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

en/codes/cpp/chapter_dynamic_programming/climbing_stairs_backtrack.cpp

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+
+/**
+ * File: climbing_stairs_backtrack.cpp
+ * Created Time: 2023-06-30
+ * Author: krahets (krahets@163.com)
+ */
+
+#include "../utils/common.hpp"
+
+/* Backtracking */
+void backtrack(vector<int> &choices, int state, int n, vector<int> &res) {
+    // When climbing to the nth step, add 1 to the number of solutions
+    if (state == n)
+        res[0]++;
+    // Traverse all choices
+    for (auto &choice : choices) {
+        // Pruning: do not allow climbing beyond the nth step
+        if (state + choice > n)
+            continue;
+        // Attempt: make a choice, update the state
+        backtrack(choices, state + choice, n, res);
+        // Retract
+    }
+}
+
+/* Climbing stairs: Backtracking */
+int climbingStairsBacktrack(int n) {
+    vector<int> choices = {1, 2}; // Can choose to climb up 1 step or 2 steps
+    int state = 0;                // Start climbing from the 0th step
+    vector<int> res = {0};        // Use res[0] to record the number of solutions
+    backtrack(choices, state, n, res);
+    return res[0];
+}
+
+/* Driver Code */
+int main() {
+    int n = 9;
+
+    int res = climbingStairsBacktrack(n);
+    cout << "There are " << res << " solutions to climb " << n << " stairs" << endl;
+
+    return 0;
+}