acdream 群赛5 组合数学

Problem B: Dice Dice Dice

Time Limit: 10 Sec  Memory Limit: 128 MB
Submit: 81  Solved: 17
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Description

There are 1111 ways in which five 6-sided dice (sides numbered 1 to 6) can be rolled so that the top three numbers sum to 15. Some examples are: 

D1,D2,D3,D4,D5 = 4,3,6,3,5 

D1,D2,D3,D4,D5 = 4,3,3,5,6 

D1,D2,D3,D4,D5 = 3,3,3,6,6 

D1,D2,D3,D4,D5 = 6,6,3,3,3 

Now we have a extended problem:

In how many ways can n m-sided dice (sides numbered 1 to m) be rolled so that the top k numbers sum to p?

Input

There are multiple test cases. (about 15 groups)

For each test case, there is only four integers n, m, k, p. (1 <= k <= n <= 20, 3 <= m <= 12)

Output

For each test case, output an integer indicating the answer.

Sample Input

5 6 3 156 6 3 15

Sample Output

11117770

HINT

#include <iostream>#include <cstdio>#include <cstring>#include <algorithm>#include <queue>#include <cmath>#include <stack>#include <map> using namespace std;#define LL long longint n,m,k,p;int re[109];LL ans;LL N(int t){    LL ret = 1;    for(int i=2;i<=t;i++)    ret*=i;    return ret;}void dfs(int t,int lim){    if(t<k){        for(int i=lim;i>0;i--)        {            re[t] = i;            dfs(t+1,i);        }    }else if(t==k){        int s = 0;        for(int i=0;i<k;i++)        s+=re[i];        if(s!=p) return ;     //   for(int i=0;i<k;i++)      //  cout<<re[i]<<" ";cout<<endl;        if(k<n)        for(int i=lim;i>0;i--)        {            re[t] = i;            dfs(t+1,i);        }        else        {            re[n]=lim;            dfs(t+1,lim);        }        return ;    }else if(t>k&&t<n)    {        for(int i=lim;i>0;i--)        {            re[t] = i;            dfs(t+1,i);        }        return ;    }    if(t>=n){        LL tmp = N(n);       // cout<<"con:"<<endl;       // for(int i=0;i<n;i++)       // cout<<re[i]<<" ";cout<<endl;       // cout<<tmp<<endl;        int c=1;        re[n] = -1;        for(int i=1;i<=n;i++)        {            if(re[i]!=re[i-1])            {                tmp/=N(c);                c=1;            }            else            c++;        }        ans+=tmp;        return ;    }}int main(){   // freopen("in.txt","r",stdin);    while(~scanf("%d%d%d%d",&n,&m,&k,&p))    {       // cout<<"<<<<<<<<<<<"<<endl;        ans = 0;        dfs(0,m);        cout<<ans<<endl;    }    return 0;}