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

en/codes/cpp/chapter_dynamic_programming/coin_change_ii.cpp

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+/**
+ * File: coin_change_ii.cpp
+ * Created Time: 2023-07-11
+ * Author: krahets (krahets@163.com)
+ */
+
+#include "../utils/common.hpp"
+
+/* Coin change II: Dynamic programming */
+int coinChangeIIDP(vector<int> &coins, int amt) {
+    int n = coins.size();
+    // Initialize dp table
+    vector<vector<int>> dp(n + 1, vector<int>(amt + 1, 0));
+    // Initialize first column
+    for (int i = 0; i <= n; i++) {
+        dp[i][0] = 1;
+    }
+    // State transition
+    for (int i = 1; i <= n; i++) {
+        for (int a = 1; a <= amt; a++) {
+            if (coins[i - 1] > a) {
+                // If exceeding the target amount, do not choose coin i
+                dp[i][a] = dp[i - 1][a];
+            } else {
+                // The sum of the two options of not choosing and choosing coin i
+                dp[i][a] = dp[i - 1][a] + dp[i][a - coins[i - 1]];
+            }
+        }
+    }
+    return dp[n][amt];
+}
+
+/* Coin change II: Space-optimized dynamic programming */
+int coinChangeIIDPComp(vector<int> &coins, int amt) {
+    int n = coins.size();
+    // Initialize dp table
+    vector<int> dp(amt + 1, 0);
+    dp[0] = 1;
+    // State transition
+    for (int i = 1; i <= n; i++) {
+        for (int a = 1; a <= amt; a++) {
+            if (coins[i - 1] > a) {
+                // If exceeding the target amount, do not choose coin i
+                dp[a] = dp[a];
+            } else {
+                // The sum of the two options of not choosing and choosing coin i
+                dp[a] = dp[a] + dp[a - coins[i - 1]];
+            }
+        }
+    }
+    return dp[amt];
+}
+
+/* Driver code */
+int main() {
+    vector<int> coins = {1, 2, 5};
+    int amt = 5;
+
+    // Dynamic programming
+    int res = coinChangeIIDP(coins, amt);
+    cout << "The number of coin combinations to make up the target amount is " << res << endl;
+
+    // Space-optimized dynamic programming
+    res = coinChangeIIDPComp(coins, amt);
+    cout << "The number of coin combinations to make up the target amount is " << res << endl;
+
+    return 0;
+}