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58 lines
1.8 KiB
58 lines
1.8 KiB
8 months ago
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/**
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* File: subset_sum_i.cpp
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* Created Time: 2023-06-21
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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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/* 回溯演算法：子集和 I */
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void backtrack(vector<int> &state, int target, vector<int> &choices, int start, vector<vector<int>> &res) {
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// 子集和等於 target 時，記錄解
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if (target == 0) {
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res.push_back(state);
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return;
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}
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// 走訪所有選擇
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// 剪枝二：從 start 開始走訪，避免生成重複子集
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for (int i = start; i < choices.size(); i++) {
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// 剪枝一：若子集和超過 target ，則直接結束迴圈
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// 這是因為陣列已排序，後邊元素更大，子集和一定超過 target
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if (target - choices[i] < 0) {
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break;
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}
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// 嘗試：做出選擇，更新 target, start
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state.push_back(choices[i]);
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// 進行下一輪選擇
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backtrack(state, target - choices[i], choices, i, res);
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// 回退：撤銷選擇，恢復到之前的狀態
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state.pop_back();
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}
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}
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/* 求解子集和 I */
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vector<vector<int>> subsetSumI(vector<int> &nums, int target) {
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vector<int> state; // 狀態（子集）
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sort(nums.begin(), nums.end()); // 對 nums 進行排序
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int start = 0; // 走訪起始點
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vector<vector<int>> res; // 結果串列（子集串列）
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backtrack(state, target, nums, start, res);
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return res;
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}
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/* Driver Code */
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int main() {
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vector<int> nums = {3, 4, 5};
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int target = 9;
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vector<vector<int>> res = subsetSumI(nums, target);
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cout << "輸入陣列 nums = ";
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printVector(nums);
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cout << "target = " << target << endl;
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cout << "所有和等於 " << target << " 的子集 res = " << endl;
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printVectorMatrix(res);
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return 0;
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}
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