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63 lines
2.0 KiB
63 lines
2.0 KiB
/**
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* File: subset_sum_ii.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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/* 回溯算法：子集和 II */
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void backtrack(vector<int> &state, int target, vector<int> &choices, int start, vector<vector<int>> &res) {
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// 子集和等于 target 时，记录解
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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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// 遍历所有选择
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// 剪枝二：从 start 开始遍历，避免生成重复子集
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// 剪枝三：从 start 开始遍历，避免重复选择同一元素
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for (int i = start; i < choices.size(); i++) {
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// 剪枝一：若子集和超过 target ，则直接结束循环
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// 这是因为数组已排序，后边元素更大，子集和一定超过 target
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if (target - choices[i] < 0) {
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break;
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}
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// 剪枝四：如果该元素与左边元素相等，说明该搜索分支重复，直接跳过
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if (i > start && choices[i] == choices[i - 1]) {
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continue;
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}
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// 尝试：做出选择，更新 target, start
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state.push_back(choices[i]);
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// 进行下一轮选择
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backtrack(state, target - choices[i], choices, i + 1, res);
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// 回退：撤销选择，恢复到之前的状态
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state.pop_back();
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}
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}
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/* 求解子集和 II */
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vector<vector<int>> subsetSumII(vector<int> &nums, int target) {
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vector<int> state; // 状态（子集）
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sort(nums.begin(), nums.end()); // 对 nums 进行排序
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int start = 0; // 遍历起始点
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vector<vector<int>> res; // 结果列表（子集列表）
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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 = {4, 4, 5};
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int target = 9;
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vector<vector<int>> res = subsetSumII(nums, target);
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cout << "输入数组 nums = ";
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printVector(nums);
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cout << "target = " << target << endl;
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cout << "所有和等于 " << 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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