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递推公式：

f(n,m)=max{f(n-1,m), f(n-1,m-w[n])+P(n,m)}

Sample Code


 1  #include < stdio.h >
 2  int  c[ 10 ][ 100 ]; /* 对应每种情况的最大价值 */
 3  int  knapsack( int  m, int  n)
  4  {
  5    int  i,j,w[ 10 ],p[ 10 ];
  6    for (i = 1 ;i < n + 1 ;i ++ )
  7          scanf( " \n%d,%d " , & w[i], & p[i]);
  8    for (i = 0 ;i < 10 ;i ++ )
  9         for (j = 0 ;j < 100 ;j ++ )
 10             c[i][j] = 0 ; /* 初始化数组 */
11    for (i = 1 ;i < n + 1 ;i ++ )
 12         for (j = 1 ;j < m + 1 ;j ++ )
 13             {
 14               if (w[i] <= j)  /* 如果当前物品的容量小于背包容量 */
15                       {
 16                         if (p[i] + c[i - 1 ][j - w[i]] > c[i - 1 ][j])
 17 
18                              /* 如果本物品的价值加上背包剩下的空间能放的物品的价值 */
19 
20                            /* 大于上一次选择的最佳方案则更新c[i][j] */
21                              c[i][j] = p[i] + c[i - 1 ][j - w[i]];
 22                               else
23                              c[i][j] = c[i - 1 ][j];
 24                       }
 25                 else  c[i][j] = c[i - 1 ][j];
 26              }
 27    return (c[n][m]);
 28                      
 29  }
 30  int  main()
 31  {
 32       int  m,n; int  i,j;
 33      scanf( " %d,%d " , & m, & n);
 34      printf( " Input each one:\n " );
 35      printf( " %d " ,knapsack(m,n));
 36      printf( " \n " ); /* 下面是测试这个数组,可删除 */
37        for (i = 0 ;i < 10 ;i ++ )
 38         for (j = 0 ;j < 15 ;j ++ )
 39           {
 40            printf( " %d  " ,c[i][j]);
 41                if (j == 14 )printf( " \n " );
 42           }
 43      system( " pause " );
 44  }
 45