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

en/codes/cpp/chapter_greedy/CMakeLists.txt

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+add_executable(coin_change_greedy coin_change_greedy.cpp)
+add_executable(fractional_knapsack fractional_knapsack.cpp)
+add_executable(max_capacity max_capacity.cpp)

en/codes/cpp/chapter_greedy/coin_change_greedy.cpp

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+/**
+ * File: coin_change_greedy.cpp
+ * Created Time: 2023-07-20
+ * Author: krahets (krahets@163.com)
+ */
+
+#include "../utils/common.hpp"
+
+/* Coin change: Greedy */
+int coinChangeGreedy(vector<int> &coins, int amt) {
+    // Assume coins list is ordered
+    int i = coins.size() - 1;
+    int count = 0;
+    // Loop for greedy selection until no remaining amount
+    while (amt > 0) {
+        // Find the smallest coin close to and less than the remaining amount
+        while (i > 0 && coins[i] > amt) {
+            i--;
+        }
+        // Choose coins[i]
+        amt -= coins[i];
+        count++;
+    }
+    // If no feasible solution is found, return -1
+    return amt == 0 ? count : -1;
+}
+
+/* Driver Code */
+int main() {
+    // Greedy: can ensure finding a global optimal solution
+    vector<int> coins = {1, 5, 10, 20, 50, 100};
+    int amt = 186;
+    int res = coinChangeGreedy(coins, amt);
+    cout << "\ncoins = ";
+    printVector(coins);
+    cout << "amt = " << amt << endl;
+    cout << "The minimum number of coins required to make up " << amt << " is " << res << endl;
+
+    // Greedy: cannot ensure finding a global optimal solution
+    coins = {1, 20, 50};
+    amt = 60;
+    res = coinChangeGreedy(coins, amt);
+    cout << "\ncoins = ";
+    printVector(coins);
+    cout << "amt = " << amt << endl;
+    cout << "The minimum number of coins required to make up " << amt << " is " << res << endl;
+    cout << "In reality, the minimum number needed is 3, i.e., 20 + 20 + 20" << endl;
+
+    // Greedy: cannot ensure finding a global optimal solution
+    coins = {1, 49, 50};
+    amt = 98;
+    res = coinChangeGreedy(coins, amt);
+    cout << "\ncoins = ";
+    printVector(coins);
+    cout << "amt = " << amt << endl;
+    cout << "The minimum number of coins required to make up " << amt << " is " << res << endl;
+    cout << "In reality, the minimum number needed is 2, i.e., 49 + 49" << endl;
+
+    return 0;
+}

en/codes/cpp/chapter_greedy/fractional_knapsack.cpp

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+/**
+ * File: fractional_knapsack.cpp
+ * Created Time: 2023-07-20
+ * Author: krahets (krahets@163.com)
+ */
+
+#include "../utils/common.hpp"
+
+/* Item */
+class Item {
+  public:
+    int w; // Item weight
+    int v; // Item value
+
+    Item(int w, int v) : w(w), v(v) {
+    }
+};
+
+/* Fractional knapsack: Greedy */
+double fractionalKnapsack(vector<int> &wgt, vector<int> &val, int cap) {
+    // Create an item list, containing two properties: weight, value
+    vector<Item> items;
+    for (int i = 0; i < wgt.size(); i++) {
+        items.push_back(Item(wgt[i], val[i]));
+    }
+    // Sort by unit value item.v / item.w from high to low
+    sort(items.begin(), items.end(), [](Item &a, Item &b) { return (double)a.v / a.w > (double)b.v / b.w; });
+    // Loop for greedy selection
+    double res = 0;
+    for (auto &item : items) {
+        if (item.w <= cap) {
+            // If the remaining capacity is sufficient, put the entire item into the knapsack
+            res += item.v;
+            cap -= item.w;
+        } else {
+            // If the remaining capacity is insufficient, put part of the item into the knapsack
+            res += (double)item.v / item.w * cap;
+            // No remaining capacity left, thus break the loop
+            break;
+        }
+    }
+    return res;
+}
+
+/* Driver Code */
+int main() {
+    vector<int> wgt = {10, 20, 30, 40, 50};
+    vector<int> val = {50, 120, 150, 210, 240};
+    int cap = 50;
+
+    // Greedy algorithm
+    double res = fractionalKnapsack(wgt, val, cap);
+    cout << "The maximum value within the bag capacity is " << res << endl;
+
+    return 0;
+}

en/codes/cpp/chapter_greedy/max_capacity.cpp

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+/**
+ * File: max_capacity.cpp
+ * Created Time: 2023-07-21
+ * Author: krahets (krahets@163.com)
+ */
+
+#include "../utils/common.hpp"
+
+/* Maximum capacity: Greedy */
+int maxCapacity(vector<int> &ht) {
+    // Initialize i, j, making them split the array at both ends
+    int i = 0, j = ht.size() - 1;
+    // Initial maximum capacity is 0
+    int res = 0;
+    // Loop for greedy selection until the two boards meet
+    while (i < j) {
+        // Update maximum capacity
+        int cap = min(ht[i], ht[j]) * (j - i);
+        res = max(res, cap);
+        // Move the shorter board inward
+        if (ht[i] < ht[j]) {
+            i++;
+        } else {
+            j--;
+        }
+    }
+    return res;
+}
+
+/* Driver Code */
+int main() {
+    vector<int> ht = {3, 8, 5, 2, 7, 7, 3, 4};
+
+    // Greedy algorithm
+    int res = maxCapacity(ht);
+    cout << "The maximum capacity is " << res << endl;
+
+    return 0;
+}

en/codes/cpp/chapter_greedy/max_product_cutting.cpp

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+/**
+ * File: max_product_cutting.cpp
+ * Created Time: 2023-07-21
+ * Author: krahets (krahets@163.com)
+ */
+
+#include "../utils/common.hpp"
+
+/* Maximum product of cutting: Greedy */
+int maxProductCutting(int n) {
+    // When n <= 3, must cut out a 1
+    if (n <= 3) {
+        return 1 * (n - 1);
+    }
+    // Greedy cut out 3s, a is the number of 3s, b is the remainder
+    int a = n / 3;
+    int b = n % 3;
+    if (b == 1) {
+        // When the remainder is 1, convert a pair of 1 * 3 into 2 * 2
+        return (int)pow(3, a - 1) * 2 * 2;
+    }
+    if (b == 2) {
+        // When the remainder is 2, do nothing
+        return (int)pow(3, a) * 2;
+    }
+    // When the remainder is 0, do nothing
+    return (int)pow(3, a);
+}
+
+/* Driver Code */
+int main() {
+    int n = 58;
+
+    // Greedy algorithm
+    int res = maxProductCutting(n);
+    cout << "Maximum cutting product is" << res << endl;
+
+    return 0;
+}