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deprecated/number_theoretic_transform.hpp
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- Last update: 2021-09-03 02:53:07+09:00
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#include "deprecated/number_theoretic_transform.hpp"
Code
#ifndef number_theoretic_transform_hpp
#define number_theoretic_transform_hpp
#include <algorithm>
#include <cassert>
#include <iostream>
#include <vector>
namespace number_theoretic_transform
{
constexpr int mod = 998244353;
constexpr int primitive = 3;
class modint
{
int val;
public:
constexpr modint() noexcept : val{0} {}
constexpr modint(long long x) noexcept : val((x %= mod) < 0 ? mod + x : x) {}
constexpr long long value() const noexcept { return val; }
constexpr modint operator++(int) noexcept { modint t = *this; return ++val, t; }
constexpr modint operator--(int) noexcept { modint t = *this; return --val, t; }
constexpr modint &operator++() noexcept { return ++val, *this; }
constexpr modint &operator--() noexcept { return --val, *this; }
constexpr modint operator-() const noexcept { return modint(-val); }
constexpr modint &operator+=(const modint &other) noexcept { return (val += other.val) < mod ? 0 : val -= mod, *this; }
constexpr modint &operator-=(const modint &other) noexcept { return (val += mod - other.val) < mod ? 0 : val -= mod, *this; }
constexpr modint &operator*=(const modint &other) noexcept { return val = (long long)val * other.val % mod, *this; }
constexpr modint &operator/=(const modint &other) noexcept { return *this *= inverse(other); }
constexpr modint operator+(const modint &other) const noexcept { return modint(*this) += other; }
constexpr modint operator-(const modint &other) const noexcept { return modint(*this) -= other; }
constexpr modint operator*(const modint &other) const noexcept { return modint(*this) *= other; }
constexpr modint operator/(const modint &other) const noexcept { return modint(*this) /= other; }
constexpr bool operator==(const modint &other) const noexcept { return val == other.val; }
constexpr bool operator!=(const modint &other) const noexcept { return val != other.val; }
constexpr bool operator!() const noexcept { return !val; }
friend constexpr modint operator+(long long x, modint y) noexcept { return modint(x) + y; }
friend constexpr modint operator-(long long x, modint y) noexcept { return modint(x) - y; }
friend constexpr modint operator*(long long x, modint y) noexcept { return modint(x) * y; }
friend constexpr modint operator/(long long x, modint y) noexcept { return modint(x) / y; }
static constexpr modint inverse(const modint &other) noexcept
{
assert(other != 0);
int a{mod}, b{other.val}, u{}, v{1}, t{};
while(b) t = a / b, a ^= b ^= (a -= t * b) ^= b, u ^= v ^= (u -= t * v) ^= v;
return {u};
}
static constexpr modint pow(modint other, long long e) noexcept
{
if(e < 0) e = e % (mod - 1) + mod - 1;
modint res{1};
while(e) { if(e & 1) res *= other; other *= other, e >>= 1; }
return res;
}
friend std::ostream &operator<<(std::ostream &os, const modint &other) noexcept { return os << other.val; }
friend std::istream &operator>>(std::istream &is, modint &other) noexcept { long long val; other = {(is >> val, val)}; return is; }
}; // class modint
class zeta_calc
{
static constexpr size_t n = __builtin_ctz(mod - 1);
modint _zeta[n + 1];
public:
constexpr zeta_calc() : _zeta{}
{
_zeta[n] = modint::pow(modint(primitive), (mod - 1) / (1 << n));
for(size_t i{n}; i; --i) _zeta[i - 1] = _zeta[i] * _zeta[i];
}
constexpr modint operator[](size_t k) const { return _zeta[k]; }
}; // class zeta_calc
constexpr zeta_calc zeta;
class inv_calc
{
static constexpr size_t n = __builtin_ctz(mod - 1);
modint _inv[n + 1];
public:
constexpr inv_calc() : _inv{1, (mod + 1) / 2} { for(size_t i{1}; i < n; ++i) _inv[i + 1] = _inv[i] * _inv[1]; }
constexpr modint operator[](size_t k) const { return _inv[k]; }
}; // class inv_calc
constexpr inv_calc inv;
using poly_t = std::vector<modint>;
void discrete_Fourier_transform(poly_t &f)
{
const size_t n{f.size()}, mask{n - 1};
assert(__builtin_popcount(n) == 1); // degree of f must be a power of two.
