FZU 1650 1752 a^b mod

Problem 1752 A^B mod C

Accept: 837    Submit: 3615
Time Limit: 1000 mSec    Memory Limit : 32768 KB

 Problem Description

Given A,B,C, You should quickly calculate the result of A^B mod C. (1<=A,B,C<2^63).

 Input

There are multiply testcases. Each testcase, there is one line contains three integers A, B and C, separated by a single space.

 Output

For each testcase, output an integer, denotes the result of A^B mod C.

 Sample Input

3 2 42 10 1000

 Sample Output

124

 Source

FZU 2009 Summer Training IV--Number Theory

题解：

大数据处理，次方用乘法，乘法用加法，保证不爆。

#include
#define ll unsigned __int64
ll mul(ll a,ll b,ll c)
{
	ll tmp=a%c,tre=0;
	while(b)
	{
		if(b&1)
			if((tre+=tmp)>=c)
			   tre-=c; 
        if((tmp<<=1)>=c)
            tmp-=c;
        b>>=1;
	}
	return tre;
}
ll mod(ll a,ll b,ll c)
{
	ll y=1;
	a=a%c;
	while(b)
	{
		if(b&1)
		    y=mul(y,a,c);
        a=mul(a,a,c);
        b>>=1;
	}
	return y;
}
int main()
{
	ll a,b,c;
	while(~scanf("%I64u%I64u%I64u",&a,&b,&c))
	{
		printf("%I64u\n",mod(a,b,c));
	}
	return 0;
}