【动态规划】PKU 1276 Cash Machine

【动态规划】PKU 1276 Cash Machine

http://acm.pku.edu.cn/JudgeOnline/problem?id=1276
题目大意：有n[i]个面值为d[i]的硬币，要用这些硬币拼出价值为cash的钱来。如果拼不出，就拼出一个小于cash的最大的面值。求这个面值。
思路：
依次考虑这n个面值，用sum[i]表示，当只用前i中面值时，是否可以拼出价值为i的钱。num[j]表示拼出价值为i的钱时，此时第i种面值用了多少个。

#include < iostream >
#include < string >
#include < algorithm >
#include < vector >
#include < cstring >
#include < cmath >
using   namespace  std;
#define  maxn 100010
int  m[ 12 ],d[ 12 ];
int  num[maxn];
bool  sum[maxn];
int  main()
{
     int  cash,n;
     while (scanf( " %d%d " , & cash, & n) != EOF)
    {
         for ( int  i = 0 ;i < n;i ++ )
        {
            scanf( " %d%d " , & m[i], & d[i]);
        }
        memset(sum, false , sizeof (sum));
        sum[ 0 ] = 1 ;
         for ( int  i = 0 ;i < n;i ++ )
        {
            memset(num, 0 , sizeof (num));
             for ( int  j = d[i];j <= cash;j ++ )
            {
                 if ( ! sum[j]  &&  sum[j - d[i]]  &&  num[j - d[i]] < m[i])
                {
                    sum[j] = 1 ;
                    num[j] = num[j - d[i]] + 1 ;
                }
            }
        }
         bool  flag = 1 ;
         for ( int  i = cash;i >= 0 ;i -- )
             if (sum[i])
            {
                printf( " %d\n " ,i);
                flag = 0 ;
                 break ;
            }
         if (flag) printf( " 0\n " );
    }
}