如何获取天真的0-1背包中的选定项目列表？

如何解决如何获取天真的0-1背包中的选定项目列表？

我有一个背包问题的天真解决方案的代码，我想获取所选项目的列表，目前它正在返回所选项目的总和。任何帮助将不胜感激。蟒蛇代码：

    def knapSack(W,wt,val,n):
 
    # Base Case
    if n == 0 or W == 0:
        return 0
 
    # If weight of the nth item is
    # more than Knapsack of capacity W,# then this item cannot be included
    # in the optimal solution
    if (wt[n-1] > W):
        return knapSack(W,n-1)
 
    # return the maximum of two cases:
    # (1) nth item included
    # (2) not included
    else:
        return max(
            val[n-1] + knapSack(
                W-wt[n-1],n-1),knapSack(W,n-1))
 
# end of function knapSack
 
 
#Driver Code
items= [a,b,c,d,e]
val = [60,100,120,125,129]
wt = [10,20,30,40,50]
W = 70
n = len(val)
print knapSack(W,n)

解决方法

所以这里的技巧是通过选择该路径返回所选项目的路径 p 以及累积的值 v。然后根据最大值 v 选择最佳路径。

def knapSack(W,wt,val,n):
 
    # Base Case
    if n == 0 or W == 0:
        return 0,[]
 
    # If weight of the nth item is
    # more than Knapsack of capacity W,# then this item cannot be included
    # in the optimal solution
    if (wt[n-1] > W):
        return knapSack(W,n-1)
 
    # return the maximum of two cases:
    # (1) nth item included
    v1,p1 = knapSack(W-wt[n-1],n-1)
    v1 += val[n-1]
    p1 = [items[n-1]] + p1
    
    # (2) not included
    v2,p2 = knapSack(W,n-1)
    
    return (v1,p1) if v1 >= v2 else (v2,p2)
    
            
if __name__ == "__main__":
    items = list('abcde')
    val = [60,100,120,125,129]
    wt = [10,20,30,40,50]
    W = 70
    n = len(val)
    val,path = knapSack(W,n)
    print(val,path)

请注意，您可以使用一些其他措施来加速此代码。最值得注意的是添加记忆，然后将其转换为自下而上的 dp 解决方案。如果您想了解更多有关如何应用这些内容的信息，请随时发表评论。