Add the section of subset sum problem. (#558)

codes/cpp/chapter_backtracking/subset_sum_i_naive.cpp

@@ -0,0 +1,54 @@
+/**
+ * File: subset_sum_i_naive.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, int total, vector<int> &choices, vector<vector<int>> &res) {
+    // 子集和等于 target 时，记录解
+    if (total == target) {
+        res.push_back(state);
+        return;
+    }
+    // 遍历所有选择
+    for (size_t i = 0; i < choices.size(); i++) {
+        // 剪枝：若子集和超过 target ，则跳过该选择
+        if (total + choices[i] > target) {
+            continue;
+        }
+        // 尝试：做出选择，更新元素和 total
+        state.push_back(choices[i]);
+        // 进行下一轮选择
+        backtrack(state, target, total + choices[i], choices, res);
+        // 回退：撤销选择，恢复到之前的状态
+        state.pop_back();
+    }
+}
+
+/* 求解子集和 I（包含重复子集） */
+vector<vector<int>> subsetSumINaive(vector<int> &nums, int target) {
+    vector<int> state;       // 状态（子集）
+    int total = 0;           // 子集和
+    vector<vector<int>> res; // 结果列表（子集列表）
+    backtrack(state, target, total, nums, res);
+    return res;
+}
+
+/* Driver Code */
+int main() {
+    vector<int> nums = {3, 4, 5};
+    int target = 9;
+
+    vector<vector<int>> res = subsetSumINaive(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;
+}