HDU 4828 - Grids (Catalan数)

题目链接 : http://acm.hdu.edu.cn/showproblem.php?pid=4828

Catalan数的公式为 C[n+1] = C[n] * (4 * n + 2) / (n + 2)

题目要求对M = 1e9+7 取模

利用乘法逆元将原式中除以(n+2)取模变为对(n+2)逆元的乘法取模

C[n+1] = C[n] * (4 * n + 2) * Pow(n+2, MOD-2) % MOD

其中Pow用快速幂解决

#include <cstdio>

#include <cstring>

#include <algorithm>

#include <cmath>

using namespace std;

typedef long long LL;

const int MAXN = 1e6+;

const int MOD = 1e9+;

LL C[MAXN];

LL QuickPow(LL x, LL n)

{

    LL ans = ;

    while(n) {

        if(n & ) ans = (ans * x) % MOD;

        x = (x * x) % MOD;

        n /= ;

    }

    return ans;

}

void Pre()

{

    C[] =  ;

    for(int i = ; i <= MAXN; i++) {

        C[i] = C[i-] * ( * i - ) % MOD * QuickPow(i + , MOD-) % MOD;

    }

}

int main()

{

    Pre();

    int t;

    int n;

    scanf("%d", &t);

    for(int cas = ; cas <= t; cas++) {

        scanf("%d", &n);

        printf("Case #%d:\n%I64d\n", cas, C[n]);

    }

    return ;

}