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hdu 2837 Calculation(指数循环节)

2014-08-11 17:24 309 查看
http://acm.hdu.edu.cn/showproblem.php?pid=2837

f
= (n%10)^(f[n/10])%m


a^b%c = a^(b%phi[c]+phi[c])%c(b >= phi[c])。每一层都要判断b是否大于等于它外面一层的模。

#include <stdio.h>
#include <iostream>
#include <map>
#include <set>
#include <list>
#include <stack>
#include <vector>
#include <math.h>
#include <string.h>
#include <queue>
#include <string>
#include <stdlib.h>
#include <algorithm>
#define LL long long
#define _LL __int64
#define eps 1e-12
#define PI acos(-1.0)
#define C 240
#define S 20
using namespace std;
const int maxn = 110;
const int mod = 1000000007;
LL n,m,phi_m;

LL Eular(LL num)
{
	LL res = num;
	for(int i = 2; i*i <= num; i++)
	{
		if(num % i == 0)
		{
			res -= res/i;
			while(num%i == 0)
				num/=i;
		}
	}
	if(num > 1)
		res -= res/num;
	return res;
}

LL pow_mod(LL a, LL n, LL m)
{
	LL res = 1;
	while(n)
	{
		if(n&1)
		{
			res = res*a;
			if(res >= m)
				res = res%m+m;
		}
		a = a*a;
		if(a >= m)
			a = a%m+m;
		n >>= 1;
	}
	return res;
}

LL solve(LL n, LL m)
{
	if(n == 0)
		return 1;
	LL p = solve(n/10,Eular(m));
	return pow_mod(n%10,p,m);
}

int main()
{
	int test;
	scanf("%d",&test);
	while(test--)
	{
		scanf("%lld %lld",&n,&m);
		LL ans = solve(n,m)%m;
		printf("%lld\n",ans);
	}
	return 0;
}
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