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71 lines
1.5 KiB
71 lines
1.5 KiB
/**
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* File: recursion.dart
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* Created Time: 2023-08-27
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* Author: liuyuxin (gvenusleo@gmail.com)
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*/
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/* 遞迴 */
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int recur(int n) {
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// 終止條件
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if (n == 1) return 1;
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// 遞：遞迴呼叫
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int res = recur(n - 1);
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// 迴：返回結果
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return n + res;
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}
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/* 使用迭代模擬遞迴 */
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int forLoopRecur(int n) {
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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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List<int> stack = [];
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int res = 0;
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// 遞：遞迴呼叫
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for (int i = n; i > 0; i--) {
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// 透過“入堆疊操作”模擬“遞”
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stack.add(i);
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}
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// 迴：返回結果
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while (!stack.isEmpty) {
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// 透過“出堆疊操作”模擬“迴”
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res += stack.removeLast();
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}
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// res = 1+2+3+...+n
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return res;
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}
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/* 尾遞迴 */
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int tailRecur(int n, int res) {
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// 終止條件
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if (n == 0) return res;
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// 尾遞迴呼叫
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return tailRecur(n - 1, res + n);
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}
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/* 費波那契數列：遞迴 */
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int fib(int n) {
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// 終止條件 f(1) = 0, f(2) = 1
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if (n == 1 || n == 2) return n - 1;
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// 遞迴呼叫 f(n) = f(n-1) + f(n-2)
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int 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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}
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/* Driver Code */
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void main() {
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int n = 5;
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int res;
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res = recur(n);
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print("\n遞迴函式的求和結果 res = $res");
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res = tailRecur(n, 0);
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print("\n尾遞迴函式的求和結果 res = $res");
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res = forLoopRecur(n);
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print("\n使用迭代模擬遞迴求和結果 res = $res");
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res = fib(n);
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print("\n費波那契數列的第 $n 項為 $res");
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}
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