competitive-programming-library

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:warning: FastFourierTransform
(math/FastFourierTransform.hpp)

Depends on

Code

#pragma once
#include "../basic/template.hpp"
#include "MyComplex.hpp"
class FastFourierTransform {
  private:
	static void dft(std::vector<MyComplex>& a) {
		int sz = a.size();
		if (sz == 1) return;
		MyComplex root =
			std::polar(1.0, (inverse ? -1 : 1) * 2.0 * acos(-1) / sz);
		std::vector<MyComplex> b(sz), roots((sz >> 1) + 1, 1);
		rep(i, sz >> 1) roots[i + 1] = roots[i] * root;
		for (int i = sz >> 1, w = 1; w < sz; i >>= 1, w <<= 1) {
			for (int j = 0; j < i; j++) {
				for (int k = 0; k < w; k++) {
					b[k + ((w * j) << 1)] =
						a[k + w * j] + a[k + w * j + (sz >> 1)];
					b[k + ((w * j) << 1) + w] =
						roots[w * j] *
						(a[k + w * j] - a[k + w * j + (sz >> 1)]);
				}
			}
			std::swap(a, b);
		}
	}

  public:
	static bool inverse;
	template <class T>
	static std::vector<double> multiply(std::vector<T> f, std::vector<T> g) {
		if (f.size() < g.size()) std::swap(f, g);
		std::vector<MyComplex> nf, ng;
		int sz = 1;
		while (sz < f.size() + g.size()) sz *= 2;
		nf.resize(sz);
		ng.resize(sz);
		rep(i, f.size()) {
			nf[i] = f[i];
			if (i < g.size()) ng[i] = g[i];
		}
		inverse = false;
		dft(nf);
		dft(ng);
		rep(i, sz) nf[i] *= ng[i];
		inverse = true;
		dft(nf);
		std::vector<double> res(sz);
		rep(i, sz) res[i] = nf[i].real() / sz;
		return res;
	}
};

bool FastFourierTransform::inverse = false;

/**
 * @title FastFourierTransform
 */
#line 2 "basic/template.hpp"
#define _CRT_SECURE_NO_WARNINGS
#ifndef __clang__
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#endif
#include <string.h>
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cfloat>
#include <chrono>
#include <climits>
#include <cmath>
#include <complex>
#include <ctime>
#include <deque>
#include <fstream>
#include <functional>
#include <iomanip>
#include <iostream>
#include <iterator>
#include <list>
#include <map>
#include <memory>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

#define rep(i, n) for (int i = 0; i < int(n); i++)
#define REP(i, n) for (int i = 1; i <= int(n); i++)
#define all(V) V.begin(), V.end()

using i128 = __int128_t;
using u128 = __uint128_t;
using uint = unsigned int;
using lint = long long;
using ulint = unsigned long long;
using IP = std::pair<int, int>;
using LP = std::pair<lint, lint>;

constexpr int INF = INT_MAX / 2;
constexpr lint LINF = LLONG_MAX / 2;
constexpr double eps = DBL_EPSILON * 10;
constexpr double PI = 3.141592653589793238462643383279;

