函数板子

exgcd

//给定 a 和 b，求出 x 和 y，使得 a * x + b * y = gcd(a, b)
LL exgcd(LL a, LL b, LL &x, LL &y){
	if (!b){
	    x = 1, y = 0;
	    return a;
	}
	LL d = exgcd(b, a % b, y, x);
	y -= ( a / b ) * x;
	return d;
}

gcd

LL gcd(LL a, LL b){
	return b ? gcd(b, a % b) : a;
}

逆元

//1.快速幂求逆元
LL inv(LL x){
	return qp(x, mod - 2, mod);
}
//2.扩展欧几里得求逆元
LL inv(LL a){
	LL x, y;
	exgcd(a, mod, x, y);
	x = (x % mod + mod) % mod;
	return x;
}
//3.线性递推求逆元
inv[1] = 1;
for (int i = 2; i <= n; i ++ )
	inv[i] = (p - p / i) * inv[p % i] % p;

快输

void print(LL x){
	if(x < 0) {putchar('-');x = -x;}
	if(x / 10) print(x / 10);
	putchar(x % 10 + '0');
}

lucas

LL qp(LL a, LL k, LL p){
	LL ans = 1;
	while (k){
		if (k & 1) ans = ans * a % p;
		k >>= 1;
		a = a * a % p;
	}
	return ans;
}
LL C(LL a, LL b, LL p){
	if (a < b) return 0;
	LL x = 1, y = 1;
	for (LL i = a, j = 1; j <= b; i --, j ++ ){
		x = x * i % p;
		y = y * j % p;
	}
	return x * qp(y, p - 2, p) % p;
}
LL lucas(LL a, LL b, LL p){
	if (a < p && b < p) return C(a, b, p);
	return C(a % p, b % p, p) * lucas(a / p, b / p, p) % p;
}

sqrt

LL mySqrt(LL x){
	LL k = sqrt(x) - 1;
	while ((k + 1) * (k + 1) <= x) k++;
	return k;
}

快速幂

LL qp(LL a, LL k, LL p){
	LL ans = 1;
	while (k){
		if (k & 1) ans = ans * a % p;
		k >>= 1;
		a = a * a % p;
	}
	return ans;
}

快读

LL read(){
	LL s = 0, w = 1;
	char ch = getchar();
	while ( ch < '0' || ch > '9') { if (ch == '-') w = -1; ch = getchar();}
	while ( ch >= '0' && ch <= '9') s = s * 10 + ch - '0', ch = getchar();
	return s * w;
}

unique

vector <LL> :: iterator unique(vector <LL> &a){
	LL j = 0;
	for (LL i = 0; i < a.size(); i++)
		if (!i || a[i] != a[i - 1])
			a[j++] = a[i];
	return a.begin() + j;
}

自动取模整数型

template<int mod>
struct ModZ{
	LL x;
	constexpr ModZ() : x() {}
	constexpr ModZ(LL x) : x(norm(x % mod)) {}
	constexpr LL norm(LL x) {return (x % mod + mod) % mod;}
	constexpr ModZ power(ModZ a, LL b) {ModZ res = 1; for (; b; b /= 2, a *= a) if (b & 1) res *= a; return res;}
	constexpr ModZ inv() {return power(*this, mod - 2);}
	constexpr ModZ &operator *= (ModZ rhs) & {x = norm(x * rhs.x); return *this;}
	constexpr ModZ &operator += (ModZ rhs) & {x = norm(x + rhs.x); return *this;}
	constexpr ModZ &operator -= (ModZ rhs) & {x = norm(x - rhs.x); return *this;}
	constexpr ModZ &operator /= (ModZ rhs) & {return *this *= rhs.inv();}
	friend constexpr ModZ operator * (ModZ lhs, ModZ rhs) {ModZ res = lhs; res *= rhs; return res;}
	friend constexpr ModZ operator + (ModZ lhs, ModZ rhs) {ModZ res = lhs; res += rhs; return res;}
	friend constexpr ModZ operator - (ModZ lhs, ModZ rhs) {ModZ res = lhs; res -= rhs; return res;}
	friend constexpr ModZ operator / (ModZ lhs, ModZ rhs) {ModZ res = lhs; res /= rhs; return res;}
	friend constexpr istream &operator >> (istream &is, ModZ &a) {LL v; is >> v; a = ModZ(v); return is;}
	friend constexpr ostream &operator << (ostream &os, const ModZ &a) {return os << a.x;}
	friend constexpr bool operator == (ModZ lhs, ModZ rhs) {return lhs.x == rhs.x;}
	friend constexpr bool operator != (ModZ lhs, ModZ rhs) {return lhs.x != rhs.x;}
};
const int mod = 998244353;
using Z = ModZ<mod>;