Add the chapter of greedy. (#633)

Add the section of fractional knapsack.

codes/cpp/CMakeLists.txt

@@ -17,3 +17,4 @@ add_subdirectory(chapter_sorting)
 add_subdirectory(chapter_divide_and_conquer)
 add_subdirectory(chapter_backtracking)
 add_subdirectory(chapter_dynamic_programming)
+add_subdirectory(chapter_greedy)

codes/cpp/chapter_greedy/CMakeLists.txt

@@ -0,0 +1,2 @@
+add_executable(coin_change_greedy coin_change_greedy.cpp)
+add_executable(fractional_knapsack fractional_knapsack.cpp)

codes/cpp/chapter_greedy/coin_change_greedy.cpp

@@ -0,0 +1,60 @@
+/**
+ * File: coin_change_greedy.cpp
+ * Created Time: 2023-07-20
+ * Author: Krahets (krahets@163.com)
+ */
+
+#include "../utils/common.hpp"
+
+/* 零钱兑换：贪心 */
+int coinChangeGreedy(vector<int> &coins, int amt) {
+    // 假设 coins 列表有序
+    int i = coins.size() - 1;
+    int count = 0;
+    // 循环进行贪心选择，直到无剩余金额
+    while (amt > 0) {
+        // 找到小于且最接近剩余金额的硬币
+        while (coins[i] > amt) {
+            i--;
+        }
+        // 选择 coins[i]
+        amt -= coins[i];
+        count++;
+    }
+    // 若未找到可行方案，则返回 -1
+    return amt == 0 ? count : -1;
+}
+
+/* Driver Code */
+int main() {
+    // 贪心：能够保证找到全局最优解
+    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 << "凑到 " << amt << " 所需的最少硬币数量为 " << res << endl;
+
+    // 贪心：无法保证找到全局最优解
+    coins = {1, 20, 50};
+    amt = 60;
+    res = coinChangeGreedy(coins, amt);
+    cout << "\ncoins = [";
+    printVector(coins);
+    cout << "amt = " << amt << endl;
+    cout << "凑到 " << amt << " 所需的最少硬币数量为 " << res << endl;
+    cout << "实际上需要的最少数量为 3 ，即 20 + 20 + 20" << endl;
+
+    // 贪心：无法保证找到全局最优解
+    coins = {1, 49, 50};
+    amt = 98;
+    res = coinChangeGreedy(coins, amt);
+    cout << "\ncoins = [";
+    printVector(coins);
+    cout << "amt = " << amt << endl;
+    cout << "凑到 " << amt << " 所需的最少硬币数量为 " << res << endl;
+    cout << "实际上需要的最少数量为 2 ，即 49 + 49" << endl;
+
+    return 0;
+}

codes/cpp/chapter_greedy/fractional_knapsack.cpp

@@ -0,0 +1,56 @@
+/**
+ * File: fractional_knapsack.cpp
+ * Created Time: 2023-07-20
+ * Author: Krahets (krahets@163.com)
+ */
+
+#include "../utils/common.hpp"
+
+/* 物品 */
+class Item {
+  public:
+    int w; // 物品重量
+    int v; // 物品价值
+
+    Item(int w, int v) : w(w), v(v) {
+    }
+};
+
+/* 分数背包：贪心 */
+double fractionalKnapsack(vector<int> &wgt, vector<int> &val, int cap) {
+    // 创建物品列表，包含两个属性：重量、价值
+    vector<Item> items;
+    for (int i = 0; i < wgt.size(); i++) {
+        items.push_back(Item(wgt[i], val[i]));
+    }
+    // 按照单位价值 item.v / item.w 从高到低进行排序
+    sort(items.begin(), items.end(), [](Item &a, Item &b) { return (double)a.v / a.w > (double)b.v / b.w; });
+    // 循环贪心选择
+    double res = 0;
+    for (auto &item : items) {
+        if (item.w <= cap) {
+            // 若剩余容量充足，则将当前物品整个装进背包
+            res += item.v;
+            cap -= item.w;
+        } else {
+            // 若剩余容量不足，则将当前物品的一部分装进背包
+            res += (double)item.v / item.w * cap;
+            // 已无剩余容量，因此跳出循环
+            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;
+
+    // 贪心算法
+    double res = fractionalKnapsack(wgt, val, cap);
+    cout << "不超过背包容量的最大物品价值为 " << res << endl;
+
+    return 0;
+}

codes/cpp/chapter_hashing/CMakeLists.txt

@@ -3,4 +3,4 @@ add_executable(array_hash_map_test array_hash_map_test.cpp)
 add_executable(hash_map_chaining hash_map_chaining.cpp)
 add_executable(hash_map_open_addressing hash_map_open_addressing.cpp)
 add_executable(simple_hash simple_hash.cpp)
-add_executable(built_in_hash built_in_hash.cpp)
+add_executable(built_in_hash built_in_hash.cpp)