FZU 1775 Counting Binary Trees 卡特兰数前n项和%m(m可为非素数

标签：blog   http   io   ar   for   on   2014   log   ef   

题目链接：点击打开链接

题意：

卡特兰数前n项和 结果%m

把答案当成2部分搞。

#include<stdio.h>
#include<cmath>
#define int __int64
const int N = 100000;
struct inverse_element{
    int x, y, q;
    void extend_Eulid(int a,int b)
     {
         if(b == 0){
              x = 1;y = 0;q = a;
         }else{
             extend_Eulid(b,a%b);
             int temp = x;
             x = y;
             y = temp - a/b*y;
         }
    }
    int find(int a, int b){
        extend_Eulid(a, b);
        return x;
    }
}inver;
int prime[N],primenum;//有primenum个素数 math.h
void PRIME(int Max_Prime){
	primenum=0;
	prime[primenum++]=2;
	for(int i=3;i<=Max_Prime;i+=2)
	for(int j=0;j<primenum;j++)
		if(i%prime[j]==0)break;
		else if(prime[j]>sqrt((double)i) || j==primenum-1)
		{
			prime[primenum++]=i;
			break;
		}
}
int P[N], D[N], top;
void fen(int m){
	top = 0;
	for(int i = 0; prime[i]*prime[i]<=m;i++){
		if(m%prime[i])continue;
		D[top] = 0;
		P[top++] = prime[i];
		while(m%prime[i] == 0)
			m/=prime[i];
	}
	if(m!=1){
		D[top] = 0;
		P[top++] = m;
	}
}
int n, m;
void mul(int &x, int y){
    x *= y;
    if(x >= m) x %= m;
    else if(x<0) x = x%m+m;
}
void work1(int &x, int u){
    for(int i = 0; i < top; i++)
        while(u%P[i] == 0)
            D[i]++, u/=P[i];
    mul(x, u);
}
void work2(int &x, int u){
    for(int i = 0; i < top; i++)
        while(u%P[i] == 0)
            D[i]--, u/=P[i];
    if(u!=1)
        mul(x, inver.find(u, m));
}
int Pow(int x, int y){
    int ans = 1;
    while(y){
        if(y&1)
            mul(ans, x);
        mul(x, x);
        y >>= 1;
    }
    return ans;
}
int work(){
	if(m==1)return 0;
	if(n==1)return 1;
	fen(m);
	int res = 1, sum = 1;
	for(int i = 2; i <= n; i++)
	{
        work1(res, 4*i-2);
        work2(res, i+1);
        int t = res;
        for(int i = 0; i < top; i++)
            mul(t, Pow(P[i],D[i]));
        sum = (sum+t)%m;
	}
    return sum;
}
#undef int
int main() {
	PRIME(100000);
	while(~scanf("%I64d %I64d", &n, &m)){
	    if(n+m == 0)break;
	//	n-=2;
		printf("%I64d\n", work()%m);
	}
	return 0;
}

FZU 1775 Counting Binary Trees 卡特兰数前n项和%m(m可为非素数

标签：blog   http   io   ar   for   on   2014   log   ef   

原文地址：http://blog.csdn.net/qq574857122/article/details/41595505