背包问题——（多重背包）

/**
 * FileName: Main
 * Author:   Jerry
 * Date:     2020/1/27 19:58
 * Description: 多重背包
 */
 
public class Main {
    /*
    *int []num 每种商品的最大售卖数
    * V 背包最大容积
    * N 商品种类数
    * */
    public static void multiplePack(int V,int N,int []weight,int []value,int []num)
    {
        int [][] dp =new int[N+1][V+1];
        int temp;
        int [] t =new int[N+1];
        //初始化动态规划数组
        for(int i=1;i<=N;i++)
        {
            for(int j=1;j<=V;j++)
            {
                if(j>=weight[i])
                {
                    int max = Math.min(num[i],j/weight[i]);
                    for(int k=0;k<=max;k++)
                    {
                        temp=Math.max(dp[i-1][j],dp[i-1][j-k*weight[i]]+k*value[i]);
                        if(dp[i][j]<temp)
                            t[i]=k;
                        dp[i][j]=Math.max(dp[i][j],temp);
                    }
                }
                else
                    dp[i][j]=dp[i-1][j];
            }
        }
        int maxValue = dp[N][V];
        System.out.println("最大价值为"+maxValue);
        int j =V;
        String numStr = "";
        for(int i=N;i>=1;i--)
        {
            if(dp[i][j]>dp[i-1][j])
            {
                numStr=numStr+"商品种类"+i+"该商品共"+t[i]+"件   ";
                j=j-weight[i];
            }
            if(j==0)
                break;
        }
        System.out.println(numStr);
    }
    public static void main(String[] args) {
        // TODO Auto-generated method stub
        int[] weight= {0,1,2,3};
        int[] value= {0,6,13,20};
        int[] num= {0,5,3,2};
        int bagV=15;
        int N=3;
        multiplePack(bagV,N,weight,value,num);
 
    }
 
 
}