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

en/codes/cpp/chapter_dynamic_programming/climbing_stairs_dp.cpp

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+/**
+ * File: climbing_stairs_dp.cpp
+ * Created Time: 2023-06-30
+ * Author: krahets (krahets@163.com)
+ */
+
+#include "../utils/common.hpp"
+
+/* Climbing stairs: Dynamic programming */
+int climbingStairsDP(int n) {
+    if (n == 1 || n == 2)
+        return n;
+    // Initialize dp table, used to store subproblem solutions
+    vector<int> dp(n + 1);
+    // Initial state: preset the smallest subproblem solution
+    dp[1] = 1;
+    dp[2] = 2;
+    // State transition: gradually solve larger subproblems from smaller ones
+    for (int i = 3; i <= n; i++) {
+        dp[i] = dp[i - 1] + dp[i - 2];
+    }
+    return dp[n];
+}
+
+/* Climbing stairs: Space-optimized dynamic programming */
+int climbingStairsDPComp(int n) {
+    if (n == 1 || n == 2)
+        return n;
+    int a = 1, b = 2;
+    for (int i = 3; i <= n; i++) {
+        int tmp = b;
+        b = a + b;
+        a = tmp;
+    }
+    return b;
+}
+
+/* Driver Code */
+int main() {
+    int n = 9;
+
+    int res = climbingStairsDP(n);
+    cout << "There are " << res << " solutions to climb " << n << " stairs" << endl;
+
+    res = climbingStairsDPComp(n);
+    cout << "There are " << res << " solutions to climb " << n << " stairs" << endl;
+
+    return 0;
+}