template <class T>
class prique : public std::priority_queue<T, std::vector<T>, std::greater<T>> {};
int popcount(uint x) {
#if __cplusplus >= 202002L
	return std::popcount(x);
#else
#ifndef __clang__
	return __builtin_popcount(x);
#endif
#endif
	x = (x & 0x55555555) + (x >> 1 & 0x55555555);
	x = (x & 0x33333333) + (x >> 2 & 0x33333333);
	x = (x & 0x0f0f0f0f) + (x >> 4 & 0x0f0f0f0f);
	x = (x & 0x00ff00ff) + (x >> 8 & 0x00ff00ff);
	return (x & 0x0000ffff) + (x >> 16 & 0x0000ffff);
}
template <class F>
inline constexpr decltype(auto) lambda_fix(F&& f) {
	return [f = std::forward<F>(f)](auto&&... args) {
		return f(f, std::forward<decltype(args)>(args)...);
	};
}
template <class T>
constexpr std::vector<T> make_vec(size_t n) {
	return std::vector<T>(n);
}
template <class T, class... Args>
constexpr auto make_vec(size_t n, Args&&... args) {
	return std::vector<decltype(make_vec<T>(args...))>(n, make_vec<T>(std::forward<Args>(args)...));
}
template <class T, class U, class Stream>
Stream& operator>>(Stream& ist, std::pair<T, U>& x) {
	return ist >> x.first >> x.second;
}
template <class T, class U, class Stream>
Stream& operator<<(Stream& ost, const std::pair<T, U>& x) {
	return ost << x.first << " " << x.second;
}
template <class Container,
		  std::enable_if_t<!std::is_same<Container, std::string>::value, std::nullptr_t> = nullptr>
auto operator>>(std::istream& ist, Container& cont)
	-> decltype(typename Container::iterator(), std::cin)& {
	Container tmp;
	while (true) {
		typename Container::value_type t;
		ist >> t;
		tmp.emplace_back(t);
		if (getchar() == '\n') break;
	}
	cont = Container(std::move(tmp));
	return ist;
}
template <class Container, class Stream,
		  std::enable_if_t<!std::is_same<Container, std::string>::value, std::nullptr_t> = nullptr>
auto operator<<(Stream& ost, const Container& cont)
	-> decltype(typename Container::iterator(), ost)& {
	for (auto it = cont.begin(); it != cont.end(); it++) {
		if (it != cont.begin()) ost << ' ';
		ost << *it;
	}
	return ost;
}
template <class Container>
auto sum(const Container& cont) -> decltype(typename Container::iterator(), 0LL) {
	lint res = 0;
	for (auto it = cont.begin(); it != cont.end(); it++) res += *it;
	return res;
}
template <class T, class U>
constexpr inline bool chmax(T& lhs, const U& rhs) noexcept {
	if (lhs < rhs) {
		lhs = rhs;
		return true;
	}
	return false;
}
template <class T, class U>
constexpr inline bool chmin(T& lhs, const U& rhs) noexcept {
	if (lhs > rhs) {
		lhs = rhs;
		return true;
	}
	return false;
}
constexpr inline lint gcd(lint a, lint b) noexcept {
	while (b) {
		lint c = a;
		a = b;
		b = c % b;
	}
	return a;
}
inline lint lcm(lint a, lint b) noexcept { return a / gcd(a, b) * b; }
constexpr bool isprime(lint n) noexcept {
	if (n == 1) return false;
	for (int i = 2; i * i <= n; i++) {
		if (n % i == 0) return false;
	}
	return true;
}
template <class T>
constexpr T mypow(T a, lint b) noexcept {
	T res(1);
	while (true) {
		if (b & 1) res *= a;
		b >>= 1;
		if (!b) break;
		a *= a;
	}
	return res;
}
constexpr lint modpow(lint a, lint b, lint m) noexcept {
	a %= m;
	lint res(1);
	while (b) {
		if (b & 1) res *= a, res %= m;
		a *= a, a %= m, b >>= 1;
	}
	return res;
}
LP extGcd(lint a, lint b) noexcept {
	if (b == 0) return {1, 0};
	LP s = extGcd(b, a % b);
	std::swap(s.first, s.second);
	s.second -= a / b * s.first;
	return s;
}
LP ChineseRem(const lint& b1, const lint& m1, const lint& b2, const lint& m2) noexcept {
	auto p = extGcd(m1, m2);
	lint g = gcd(m1, m2), l = m1 / g * m2;
	lint tmp = (b2 - b1) / g * p.first % (m2 / g);
	lint r = (b1 + m1 * tmp + l) % l;
	return {r, l};
}
int LCS(const std::string& a, const std::string& b) {
	auto dp = make_vec<int>(a.size() + 1, b.size() + 1);
	rep(i, a.size()) {
		rep(j, b.size()) {
			chmax(dp[i + 1][j], dp[i][j]);
			chmax(dp[i][j + 1], dp[i][j]);
			if (a[i] == b[j]) chmax(dp[i + 1][j + 1], dp[i][j] + 1);
		}
		chmax(dp[i + 1][b.size()], dp[i][b.size()]);
	}
	rep(j, b.size()) chmax(dp[a.size()][j + 1], dp[a.size()][j]);
	return dp[a.size()][b.size()];
}
template <class T, std::enable_if_t<std::is_convertible<int, T>::value, std::nullptr_t> = nullptr>
void compress(std::vector<T>& vec) {
	auto tmp = vec;
	std::sort(all(tmp));
	tmp.erase(std::unique(all(tmp)), tmp.end());
	for (T& i : vec) i = std::lower_bound(all(tmp), i) - tmp.begin();
}
template <class T>
void compress(T* l, T* r) {
	std::vector<T> tmp(l, r);
	std::sort(all(tmp));
	tmp.erase(std::unique(all(tmp)), tmp.end());
	for (auto i = l; i < r; i++) {
		*i = std::lower_bound(all(tmp), *i) - tmp.begin();
	}
}
template <class InputIter>
void compress(InputIter l, InputIter r) {
	std::vector<typename InputIter::value_type> tmp(l, r);
	std::sort(all(tmp));
	tmp.erase(std::unique(all(tmp)), tmp.end());
	for (auto i = l; i < r; i++) {
		*i = std::lower_bound(all(tmp), *i) - tmp.begin();
	}
}
template <class InputIter,
		  std::enable_if_t<std::is_same<typename InputIter::value_type, std::pair<IP, int>>::value,
						   std::nullptr_t> = nullptr>
void mo_sort(InputIter l, InputIter r, int N) {
	const int M = std::max(1.0, std::sqrt(lint(N) * N / std::distance(l, r)));
	std::sort(l, r, [M](const auto& lhs, const auto& rhs) {
		if (lhs.first.first / M < rhs.first.first / M) return true;
		if (lhs.first.first / M == rhs.first.first / M) return lhs.first.second < rhs.first.second;
		return false;
	});
	int before = -1, cnt = 0;
	bool f = false;
	for (InputIter i = l; i != r; i++) {
		if (before != i->first.first / M) {
			if (f) std::reverse(i - cnt, i);
			f ^= true, before = i->first.first / M, cnt = 1;
		} else
			cnt++;
	}
	if (f) std::reverse(r - cnt, r);
}
template <class T>
std::vector<T> xor_bases(const std::vector<T>& vec) {
	std::vector<T> res;
	for (T i : vec) {
		for (T j : res) {
			chmin(i, i ^ j);
		}
		if (i) res.emplace_back(i);
	}
	return res;
}
#line 3 "math/MyComplex.hpp"
class MyComplex {
	double realvalue, imagvalue;

