add python code

public/py/ch3/bag01/knapsack01.py

@@ -0,0 +1,47 @@
+"""
+0/1 背包问题 — 动态规划经典问题
+给定容量 W 和价值/重量数组，求最大价值
+"""
+
+def knapsack_01(weights, values, W):
+    """0/1背包 DP 解法"""
+    n = len(weights)
+    # dp[i][w] 表示前 i 个物品在容量 w 下的最大价值
+    dp = [[0] * (W + 1) for _ in range(n + 1)]
+
+    for i in range(1, n + 1):
+        for w in range(1, W + 1):
+            if weights[i - 1] <= w:
+                # 选或不选当前物品
+                dp[i][w] = max(
+                    dp[i - 1][w],
+                    dp[i - 1][w - weights[i - 1]] + values[i - 1]
+                )
+            else:
+                dp[i][w] = dp[i - 1][w]
+
+    return dp[n][W]
+
+def knapsack_01_optimized(weights, values, W):
+    """空间优化版：一维数组"""
+    dp = [0] * (W + 1)
+
+    for i in range(len(weights)):
+        for w in range(W, weights[i] - 1, -1):
+            dp[w] = max(dp[w], dp[w - weights[i]] + values[i])
+
+    return dp[W]
+
+if __name__ == "__main__":
+    weights = [2, 3, 4, 5]
+    values = [3, 4, 5, 6]
+    W = 8
+
+    result1 = knapsack_01(weights, values, W)
+    result2 = knapsack_01_optimized(weights, values, W)
+
+    print(f"物品重量: {weights}")
+    print(f"物品价值: {values}")
+    print(f"背包容量: {W}")
+    print(f"最大价值 (二维DP): {result1}")
+    print(f"最大价值 (一维优化): {result2}")