【模板】modint
latest version: https://raw.githubusercontent.com/caijianhong/template-poly/main/poly/modint.hpp
update on 2024.10.7：upload modint.min.hpp 作为一个关掉 clang-format 的比较舒服的版本
modint (clang-format on, version 3, support dynamic_modint)
template <class T>
using must_int = enable_if_t<is_integral<T>::value, int>;
template <unsigned umod>
struct modint {
static constexpr int mod = umod;
unsigned v;
modint() : v(0) {}
template <class T, must_int<T> = 0>
modint(T x) {
x %= mod;
v = x < 0 ? x + mod : x;
}
modint operator+() const { return *this; }
modint operator-() const { return modint() - *this; }
friend int raw(const modint &self) { return self.v; }
friend ostream& operator<<(ostream& os, const modint &self) {
return os << raw(self);
}
modint &operator+=(const modint &rhs) {
v += rhs.v;
if (v >= umod) v -= umod;
return *this;
}
modint &operator-=(const modint &rhs) {
v -= rhs.v;
if (v >= umod) v += umod;
return *this;
}
modint &operator*=(const modint &rhs) {
v = 1ull * v * rhs.v % umod;
return *this;
}
modint &operator/=(const modint &rhs) {
assert(rhs.v);
return *this *= qpow(rhs, mod - 2);
}
template <class T, must_int<T> = 0>
friend modint qpow(modint a, T b) {
modint r = 1;
for (; b; b >>= 1, a *= a)
if (b & 1) r *= a;
return r;
}
friend modint operator+(modint lhs, const modint &rhs) { return lhs += rhs; }
friend modint operator-(modint lhs, const modint &rhs) { return lhs -= rhs; }
friend modint operator*(modint lhs, const modint &rhs) { return lhs *= rhs; }
friend modint operator/(modint lhs, const modint &rhs) { return lhs /= rhs; }
bool operator==(const modint &rhs) const { return v == rhs.v; }
bool operator!=(const modint &rhs) const { return v != rhs.v; }
};
dynamic_modint：去掉 static constexpr int mod = P; 改为 static unsigned P;，template <unsigned P> 改为 template<int id>，类外进行 P 的定义。
template <class T>
using must_int = enable_if_t<is_integral<T>::value, int>;
template <int id>
struct modint {
static int mod;
static unsigned umod;
static void setmod(int p) { mod = umod = p; }
unsigned v;
modint() : v(0) {}
template <class T, must_int<T> = 0>
modint(T x) {
x %= mod;
v = x < 0 ? x + mod : x;
}
modint operator+() const { return *this; }
modint operator-() const { return modint() - *this; }
friend int raw(const modint &self) { return self.v; }
friend ostream& operator<<(ostream& os, const modint &self) {
return os << raw(self);
}
modint &operator+=(const modint &rhs) {
v += rhs.v;
if (v >= umod) v -= umod;
return *this;
}
modint &operator-=(const modint &rhs) {
v -= rhs.v;
if (v >= umod) v += umod;
return *this;
}
modint &operator*=(const modint &rhs) {
v = 1ull * v * rhs.v % umod;
return *this;
}
modint &operator/=(const modint &rhs) {
assert(rhs.v);
return *this *= qpow(rhs, mod - 2);
}
template <class T, must_int<T> = 0>
friend modint qpow(modint a, T b) {
modint r = 1;
for (; b; b >>= 1, a *= a)
if (b & 1) r *= a;
return r;
}
friend modint operator+(modint lhs, const modint &rhs) { return lhs += rhs; }
friend modint operator-(modint lhs, const modint &rhs) { return lhs -= rhs; }
friend modint operator*(modint lhs, const modint &rhs) { return lhs *= rhs; }
friend modint operator/(modint lhs, const modint &rhs) { return lhs /= rhs; }
bool operator==(const modint &rhs) const { return v == rhs.v; }
bool operator!=(const modint &rhs) const { return v != rhs.v; }
};
template <int id>
unsigned modint<id>::umod;
template <int id>
int modint<id>::mod;
设置模数例：
typedef modint<-1> mint;
mint.setmod(998244353);
dynamic_modint with Montgomery Reduction
template <class T>
using must_int = enable_if_t<is_integral<T>::value>*;
struct Montgomery {
typedef unsigned u32;
typedef unsigned long long u64;
u32 umod, niv, R, R2;
Montgomery() {}
Montgomery(u32 m) : umod(m), niv(2 + m), R(-m % m), R2(-(u64)m % m) {
for (int i = 0; i < 4; i++) niv *= 2 + m * niv;
}
u32 reduce(u64 x) {
x = (x + (u64)((u32)x * niv) * umod) >> 32;
return x >= umod ? x - umod : x;