  public:
	MyComplex() : realvalue(0), imagvalue(0) {}
	template <class T, class U>
	MyComplex(const T& realvalue, const U& imagvalue)
		: realvalue(realvalue), imagvalue(imagvalue) {}
	template <class T>
	MyComplex(const T& realvalue) : realvalue(realvalue), imagvalue(0) {}
	template <class T>
	MyComplex(const std::complex<T>& c)
		: realvalue(c.real()), imagvalue(c.imag()) {}
	double& real() { return this->realvalue; }
	double& imag() { return this->imagvalue; }
	double abs() const { return hypot(realvalue, imagvalue); }
	MyComplex& operator+=(const MyComplex& rhs) {
		this->realvalue += rhs.realvalue;
		this->imagvalue += rhs.imagvalue;
		return *this;
	}
	MyComplex& operator-=(const MyComplex& rhs) {
		this->realvalue -= rhs.realvalue;
		this->imagvalue -= rhs.imagvalue;
		return *this;
	}
	MyComplex& operator*=(const MyComplex& rhs) {
		double pastreal = this->realvalue;
		this->realvalue =
			this->realvalue * rhs.realvalue - this->imagvalue * rhs.imagvalue;
		this->imagvalue =
			pastreal * rhs.imagvalue + rhs.realvalue * this->imagvalue;
		return *this;
	}
	MyComplex& operator/=(const MyComplex& rhs) {
		*this *= MyComplex(rhs.realvalue, -rhs.imagvalue);
		double dnm =
			rhs.realvalue * rhs.realvalue - rhs.imagvalue * rhs.imagvalue;
		this->realvalue /= dnm;
		this->imagvalue /= dnm;
		return *this;
	}

	template <class T>
	MyComplex operator+(const T& rhs) const {
		return MyComplex(*this) += rhs;
	}
	template <class T>
	MyComplex& operator+=(const T& rhs) const {
		return operator+=(MyComplex(rhs));
	}
	template <class T>
	MyComplex operator-(const T& rhs) const {
		return MyComplex(*this) -= rhs;
	}
	template <class T>
	MyComplex& operator-=(const T& rhs) const {
		return operator-=(MyComplex(rhs));
	}
	template <class T>
	MyComplex operator*(const T& rhs) const {
		return MyComplex(*this) *= rhs;
	}
	template <class T>
	MyComplex& operator*=(const T& rhs) const {
		return operator*=(MyComplex(rhs));
	}
	template <class T>
	MyComplex operator/(const T& rhs) const {
		return MyComplex(*this) /= rhs;
	}
	template <class T>
	MyComplex& operator/=(const T& rhs) const {
		return operator/=(MyComplex(rhs));
	}
};

/**
 * @title MyComplex
 */
#line 4 "math/FastFourierTransform.hpp"
class FastFourierTransform {
  private:
	static void dft(std::vector<MyComplex>& a) {
		int sz = a.size();
		if (sz == 1) return;
		MyComplex root =
			std::polar(1.0, (inverse ? -1 : 1) * 2.0 * acos(-1) / sz);
		std::vector<MyComplex> b(sz), roots((sz >> 1) + 1, 1);
		rep(i, sz >> 1) roots[i + 1] = roots[i] * root;
		for (int i = sz >> 1, w = 1; w < sz; i >>= 1, w <<= 1) {
			for (int j = 0; j < i; j++) {
				for (int k = 0; k < w; k++) {
					b[k + ((w * j) << 1)] =
						a[k + w * j] + a[k + w * j + (sz >> 1)];
					b[k + ((w * j) << 1) + w] =
						roots[w * j] *
						(a[k + w * j] - a[k + w * j + (sz >> 1)]);
				}
			}
			std::swap(a, b);
		}
	}

  public:
	static bool inverse;
	template <class T>
	static std::vector<double> multiply(std::vector<T> f, std::vector<T> g) {
		if (f.size() < g.size()) std::swap(f, g);
		std::vector<MyComplex> nf, ng;
		int sz = 1;
		while (sz < f.size() + g.size()) sz *= 2;
		nf.resize(sz);
		ng.resize(sz);
		rep(i, f.size()) {
			nf[i] = f[i];
			if (i < g.size()) ng[i] = g[i];
		}
		inverse = false;
		dft(nf);
		dft(ng);
		rep(i, sz) nf[i] *= ng[i];
		inverse = true;
		dft(nf);
		std::vector<double> res(sz);
		rep(i, sz) res[i] = nf[i].real() / sz;
		return res;
	}
};

bool FastFourierTransform::inverse = false;

/**
 * @title FastFourierTransform
 */
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