"""
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}")