}
};
template <int id>
struct modint {
static int mod;
static unsigned umod;
static Montgomery mont;
static void setmod(int p) {
mod = umod = p;
mont = Montgomery(p);
}
unsigned v;
modint() : v(0) {}
modint(unsigned x) : v(mont.reduce(1ull * x * mont.R2)) {}
template <class T, must_int<T> = nullptr>
modint(T x) : modint((unsigned)(x %= mod, x < 0 ? x + mod : x)) {}
modint operator+() const { return *this; }
modint operator-() const { return modint() - *this; }
friend int raw(const modint &self) { return mont.reduce(self.v); }
friend ostream &operator<<(ostream &os, const modint &self) {
return os << raw(self);
}
modint &operator+=(const modint &rhs) {
v += rhs.v;
if (v >= umod) v -= umod;
return *this;
}
modint &operator-=(const modint &rhs) {
v -= rhs.v;
if (v >= umod) v += umod;
return *this;
}
modint &operator*=(const modint &rhs) {
v = mont.reduce(1ull * v * rhs.v);
return *this;
}
modint &operator/=(const modint &rhs) {
assert(rhs.v);
return *this *= qpow(rhs, mod - 2);
}
template <class T, must_int<T> = nullptr>
friend modint qpow(modint a, T b) {
modint r = 1;
for (; b; b >>= 1, a *= a)
if (b & 1) r *= a;
return r;
}
friend modint operator+(modint lhs, const modint &rhs) { return lhs += rhs; }
friend modint operator-(modint lhs, const modint &rhs) { return lhs -= rhs; }
friend modint operator*(modint lhs, const modint &rhs) { return lhs *= rhs; }
friend modint operator/(modint lhs, const modint &rhs) { return lhs /= rhs; }
bool operator==(const modint &rhs) const { return v == rhs.v; }
bool operator!=(const modint &rhs) const { return v != rhs.v; }
};
template <int id>
unsigned modint<id>::umod;
template <int id>
int modint<id>::mod;
template <int id>
Montgomery modint<id>::mont;
modint (clang-format on, version 2)
template <unsigned P> struct modint {
unsigned v; modint() : v(0) {}
template <class T> modint(T x) { x %= (int)P, v = x < 0 ? x + P : x; }
modint operator+() const { return *this; }
modint operator-() const { return modint(0) - *this; }
modint inv() const { return assert(v), qpow(*this, P - 2); }
friend int raw(const modint &self) { return self.v; }
template <class T> friend modint qpow(modint a, T b) {
modint r = 1;
for (; b; b >>= 1, a *= a) if (b & 1) r *= a;
return r;
}
modint &operator+=(const modint &rhs) { if (v += rhs.v, v >= P) v -= P; return *this; }
modint &operator-=(const modint &rhs) { if (v -= rhs.v, v >= P) v += P; return *this; }
modint &operator*=(const modint &rhs) { v = 1ull * v * rhs.v % P; return *this; }
modint &operator/=(const modint &rhs) { return *this *= rhs.inv(); }
friend modint operator+(modint lhs, const modint &rhs) { return lhs += rhs; }
friend modint operator-(modint lhs, const modint &rhs) { return lhs -= rhs; }
friend modint operator*(modint lhs, const modint &rhs) { return lhs *= rhs; }
friend modint operator/(modint lhs, const modint &rhs) { return lhs /= rhs; }
friend bool operator==(const modint &lhs, const modint &rhs) { return lhs.v == rhs.v; }
friend bool operator!=(const modint &lhs, const modint &rhs) { return lhs.v != rhs.v; }
};
modint by cjl
struct m{
int x;m(int o=0){x=o;}m(lll o){x=o%mod;}m&operator+=(m a){return(x+=a.x)%=mod,*this;}m&operator-=(m a){return(x+=mod-a.x)%=mod,*this;}
m&operator*=(m a){return(x=1ll*x*a.x%mod),*this;}m&operator^=( int b){m a=*this;x=1;while(b)(b&1)&&(*this*=a,1),a*=a,b>>=1;return*this;}
m&operator/=(m a){return*this*=(a^=mod-2);}friend m operator+(m a,m b){return a+=b;}friend m operator-(m a,m b){return a-=b;}
friend m operator*(m a,m b){return a*=b;}friend m operator/(m a,m b){return a/=b;}friend m operator^(m a, int b){return a^=b;}
m operator-(){return 0-*this;}bool operator==(const m b)const{return x==b.x;}
};
仿照 atcoder library 写的：modint (version 1)
typedef long long LL;
template<unsigned P> struct modint{
unsigned v; modint():v(0){}
template<class T> modint(T x):v((x%int(P)+int(P))%int(P)){}
modint operator-()const{return modint(P-v);}
