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

en/codes/cpp/chapter_dynamic_programming/coin_change.cpp

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+/**
+ * File: coin_change.cpp
+ * Created Time: 2023-07-11
+ * Author: krahets (krahets@163.com)
+ */
+
+#include "../utils/common.hpp"
+
+/* Coin change: Dynamic programming */
+int coinChangeDP(vector<int> &coins, int amt) {
+    int n = coins.size();
+    int MAX = amt + 1;
+    // Initialize dp table
+    vector<vector<int>> dp(n + 1, vector<int>(amt + 1, 0));
+    // State transition: first row and first column
+    for (int a = 1; a <= amt; a++) {
+        dp[0][a] = MAX;
+    }
+    // State transition: the rest of the rows and columns
+    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 smaller value between not choosing and choosing coin i
+                dp[i][a] = min(dp[i - 1][a], dp[i][a - coins[i - 1]] + 1);
+            }
+        }
+    }
+    return dp[n][amt] != MAX ? dp[n][amt] : -1;
+}
+
+/* Coin change: Space-optimized dynamic programming */
+int coinChangeDPComp(vector<int> &coins, int amt) {
+    int n = coins.size();
+    int MAX = amt + 1;
+    // Initialize dp table
+    vector<int> dp(amt + 1, MAX);
+    dp[0] = 0;
+    // 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 smaller value between not choosing and choosing coin i
+                dp[a] = min(dp[a], dp[a - coins[i - 1]] + 1);
+            }
+        }
+    }
+    return dp[amt] != MAX ? dp[amt] : -1;
+}
+
+/* Driver code */
+int main() {
+    vector<int> coins = {1, 2, 5};
+    int amt = 4;
+
+    // Dynamic programming
+    int res = coinChangeDP(coins, amt);
+    cout << "The minimum number of coins required to make up the target amount is " << res << endl;
+
+    // Space-optimized dynamic programming
+    res = coinChangeDPComp(coins, amt);
+    cout << "The minimum number of coins required to make up the target amount is " << res << endl;
+
+    return 0;
+}