur(n - 1, res + n)
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def fib(n: int) -> int:
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"""費波那契數列：遞迴"""
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# 終止條件 f(1) = 0, f(2) = 1
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if n == 1 or n == 2:
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return n - 1
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# 遞迴呼叫 f(n) = f(n-1) + f(n-2)
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res = fib(n - 1) + fib(n - 2)
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# 返回結果 f(n)
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return res
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"""Driver Code"""
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if __name__ == "__main__":
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n = 5
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res = recur(n)
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print(f"\n遞迴函式的求和結果 res = {res}")
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res = for_loop_recur(n)
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print(f"\n使用迭代模擬遞迴求和結果 res = {res}")
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res = tail_recur(n, 0)
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print(f"\n尾遞迴函式的求和結果 res = {res}")
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res = fib(n)
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print(f"\n費波那契數列的第 {n} 項為 {res}")
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