modint inv()const{return assert(v),qpow(*this,LL(P)-2);}
modint&operator+=(const modint&rhs){if(v+=rhs.v,v>=P) v-=P; return *this;}
modint&operator-=(const modint&rhs){return *this+=-rhs;}
modint&operator*=(const modint&rhs){v=1ull*v*rhs.v%P; return *this;}
modint&operator/=(const modint&rhs){return *this*=rhs.inv();}
friend int raw(const modint&self){return self.v;}
friend modint qpow(modint a,LL b){modint r=1;for(;b;b>>=1,a*=a) if(b&1) r*=a; return r;}
friend modint operator+(modint lhs,const modint&rhs){return lhs+=rhs;}
friend modint operator-(modint lhs,const modint&rhs){return lhs-=rhs;}
friend modint operator*(modint lhs,const modint&rhs){return lhs*=rhs;}
friend modint operator/(modint lhs,const modint&rhs){return lhs/=rhs;}
friend bool operator==(const modint&lhs,const modint&rhs){return lhs.v==rhs.v;}
friend bool operator!=(const modint&lhs,const modint&rhs){return lhs.v!=rhs.v;}
};
注意那个 int(P) 非常重要，因为数字和模数都是 unsigned，传进来负数会模成奇怪东西。
精简版：但好像并没有（using modint = Z）
template<unsigned P> struct modint{
unsigned v; using Z=modint; modint():v(0){}
template<class T> modint(T x):v((x%int(P)+int(P))%int(P)){}
Z operator-()const{return Z(P-v);}
Z inv()const{return qpow(*this,LL(P)-2);}
Z&operator+=(Z b){if(v+=b.v,v>=P) v-=P; return *this;}
Z&operator-=(Z b){return *this+=-b;}
Z&operator*=(Z b){v=1ull*v*b.v%P; return *this;}
Z&operator/=(Z b){return *this*=b.inv();}
friend int raw(const Z&self){return self.v;}
friend Z qpow(Z a,LL b){Z r=1;for(;b;b>>=1,a*=a) if(b&1) r*=a; return r;}
friend Z operator+(Z a,Z b){return a+=b;}
friend Z operator-(Z a,Z b){return a-=b;}
friend Z operator*(Z a,Z b){return a*=b;}
friend Z operator/(Z a,Z b){return a/=b;}
};
使用例
typedef modint<998244353> Z;
int main(){
// #ifdef LOCAL
// freopen("input.in","r",stdin);
// #endif
Z a=-1,b=-2;
printf("%d %d\n",raw(a),raw(b));
printf("%d\n",raw(a+b));
printf("%d\n",raw(a-b));
printf("%d\n",raw(a*b));
printf("%d\n",raw(a/b));
printf("%d\n",raw(qpow(a,2)));
return 0;
}
C_prime (clang-format off)
using mint=modint<998244353>;
template<int N> struct C_prime{
mint fac[N+10],ifac[N+10];
C_prime(){
for(int i=raw(fac[0]=1);i<=N;i++) fac[i]=fac[i-1]*i;
ifac[N]=1/fac[N];for(int i=N;i>=1;i--) ifac[i-1]=ifac[i]*i;
}
mint operator()(int n,int m){return n>=m?fac[n]*ifac[m]*ifac[n-m]:0;}
};
C_prime (clang-format on)
typedef modint<998244353> mint;
template <int N>
struct C_prime {
mint fac[N + 10], ifac[N + 10];
C_prime() {
for (int i = raw(fac[0] = 1); i <= N; i++) fac[i] = fac[i - 1] * i;
ifac[N] = 1 / fac[N];
for (int i = N; i >= 1; i--) ifac[i - 1] = ifac[i] * i;
}
mint operator()(int n, int m) {
return n >= m ? fac[n] * ifac[m] * ifac[n - m] : 0;
}
};
注意：modint 无法存 -1，所以要用到 -1 就 throw 一个异常出去。
注意：int raw(modint) 是用来返回这个 modint 里面的值的，和 atcoder-library 是相反的（怎么没发现）。然后并没有不进行取模的 modint 的构造函数，但是 modint::v 是 public 的。然后没写自增和自减。
本家（atcoder/modint.hpp）
#ifndef ATCODER_MODINT_HPP
#define ATCODER_MODINT_HPP 1
#include <cassert>
#include <numeric>
#include <type_traits>
#ifdef _MSC_VER
#include <intrin.h>
#endif
#include "atcoder/internal_math"
#include "atcoder/internal_type_traits"
namespace atcoder {
namespace internal {
struct modint_base {};
struct static_modint_base : modint_base {};
template <class T> using is_modint = std::is_base_of<modint_base, T>;
template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>;
} // namespace internal
template <int m, std::enable_if_t<(1 <= m)>* = nullptr>
struct static_modint : internal::static_modint_base {
using mint = static_modint;
public:
static constexpr int mod() { return m; }
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
static_modint() : _v(0) {}
template <class T, internal::is_signed_int_t<T>* = nullptr>
static_modint(T v) {
long long x = (long long)(v % (long long)(umod()));
if (x < 0) x += umod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T>* = nullptr>
static_modint(T v) {
_v = (unsigned int)(v % umod());
