动态规划求解0-1背包

C代码实现如下：

#include <stdio.h>
#include <stdlib.h>

int** DP(int num, int Weight, int*w, int *v);
void output(int *c, int *w, int weight, int **ptr, int num);
int main()
{   

    
    int w[] = {3, 4, 7, 8, 9};
    int v[] = {4, 5, 10, 11, 13};
    int num = 5, weight = 17;
    int out[5] = {0};
    int i = 0, j = 0;
    int **ptr = NULL;
    
    ptr = DP(num, weight, w, v);
    output(out, w, weight, ptr, num);

    for(i = 0; i< num; i++)
    {
        for(j = 0; j < weight + 1; j++)
        {
            printf("%2d ", ptr[i][j]);
        }
        printf("
");
        free(ptr[i]);
        ptr[i] = NULL;
    }
    printf("
");
    free(ptr);
    ptr = NULL;

    for(i = 0; i < num; i++)
    {
        printf("%d ", out[i]);
    }
    printf("
");
    system("pause");
    return 0;
}


int** DP(int num, int Weight, int*w, int *v)
{
     int **arr = (int**)calloc(num, sizeof(int*));
     int i = 0, j = 0;
     for(i = 0; i < num; i++)
     {
         arr[i] = (int*)calloc(Weight + 1, sizeof(int));
     }

     for(i = 0; i < Weight + 1; i++)
     {
         arr[0][i] = 0;
     }
     for(i = 0; i < num; i++)
     {
         arr[i][0] = 0;
         for(j = 0; j < Weight + 1; j++)
         {  
             if(w[i] <= j)
             {   
                 if(i == 0)
                 {
                     arr[i][j] = v[i];
                 }
                 else
                 {
                     if(v[i] + arr[i - 1][j - w[i]] >= arr[i - 1][j])
                     {
                         arr[i][j] = v[i] + arr[i-1][j- w[i]];
                     }
                     else
                     {
                         arr[i][j] = arr[i - 1][j];
                     }
                 }     
             }
             else
             {   
                 if(i == 0)
                 {
                     arr[i][j] = 0;
                 }
                 else
                 {
                     arr[i][j] = arr[i - 1][j];
                 }
                 
             }

         }
     }

    return arr;
}

void output(int *c, int *w, int weight, int **ptr, int num)
{
   int i = 0;

   for(i = num - 1; i >=1; i--)
   {
       if(ptr[i][weight] == ptr[i - 1][weight])
       {
           c[i] = 0;
       }
       else
       {
           c[i] = 1;
           weight -= w[i];
       }

    
   }

   if(ptr[i][weight] == 0)
   {
       c[i] = 0;
   }
   else
   {
       c[i] = 1;
   }

}