static poly_t g; g.resize(n);
for(size_t i{n >> 1}, ii{1}; i; i >>= 1, ++ii, swap(f, g))
{
modint powzeta{1};
for(size_t j{}; j < n; powzeta *= zeta[ii])
{
for(size_t k{}, x{mask & j << 1}, y{mask & (i + (j << 1))}; k < i; ++k, ++j, ++x, ++y)
{
g[j] = f[x] + powzeta * f[y];
}
}
}
}
void inverse_discrete_Fourier_transform(poly_t &f)
{
discrete_Fourier_transform(f), reverse(next(f.begin()), f.end());
const size_t k = __builtin_ctz(f.size()); for(modint &e : f) e *= inv[k];
}
poly_t convolute(poly_t f, poly_t g)
{
if(f.empty() || g.empty()) return poly_t();
const size_t deg_f{f.size() - 1}, deg_g{g.size() - 1}, deg_h{deg_f + deg_g}, n(1u << (32 - __builtin_clz(deg_h)));
static poly_t h;
f.resize(n, 0), g.resize(n, 0), h.resize(n);
discrete_Fourier_transform(f), discrete_Fourier_transform(g);
for(size_t i{}; i < n; ++i) h[i] = f[i] * g[i];
inverse_discrete_Fourier_transform(h); h.resize(deg_h + 1);
return h;
}
} // namespace Number_theoretic_transform
#endif // number_theoretic_transform_hpp#line 1 "deprecated/number_theoretic_transform.hpp"
#include <algorithm>
#include <cassert>
#include <iostream>
#include <vector>
namespace number_theoretic_transform
{
constexpr int mod = 998244353;
constexpr int primitive = 3;
class modint
{
int val;
public:
constexpr modint() noexcept : val{0} {}
constexpr modint(long long x) noexcept : val((x %= mod) < 0 ? mod + x : x) {}
constexpr long long value() const noexcept { return val; }
constexpr modint operator++(int) noexcept { modint t = *this; return ++val, t; }
constexpr modint operator--(int) noexcept { modint t = *this; return --val, t; }
constexpr modint &operator++() noexcept { return ++val, *this; }
constexpr modint &operator--() noexcept { return --val, *this; }
constexpr modint operator-() const noexcept { return modint(-val); }
constexpr modint &operator+=(const modint &other) noexcept { return (val += other.val) < mod ? 0 : val -= mod, *this; }
constexpr modint &operator-=(const modint &other) noexcept { return (val += mod - other.val) < mod ? 0 : val -= mod, *this; }
constexpr modint &operator*=(const modint &other) noexcept { return val = (long long)val * other.val % mod, *this; }
constexpr modint &operator/=(const modint &other) noexcept { return *this *= inverse(other); }
constexpr modint operator+(const modint &other) const noexcept { return modint(*this) += other; }
constexpr modint operator-(const modint &other) const noexcept { return modint(*this) -= other; }
constexpr modint operator*(const modint &other) const noexcept { return modint(*this) *= other; }
constexpr modint operator/(const modint &other) const noexcept { return modint(*this) /= other; }
constexpr bool operator==(const modint &other) const noexcept { return val == other.val; }
constexpr bool operator!=(const modint &other) const noexcept { return val != other.val; }
constexpr bool operator!() const noexcept { return !val; }
friend constexpr modint operator+(long long x, modint y) noexcept { return modint(x) + y; }
friend constexpr modint operator-(long long x, modint y) noexcept { return modint(x) - y; }
friend constexpr modint operator*(long long x, modint y) noexcept { return modint(x) * y; }
friend constexpr modint operator/(long long x, modint y) noexcept { return modint(x) / y; }
static constexpr modint inverse(const modint &other) noexcept
{
assert(other != 0);
int a{mod}, b{other.val}, u{}, v{1}, t{};
while(b) t = a / b, a ^= b ^= (a -= t * b) ^= b, u ^= v ^= (u -= t * v) ^= v;
return {u};
}
static constexpr modint pow(modint other, long long e) noexcept
{
if(e < 0) e = e % (mod - 1) + mod - 1;
modint res{1};
while(e) { if(e & 1) res *= other; other *= other, e >>= 1; }
return res;
}
friend std::ostream &operator<<(std::ostream &os, const modint &other) noexcept { return os << other.val; }
friend std::istream &operator>>(std::istream &is, modint &other) noexcept { long long val; other = {(is >> val, val)}; return is; }
}; // class modint
class zeta_calc
{
static constexpr size_t n = __builtin_ctz(mod - 1);
modint _zeta[n + 1];
public:
constexpr zeta_calc() : _zeta{}
{
_zeta[n] = modint::pow(modint(primitive), (mod - 1) / (1 << n));
for(size_t i{n}; i; --i) _zeta[i - 1] = _zeta[i] * _zeta[i];
}
constexpr modint operator[](size_t k) const { return _zeta[k]; }
}; // class zeta_calc
constexpr zeta_calc zeta;
class inv_calc
{
static constexpr size_t n = __builtin_ctz(mod - 1);
modint _inv[n + 1];
public:
constexpr inv_calc() : _inv{1, (mod + 1) / 2} { for(size_t i{1}; i < n; ++i) _inv[i + 1] = _inv[i] * _inv[1]; }
constexpr modint operator[](size_t k) const { return _inv[k]; }
}; // class inv_calc
constexpr inv_calc inv;
using poly_t = std::vector<modint>;
void discrete_Fourier_transform(poly_t &f)
{
const size_t n{f.size()}, mask{n - 1};
assert(__builtin_popcount(n) == 1); // degree of f must be a power of two.
static poly_t g; g.resize(n);
for(size_t i{n >> 1}, ii{1}; i; i >>= 1, ++ii, swap(f, g))
{
modint powzeta{1};
for(size_t j{}; j < n; powzeta *= zeta[ii])
{
for(size_t k{}, x{mask & j << 1}, y{mask & (i + (j << 1))}; k < i; ++k, ++j, ++x, ++y)
{
g[j] = f[x] + powzeta * f[y];
}
}
}
}
void inverse_discrete_Fourier_transform(poly_t &f)
{
discrete_Fourier_transform(f), reverse(next(f.begin()), f.end());
const size_t k = __builtin_ctz(f.size()); for(modint &e : f) e *= inv[k];
}
poly_t convolute(poly_t f, poly_t g)
{
if(f.empty() || g.empty()) return poly_t();
const size_t deg_f{f.size() - 1}, deg_g{g.size() - 1}, deg_h{deg_f + deg_g}, n(1u << (32 - __builtin_clz(deg_h)));
static poly_t h;
f.resize(n, 0), g.resize(n, 0), h.resize(n);
discrete_Fourier_transform(f), discrete_Fourier_transform(g);
for(size_t i{}; i < n; ++i) h[i] = f[i] * g[i];
inverse_discrete_Fourier_transform(h); h.resize(deg_h + 1);
return h;
}
} // namespace Number_theoretic_transform