zoj Exchange Cards

Exchange Cards

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Time Limit: 2 Seconds Memory Limit: 65536 KB

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As a basketball fan, Mike is also fond of collecting basketball player cards. But as a student, he can not always get the money to buy new cards, so sometimes he will exchange with his friends for cards he likes. Of course, different cards have different value, and Mike must use cards he owns to get the new one. For example, to get a card of value 10$, he can use two 5$ cards or three 3$ cards plus one 1$ card, depending on the kinds of cards he have and the number of each kind of card. And Sometimes he will involve unfortunately in a bad condition that he has not got the exact value of the card he is looking for (fans always exchange cards for equivalent value).

Here comes the problem, given the card value he plans to get and the cards he has, Mike wants to fix how many ways he can get it. So it's you task to write a program to figure it out.

Input

The problem consists of multiple test cases, terminated by EOF. There's a blank line between two inputs.

The first line of each test case gives n, the value of the card Mike plans to get andm, the number of different kinds of cards Mike has. n will be an integer number between 1 and 1000.m will be an integer number between 1 and 10.

The next m lines give the information of different kinds of cards Mike have. Each line contains two integers,val and num, representing the value of this kind of card, and the number of this kind of card Mike have.

Note: different kinds of cards will have different value, eachval and num will be an integer greater than zero.

Output

For each test case, output in one line the number of different ways Mike could exchange for the card he wants. You can be sure that the output will fall into an integer value.

Output a blank line between two test cases.

Sample Input

5 22 13 110 510 27 25 32 21 5

Sample Output

17

多重背包 dfs解法~

数据比较小~~~~~

在寻找方向的时候纠结了一下，因为多重背包是有多个相同的值的，为了能再次访问，需要定义一个m 来作为向下递归的起点~

code:

#include<iostream>#include<string.h>using namespace std;int countn[10000];int SUM,n;int ans;int sum;void dfs(int m,int sum){if(sum==SUM){ans++;return;}for(int i=m;i<=SUM;i++){if(countn[i]&&i+sum<=SUM){countn[i]--;sum+=i;dfs(i,sum);//这里并没有把当前值定为sum而是定为了 i   因为可能会有多个相同值，需要重复访问~(多重背包你懂得~） sum-=i;countn[i]++;}}}int main(){int a,b;int T=0;while(cin>>SUM>>n){     if(T)        cout<<endl;        T++;memset(countn,0,sizeof(countn));for(int i=0;i<n;i++)    {    cin>>a>>b;       countn[a]=b;    }    ans=0;            dfs(0,0);    cout<<ans<<endl;        }return 0;}