Add the chapter of greedy. (#633)

Add the section of fractional knapsack.

codes/python/chapter_greedy/coin_change_greedy.py

@@ -0,0 +1,48 @@
+"""
+File: coin_change_greedy.py
+Created Time: 2023-07-18
+Author: Krahets (krahets@163.com)
+"""
+
+
+def coin_change_greedy(coins: list[int], amt: int) -> int:
+    """零钱兑换：贪心"""
+    # 假设 coins 列表有序
+    i = len(coins) - 1
+    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 -= 1
+        # 选择 coins[i]
+        amt -= coins[i]
+        count += 1
+    # 若未找到可行方案，则返回 -1
+    return count if amt == 0 else -1
+
+
+"""Driver Code"""
+if __name__ == "__main__":
+    # 贪心：能够保证找到全局最优解
+    coins = [1, 5, 10, 20, 50, 100]
+    amt = 186
+    res = coin_change_greedy(coins, amt)
+    print(f"\ncoins = {coins}, amt = {amt}")
+    print(f"凑到 {amt} 所需的最少硬币数量为 {res}")
+
+    # 贪心：无法保证找到全局最优解
+    coins = [1, 20, 50]
+    amt = 60
+    res = coin_change_greedy(coins, amt)
+    print(f"\ncoins = {coins}, amt = {amt}")
+    print(f"凑到 {amt} 所需的最少硬币数量为 {res}")
+    print(f"实际上需要的最少数量为 3 ，即 20 + 20 + 20")
+
+    # 贪心：无法保证找到全局最优解
+    coins = [1, 49, 50]
+    amt = 98
+    res = coin_change_greedy(coins, amt)
+    print(f"\ncoins = {coins}, amt = {amt}")
+    print(f"凑到 {amt} 所需的最少硬币数量为 {res}")
+    print(f"实际上需要的最少数量为 2 ，即 49 + 49")

codes/python/chapter_greedy/fractional_knapsack.py

@@ -0,0 +1,46 @@
+"""
+File: fractional_knapsack.py
+Created Time: 2023-07-19
+Author: Krahets (krahets@163.com)
+"""
+
+
+class Item:
+    """物品"""
+
+    def __init__(self, w: int, v: int):
+        self.w = w  # 物品重量
+        self.v = v  # 物品价值
+
+
+def fractional_knapsack(wgt: list[int], val: list[int], cap: int) -> int:
+    """分数背包：贪心"""
+    # 创建物品列表，包含两个属性：重量、价值
+    items = [Item(w, v) for w, v in zip(wgt, val)]
+    # 按照单位价值 item.v / item.w 从高到低进行排序
+    items.sort(key=lambda item: item.v / item.w, reverse=True)
+    # 循环贪心选择
+    res = 0
+    for item in 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 += (item.v / item.w) * cap
+            # 已无剩余容量，因此跳出循环
+            break
+    return res
+
+
+"""Driver Code"""
+if __name__ == "__main__":
+    wgt = [10, 20, 30, 40, 50]
+    val = [50, 120, 150, 210, 240]
+    cap = 50
+    n = len(wgt)
+
+    # 贪心算法
+    res = fractional_knapsack(wgt, val, cap)
+    print(f"不超过背包容量的最大物品价值为 {res}")