}
unsigned int val() const { return _v; }
mint& operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint& operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
mint& operator+=(const mint& rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator-=(const mint& rhs) {
_v -= rhs._v;
if (_v >= umod()) _v += umod();
return *this;
}
mint& operator*=(const mint& rhs) {
unsigned long long z = _v;
z *= rhs._v;
_v = (unsigned int)(z % umod());
return *this;
}
mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
mint pow(long long n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const {
if (prime) {
assert(_v);
return pow(umod() - 2);
} else {
auto eg = internal::inv_gcd(_v, m);
assert(eg.first == 1);
return eg.second;
}
}
friend mint operator+(const mint& lhs, const mint& rhs) {
return mint(lhs) += rhs;
}
friend mint operator-(const mint& lhs, const mint& rhs) {
return mint(lhs) -= rhs;
}
friend mint operator*(const mint& lhs, const mint& rhs) {
return mint(lhs) *= rhs;
}
friend mint operator/(const mint& lhs, const mint& rhs) {
return mint(lhs) /= rhs;
}
friend bool operator==(const mint& lhs, const mint& rhs) {
return lhs._v == rhs._v;
}
friend bool operator!=(const mint& lhs, const mint& rhs) {
return lhs._v != rhs._v;
}
private:
unsigned int _v;
static constexpr unsigned int umod() { return m; }
static constexpr bool prime = internal::is_prime<m>;
};
template <int id> struct dynamic_modint : internal::modint_base {
using mint = dynamic_modint;
public:
static int mod() { return (int)(bt.umod()); }
static void set_mod(int m) {
assert(1 <= m);
bt = internal::barrett(m);
}
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
dynamic_modint() : _v(0) {}
template <class T, internal::is_signed_int_t<T>* = nullptr>
dynamic_modint(T v) {
long long x = (long long)(v % (long long)(mod()));
if (x < 0) x += mod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T>* = nullptr>
dynamic_modint(T v) {
_v = (unsigned int)(v % mod());
}
unsigned int val() const { return _v; }
mint& operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint& operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
mint& operator+=(const mint& rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator-=(const mint& rhs) {
_v += mod() - rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator*=(const mint& rhs) {
_v = bt.mul(_v, rhs._v);
return *this;
}
mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
mint pow(long long n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const {
auto eg = internal::inv_gcd(_v, mod());
assert(eg.first == 1);
return eg.second;
}
friend mint operator+(const mint& lhs, const mint& rhs) {
return mint(lhs) += rhs;
}
friend mint operator-(const mint& lhs, const mint& rhs) {
return mint(lhs) -= rhs;
}
friend mint operator*(const mint& lhs, const mint& rhs) {
return mint(lhs) *= rhs;
}
friend mint operator/(const mint& lhs, const mint& rhs) {
return mint(lhs) /= rhs;
}
friend bool operator==(const mint& lhs, const mint& rhs) {
return lhs._v == rhs._v;
}
friend bool operator!=(const mint& lhs, const mint& rhs) {
return lhs._v != rhs._v;
}
private:
unsigned int _v;
static internal::barrett bt;
static unsigned int umod() { return bt.umod(); }
};
template <int id> internal::barrett dynamic_modint<id>::bt(998244353);
using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;
namespace internal {
template <class T>
using is_static_modint = std::is_base_of<internal::static_modint_base, T>;
template <class T>
using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;
template <class> struct is_dynamic_modint : public std::false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};
template <class T>
using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;
} // namespace internal
} // namespace atcoder
#endif // ATCODER_MODINT_HPP
本文来自博客园，作者：caijianhong，转载请注明原文链接：https://www.cnblogs.com/caijianhong/p/template-modint.html
