hello-algo/codes/cpp/chapter_backtracking/subset_sum_i.cpp

/**
 * File: subset_sum_i.cpp
 * Created Time: 2023-06-21
 * Author: krahets (krahets@163.com)
 */

#include "../utils/common.hpp"

/* 回溯算法：子集和 I */
void backtrack(vector<int> &state, int target, vector<int> &choices, int start, vector<vector<int>> &res) {
    // 子集和等于 target 时，记录解
    if (target == 0) {
        res.push_back(state);
        return;
    }
    // 遍历所有选择
    // 剪枝二：从 start 开始遍历，避免生成重复子集
    for (int i = start; i < choices.size(); i++) {
        // 剪枝一：若子集和超过 target ，则直接结束循环
        // 这是因为数组已排序，后边元素更大，子集和一定超过 target
        if (target - choices[i] < 0) {
            break;
        }
        // 尝试：做出选择，更新 target, start
        state.push_back(choices[i]);
        // 进行下一轮选择
        backtrack(state, target - choices[i], choices, i, res);
        // 回退：撤销选择，恢复到之前的状态
        state.pop_back();
    }
}

/* 求解子集和 I */
vector<vector<int>> subsetSumI(vector<int> &nums, int target) {
    vector<int> state;              // 状态（子集）
    sort(nums.begin(), nums.end()); // 对 nums 进行排序
    int start = 0;                  // 遍历起始点
    vector<vector<int>> res;        // 结果列表（子集列表）
    backtrack(state, target, nums, start, res);
    return res;
}

/* Driver Code */
int main() {
    vector<int> nums = {3, 4, 5};
    int target = 9;

    vector<vector<int>> res = subsetSumI(nums, target);

    cout << "输入数组 nums = ";
    printVector(nums);
    cout << "target = " << target << endl;
    cout << "所有和等于 " << target << " 的子集 res = " << endl;
    printVectorMatrix(res);

    return 0;
}