Add the initial EN translation for C++ code (#1346)

en/codes/cpp/chapter_backtracking/subset_sum_i_naive.cpp

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+/**
+ * File: subset_sum_i_naive.cpp
+ * Created Time: 2023-06-21
+ * Author: krahets (krahets@163.com)
+ */
+
+#include "../utils/common.hpp"
+
+/* Backtracking algorithm: Subset Sum I */
+void backtrack(vector<int> &state, int target, int total, vector<int> &choices, vector<vector<int>> &res) {
+    // When the subset sum equals target, record the solution
+    if (total == target) {
+        res.push_back(state);
+        return;
+    }
+    // Traverse all choices
+    for (size_t i = 0; i < choices.size(); i++) {
+        // Pruning: if the subset sum exceeds target, skip that choice
+        if (total + choices[i] > target) {
+            continue;
+        }
+        // Attempt: make a choice, update elements and total
+        state.push_back(choices[i]);
+        // Proceed to the next round of selection
+        backtrack(state, target, total + choices[i], choices, res);
+        // Retract: undo the choice, restore to the previous state
+        state.pop_back();
+    }
+}
+
+/* Solve Subset Sum I (including duplicate subsets) */
+vector<vector<int>> subsetSumINaive(vector<int> &nums, int target) {
+    vector<int> state;       // State (subset)
+    int total = 0;           // Subset sum
+    vector<vector<int>> res; // Result list (subset list)
+    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 << "Input array nums = ";
+    printVector(nums);
+    cout << "target = " << target << endl;
+    cout << "All subsets summing to " << target << "is" << endl;
+    printVectorMatrix(res);
+
+    return 0;
+}