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44 lines
1.1 KiB
44 lines
1.1 KiB
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/**
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* File: climbing_stairs_backtrack.cpp
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* Created Time: 2023-06-30
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* Author: krahets (krahets@163.com)
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*/
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#include "../utils/common.hpp"
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/* 回溯 */
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void backtrack(vector<int> &choices, int state, int n, vector<int> &res) {
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// 當爬到第 n 階時，方案數量加 1
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if (state == n)
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res[0]++;
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// 走訪所有選擇
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for (auto &choice : choices) {
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// 剪枝：不允許越過第 n 階
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if (state + choice > n)
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continue;
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// 嘗試：做出選擇，更新狀態
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backtrack(choices, state + choice, n, res);
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// 回退
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}
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}
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/* 爬樓梯：回溯 */
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int climbingStairsBacktrack(int n) {
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vector<int> choices = {1, 2}; // 可選擇向上爬 1 階或 2 階
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int state = 0; // 從第 0 階開始爬
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vector<int> res = {0}; // 使用 res[0] 記錄方案數量
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backtrack(choices, state, n, res);
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return res[0];
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}
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/* Driver Code */
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int main() {
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int n = 9;
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int res = climbingStairsBacktrack(n);
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cout << "爬 " << n << " 階樓梯共有 " << res << " 種方案" << endl;
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return 0;
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}
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