快速幂

快速幂

无函数快速幂

#include<cstdio>
#include<cmath>
using namespace std;
int main()
{
	long long b, p, k;
	scanf("%lld%lld%lld", &b, &p, &k);
	long long s, a;
	s = b%k;
	a = 1;
	for(int i=1; i<=p; i++)
	{
		s = s*b%k;
		if(s==b%k) break;
		a++;
	}
	printf("%lld^%lld mod %lld=", b, p, k);
	p = p%a;
	s = 1;
	if(p==0) p=a;
	for(int i=1; i<=p; i++) s=s*b%k;
	printf("%lld", s);
	return 0;
}

递归

• 递归求快速幂

#include<cstdio>
using namespace std;
int f(int x, int n, int m)
{
	if(n == 0) return 1%m;
	if(n == 1) return x%m;
	long long y = f(x, n/2, m);
	y = (y%m)*(y%m)%m;
	if(n%2==1) y = (y%m)*(x%m)%m;
	return y;
}
int main()
{
	int x, n, m;
	long long z;
	scanf("%d %d %d", &x, &n, &m);
	z = f(x, n, m);
	printf("%d^%d mod %d=%lld", x, n, m, z);
	return 0;
}

递推

• 非递归求快速幂[(a^b)%n]

#include<cstdio>
#define ll long long
using namespace std;
ll pow(ll a, ll b, ll n)
{
	ll ans=1;
	while(b)
	{
		if(b%2 == 1) ans*=a;
		a = (a*a)%n;
		b=b/2;
	}
	return ans;
}
ll a, b, n;
int main()
{
	scanf("%lld%lld%lld", &a, &b, &n);
	printf("%lld", pow(a, b, n));
	return 0;
}