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hdu 4767 Bell

从易做图查到两个公式:
 
 
 
易做图网址:http://en.易做图.org/wiki/Bell_number
通过这两个公式可以把Bn分别对于mod拆分成的五个素数取余,然后通过中国剩余定理把这五个素数得到的结果组合起来
 
对于取余的算法是采用递推的方式
 
 
#include <iostream>  
#include <stack>  
#include <queue>  
#include <cstdio>  
#include <cstdlib>  
#include <cmath>  
#include <set>  
#include <vector>  
#include <cstring>  
#include <algorithm>  
  
#define INF 0x7ffffffffffLL  
#define N 50  
#define LL long long  
#define mod 95041567  
  
using namespace std;  
  
LL num[N][N], q[N];  
int p[5] = {31, 37, 41, 43, 47}, arr[5];  
  
void Preprocessing(){  
    q[0] = q[1]= 1;  
    num[0][0] = num[1][0] = 1, num[1][1] = 2;  
    for(int i = 2; i < 50; ++i){  
        q[i] = num[i][0] = num[i - 1][i - 1];  
        for(int j = 1; j <= i; ++j)  
            num[i][j] = (num[i - 1][j - 1] + num[i][j - 1]) %mod;   
    }  
}  
  
int cal(int x, LL n){  
    int _q[N];  
    for(int i = 0; i <= x; ++i) _q[i] = q[i] % x;  
  
    int len = 0;  
    int _mod[15];  
    while(n){  
        _mod[len++] = n % x;  
        n /= x;  
    }  
  
    int _arr[N];  
    for(int i = 1; i < len; ++i)  
        for(int j = 1; j <= _mod[i]; ++j){  
            for(int k = 0; k < x; ++k)  
                _arr[k] = (_q[k] * i + _q[k + 1]) % x;  
            _arr[x] = (_arr[0] + _arr[1]) % x;  
            for(int k = 0; k <= x; ++k) _q[k] = _arr[k];  
        }  
    return _arr[_mod[0]];  
}  
  
void 易做图(LL a, LL b, LL &x, LL &y){  
    if(!b){  
        x = 1;  
        y = 0;  
      //  printf("d = %I64d x = %I64d\n", d, x);  
        return;  
    }  
    易做图(b, a % b, y, x);  
    y -= a / b * x;  
}  
  
LL china(){  
    LL d, y, x = 0;  
    for(int i = 0; i < 5; ++i){  
        LL w = mod / p[i];  
  
        易做图(p[i], w, d, y);  
        x = (x + y * w * arr[i]) % mod;  
  
    }  
    return (x + mod) % mod;  
}  
  
int main()  
{  
   // freopen("in.txt","r",stdin);  
    Preprocessing();  
  
    int t;  
    scanf("%d", &t);  
  
    while(t--){  
        LL n;  
        scanf("%I64d", &n);  
        if(n < 50){  
            printf("%I64d\n", q[n]);  
            continue;  
        }  
        for(int i = 0; i < 5; ++i)  
            arr[i] = cal(p[i], n);  
       // for(int i = 0; i < 5; ++i) printf("%I64d ", arr[i]);  
  
    printf("%I64d\n", china());  
    }  
    return 0;  
}  

 

 
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