數論初步模板

Gcd

#include <bits/stdc++.h>

typedef long long ll;

ll gcd(ll n, ll m)
{
	if (!m)
		return n;
	return gcd(m, n % m);
}

int main(int argc, char **argv)
{
	std::ios_base::sync_with_stdio(false);
	ll n, m;
	std::cin >> n >> m;
	std::cout << gcd(n, m) << std::endl;
	return 0;
}

ExGcd

#include <bits/stdc++.h>

typedef long long ll;

void ExGcd(ll n, ll m, ll &d, ll &x, ll &y)
{
	if (!m)
	{
		d = n;
		x = 1;
		y = 0;
		return;
	}
	ExGcd(m, n % m, d, y, x);
	y -= (n / m) * x;
}

int main(int argc, char **argv)
{
	std::ios_base::sync_with_stdio(false);
	ll n, m, d, a, b;
	std::cin >> n >> m;
	ExGcd(n, m, d, a, b);
	std::cout << d << ' ' << a << ' ' << b << std::endl;
	return 0;
}

快速冪/快速乘取模

#include <bits/stdc++.h>

typedef long long ll;

ll kysumi(ll x, ll y, const ll p = 998244353ll)
{
	ll ans = 1;
	while (y)
	{
		if (y & 1)
			ans = ans * x % p;
		x = x * x % p;
		y >>= 1;
	}
	return ans;
}

int main(int argc, char **argv)
{
	std::ios_base::sync_with_stdio(false);
	ll n, m;
	std::cin >> n >> m;
	std::cout << kysumi(n, m) << std::endl;
	return 0;
}

素數篩法

#include <bits/stdc++.h>

const size_t _Siz = 210002;

bool notPrime[_Siz] = { true, true };

int prime[_Siz] = { 0 }, tot = 0, phi[_Siz]= { 0 };

void ul(const int n)
{
	for (int i = 2; i <= n; i++)
	{
		if (!notPrime[i])
        {
			prime[tot++] = i;
        	phi[i] = i - 1;
        }
		for (int j = 0; j < tot && i * prime[j] < n; j++)
		{
			notPrime[i * prime[j]] = true;
			if (i % prime[j] == 0)
			{
				phi[i * prime[j]] = phi[i] * prime[j];
				break;
			}
			else
				phi[i * prime[j]] = phi[i] * (prime[j] - 1);
		}
	}
}

int main(int argc, char **argv)
{
	std::ios_base::sync_with_stdio(false);
	ll n, m;
	std::cin >> n;
	ul(n);
	for (int i = 1; i <= tot; i++)
		std::cout << prime[i] << '\t';
	return 0;
}