HDU 2643 Rank

Problem Description

Recently in Teddy's hometown there is a competition named "Cow Year Blow Cow".N competitors had took part in this competition.The competition was so intense that the rank was changing and changing.
Now the question is:
How many different ways that n competitors can rank in a competition, allowing for the possibility of ties. 
as the answer will be very large,you can just output the answer MOD 20090126.
Here are the ways when N = 2:
P1 < P2
P2 < P1
P1 = P2 

 

Input

The first line will contain a T,then T cases followed.
each case only contain one integer N (N <= 100),indicating the number of people.

 

Output

One integer pey line represent the answer MOD 20090126.

第二类斯特林数，把排名看做箱子，相当于n个不同的球放一个箱子，放两个箱子。。放n个不同的箱子的方法总和

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <queue>
#include <bitset>
using namespace std;
typedef long long LL;
#define MOD 20090126
LL s[105][105],n,k,T,fac[105];
int main(){
  // freopen("test.in","r",stdin);
  cin >> T;
  memset(s,0,sizeof(s));
  s[1][1] = 1;
  fac[1] = 1;
  for (int i=2;i<=100;i++){
    fac[i] = fac[i-1] * i % MOD;
    s[i][1] = 1;
    s[i][0] = 0;
    for (int j=2;j<=100;j++){
      if (i >= j)
        s[i][j] = (s[i-1][j-1] % MOD + j*s[i-1][j] % MOD) % MOD;
      else
        s[i][j] = 0;
    }
  }
  // cout <<s[3][1] << s[3][2] << s[3][3]<< endl;
  for (int i=1;i<=T;i++){
    cin >> n;
    LL ans = 0;
    for (int i=1;i<=n;i++){
      ans = (ans + s[n][i] * fac[i]) % MOD;
    }
    cout << ans << endl;
  }
  return 0;
}