代码模板

代码模板

数论

快速幂

int qmi(int a, int b, int p) {
	int res = 1;
	while (b) {
		if (b & 1) res = res * a % p;
		a = a * a % p;
		b >>= 1;
	}
	return res;
}

线性筛法（素数+欧拉函数）

int st[N1], pri[N1], cnt, phi[N1];
int getp(int n) {
	phi[1] = 1;
	for (int i = 2; i <= n; i ++ ) {
		if (!st[i]) pri[ ++ cnt] = i, phi[i] = i - 1;
		for (int j = 1; j <= cnt && pri[j] <= n / i; j ++ ) {
			st[pri[j] * i] = pri[j];
			if (i % pri[j] == 0) {
				phi[pri[j] * i] = phi[i] * pri[j];
				break;
			}
			phi[pri[j] * i] = phi[i] * (pri[j] - 1);
		}
	}
}

扩展欧几里得算法

int exgcd(int a, int b, int &x, int &y) {
	if (b == 0) {
		x = 1;
		y = 0;
		return a;
	}
    /*
	int d = exgcd(b, a % b, x, y);
	int tmp = x;
	x = y;
	y = tmp - a / b * y;
	*/
    int d = exgcd(b, a % b, y, x);
	y -= a / b * x;
	return d;
}

欧拉函数（一个数）

int phi_(int x) {
	int phi = x;
	for (int i = 2; i <= x / i; i ++ ) {
		if (x % i == 0) {
			phi = phi * (i - 1) / i;
			while (x % i == 0) x /= i;
		}
	}
	if (x > 1) phi = phi * (x - 1) / x;
	return phi;
}

ll phi(int p){
	ll ret=p;
	for(int i=2;i*i<=p;++i){
		if(p%i==0){
			ret-=ret/i;
			while(p%i==0)p/=i;
		}
	}
	if(p>1)ret-=ret/p;
	return ret;
}

递推求逆元

void getinv(int n, int p) {
	inv[1] = 1;
	for (int i = 2; i <= n; i ++ ) inv[i] = inv[p % i] * (p - p / i) % p;
}