add python code

public/py/ch3/bag01/knapsack01.py

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+"""
+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}")

public/py/ch3/lcs/lcs.py

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+"""
+最长公共子序列 (LCS) — 动态规划
+比较两个序列的相似度
+"""
+
+def lcs_length(X, Y):
+    """计算 LCS 长度并返回 DP 表"""
+    m, n = len(X), len(Y)
+    dp = [[0] * (n + 1) for _ in range(m + 1)]
+
+    for i in range(1, m + 1):
+        for j in range(1, n + 1):
+            if X[i - 1] == Y[j - 1]:
+                dp[i][j] = dp[i - 1][j - 1] + 1
+            else:
+                dp[i][j] = max(dp[i - 1][j], dp[i][j - 1])
+
+    return dp[m][n], dp
+
+def lcs_backtrack(X, Y, dp):
+    """回溯找出 LCS 序列"""
+    i, j = len(X), len(Y)
+    result = []
+
+    while i > 0 and j > 0:
+        if X[i - 1] == Y[j - 1]:
+            result.append(X[i - 1])
+            i -= 1
+            j -= 1
+        elif dp[i - 1][j] > dp[i][j - 1]:
+            i -= 1
+        else:
+            j -= 1
+
+    return ''.join(reversed(result))
+
+if __name__ == "__main__":
+    X = "ABCBDAB"
+    Y = "BDCABB"
+
+    length, dp_table = lcs_length(X, Y)
+    lcs_str = lcs_backtrack(X, Y, dp_table)
+
+    print(f"序列 X: {X}")
+    print(f"序列 Y: {Y}")
+    print(f"LCS 长度: {length}")
+    print(f"LCS 序列: {lcs_str}")