POJ3181 Dollar Dayz

Description

Farmer John goes to Dollar Days at The Cow Store and discovers an unlimited number of tools on sale. During his first visit, the tools are selling variously for $1, $2, and $3. Farmer John has exactly $5 to spend. He can buy 5 tools at $1 each or 1 tool at $3 and an additional 1 tool at $2. Of course, there are other combinations for a total of 5 different ways FJ can spend all his money on tools. Here they are: 

1 @ US$3 + 1 @ US$2 1 @ US$3 + 2 @ US$1 1 @ US$2 + 3 @ US$1 2 @ US$2 + 1 @ US$1 5 @ US$1

Input

A single line with two space-separated integers: N and K.

Output

A single line with a single integer that is the number of unique ways FJ can spend his money.

Sample Input

5 3

Sample Output

5

多重背包+高精度

dp【i】=dp【i-1】+dp【i-j】

#include<cstdio>
#include<iostream>
#include<algorithm>
#include<cstring>
using namespace std;
#define N 50010
long long int inf,b[N],a[N];
int main()
{
  long long int n,m,i,j;
  for(inf=1,i=1;i<18;i++) inf*=10;
  scanf("%lld %lld",&m,&n);
    memset(a,0,sizeof(a));
    memset(b,0,sizeof(b));
       a[0]=1;
    for(i=1;i<=n;i++) 
    {
      for(j=i;j<=m;j++)
      {
        b[j]=b[j]+b[j-i]+(a[j]+a[j-i])/inf;
        a[j]=(a[j]+a[j-i])%inf;
      }
    }
    if(b[m]) cout<<b[m];
     cout<<a[m]<<endl;
  return 0;
 }