使用动态规划求解背包

我正在使用我在此链接中找到的算法来实现背包问题的片段背包问题 http://www.es.ele.tue.nl/education/5MC10/Solutions/knapsack.pdf

I have also attached the snippet of the algorithm here too.

我为该算法编写了以下 python 代码片段。这里是：

def knapsack(v,w,n,W):
    V = [[None for x in range(W+1)] for x in range(len(v)+1)]

    for wy in range(W+1):
        V[0][wy] = 0

    for i in range(1,n+1):
        for wx in range(W+1):
            # print i,wx
            if w[i] <= wx:

                V[i][wx] = max(V[i-1][wx], v[i]+V[i-1][wx-w[i]])
            else:
                V[i][wx] = V[i-1][wx]
    return V[n][W]

print knapsack(v = [10,40,30,50],w=[5,4,6,3],n=4,W=10)

我应该得到输出90在位置[4,9]。我在这里做错了什么？

我不确定，但我认为错误是

• 元素v and w是从 0 开始的索引（0 到 n-1）
• 您正在范围内迭代1 to n
• So w[n] or v[n]会扔IndexError

更新代码：

def knapsack(v,w,n,W):
    V = [[None for x in range(W+1)] for x in range(len(v)+1)]

    for wy in range(W+1):
        V[0][wy] = 0

    for i in range(1,n+1):
        for wx in range(W+1):
            # print i,wx
            if w[i-1] <= wx:

                V[i][wx] = max(V[i-1][wx], v[i-1]+V[i-1][wx-w[i-1]])
            else:
                V[i][wx] = V[i-1][wx]
    return V[n][W]

print knapsack(v = [10,40,30,50],w=[5,4,6,3],n=4,W=10)

现在的输出是90.

检查结果在Ideone http://ideone.com/sn4a5g