模幂运算

Posted 2020-12-26 darkchii

　　https://en.wikipedia.org/wiki/Modular_exponentiation

　　该算法在一些数论题中十分有用。算法用于快速求解同余方程 $ c = a^b mod M $ ，其中 a, b, M 已知。

　　code:

#include <iostream>
#define ll long long
ll modexpo(ll base, ll expo, ll mod)
{
	if (mod == 1) return 0;
	ll res = 1; while (expo > 0)
	{
		if (expo & 1)	res = (res*base) % mod;
		base = (base*base) % mod; expo >>= 1;
	}
	return res;
}
int main()
{
	std::cout << modexpo(2,3,5) << std::endl;
	return 0;
}