使用动态编程的背包无法给出正确的答案

Question

我正在使用我在此链接Knapsack Problem

中找到的算法实现背包问题的片段

我之前在Stack Overflow上问过这个问题，我在从程序的return语句中获取输出时遇到了问题。您可以在Previous question

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我也在这里附上了算法的片段。

我为该算法编写了以下python代码段。这是：

def knapsack(v,w,n,W):
    V = [[None for x in range(W+1)] for x in range(len(v)+1)]
    keep = [[0 for x in range(W+1)] for x in range(len(v)+1)]
    # print keep

    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]])
                keep[i][wx] = 1
            else:
                V[i][wx] = V[i-1][wx]
                keep[i][wx] = 0
    K = W
    # print keep
    for i in range(n,0,-1):
        if keep[i][K] == 1:
            print i
            K = K - w[i-1]

    return V[n][W]

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

我应该以 4,2 作为我的价值，但获得 4,3 。请纠正我出错的地方。

Answer 1

if语句中的问题：

        if w[i-1] <= wx:

            V[i][wx] = max(V[i-1][wx], v[i-1]+V[i-1][wx-w[i-1]])
            keep[i][wx] = 1
        else:
            V[i][wx] = V[i-1][wx]
            keep[i][wx] = 0

你正在做的(w[i-1] <= wx) and (v[i-1]+V[i-1][wx-w[i-1]] <= V[i-1][wx])的

            V[i][wx] = max(V[i-1][wx], v[i-1]+V[i-1][wx-w[i-1]])
            keep[i][wx] = 1

但你应该

            V[i][wx] = V[i-1][wx]
            keep[i][wx] = 0