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 1 #include <iostream>
 2 using namespace std;
 3 
 4 //物品数据结构
 5 typedef struct commodity
 6 {
 7     int value;  //价值
 8     int weight; //重量
 9 }commodity;
10 
11 const int N = 3;  //物品个数
12 const int W = 50; //背包的容量
13 
14 //初始物品信息
15 commodity goods[N+1]={{0,0},{60,10},{100,20},{120,30}};
16 int select[N+1][W+1];
17 
18 int max_value();
19 
20 int main()
21 {
22     int maxvalue = max_value();
23     cout<<"The max value is: ";
24     cout<<maxvalue<<endl;
25     int remainspace = W;
26     //输出所选择的物品列表：
27     for(int i=N; i>=1; i--)
28     {
29         if (remainspace >= goods[i].weight)
30         {
31              if ((select[i][remainspace]-select[i-1][remainspace-goods[i].weight]==goods[i].value))
32              {
33                  cout << "item " << i << " is selected!" << endl;
34                  remainspace = remainspace - goods[i].weight;//如果第i个物品被选择，那么背包剩余容量将减去第i个物品的重量 ;
35              }
36         }
37     }
38     return 0;
39 }
40 int max_value()
41 {
42     //初始没有物品时候，背包的价值为0
43     for(int w=1;w<=W;++w)
44         select[0][w] = 0;
45     for(int i=1;i<=N;++i)
46     {
47         select[i][0] = 0;  //背包容量为0时，最大价值为0
48            for(int w=1;w<=W;++w)
49            {
50                if(goods[i].weight <= w)  //当前物品i的重量小于等于w，进行选择
51                {
52                    if( (goods[i].value + select[i-1][w-goods[i].weight]) > select[i-1][w])
53                     select[i][w] = goods[i].value + select[i-1][w-goods[i].weight];
54                    else
55                     select[i][w] = select[i-1][w];
56                }
57                else //当前物品i的重量大于w，不选择
58                  select[i][w] = select[i-1][w];
59            }
60     }
61     return select[N][W];  //最终求得最大值
62 }