NYOJ516(优化)

题目：http://acm.nyist.net/JudgeOnline/problem.php?pid=516

 

不能直接逐项快速幂计算。

#include <iostream>
#include <string.h>
#include <stdio.h>
#include <math.h>

using namespace std;
typedef long long LL;
const int N = 10000005;
const LL MOD = 1000000007;

bool prime[N];
int p[N];
int k;
LL ans,a,x;

void isprime()
{
    k = 0;
    int i,j;
    memset(prime,true,sizeof(prime));
    for(i=2; i<N; i++)
    {
        if(prime[i])
        {
            p[k++] = i;
            for(j=i+i; j<N; j+=i)
            {
                prime[j] = false;
            }
        }
    }
}

void quick_mod()
{
    while(x)
    {
        if(x&1)
        {
            ans = ans*a%MOD;
            x--;
        }
        x>>=1;
        a=a*a%MOD;
    }
}

int main()
{
    int n;
    isprime();
    while(~scanf("%d",&n))
    {
        if(n==0) break;
        ans = 1;
        x = 0;
        a = 1;
        for(int i=0; p[i] <= n; i++)
        {
            int t = n;
            int cnt = 0;
            while(t)
            {
                cnt += t/p[i];
                t /= p[i];
            }
            if(cnt > 1)
            {
                if(cnt&1) cnt--;
                if(cnt == x) a = a * p[i] % MOD;
                else
                {
                    quick_mod();
                    x = cnt;
                    a = p[i];
                }
            }
            else
            {
                quick_mod();
                break;
            }
        }
        printf("%lld\n",ans);
    }
    return 0;
}