mmrz's library

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verify/yosupo/convolution_mod.test.cpp

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• Last update: 2025-07-05 17:21:00+09:00
• Problem: https://judge.yosupo.jp/problem/convolution_mod

Depends on

• 形式的冪級数ライブラリ (math/formal_power_series.hpp)
• modint (math/modint.hpp)
• math/power.hpp
• template/template.hpp

Code

#define PROBLEM "https://judge.yosupo.jp/problem/convolution_mod"

#include "./../../template/template.hpp"
#include "./../../math/modint.hpp"
using mint998 = modint<998244353>;
#include "./../../math/formal_power_series.hpp"
using fps = formal_power_series<mint998>;

using namespace mmrz;

void mmrz::solve(){
	int n, m;
	cin >> n >> m;
	fps a(n), b(m);
	rep(i, n){
		int _a;
		cin >> _a;
		a[i] = _a;
	}
	rep(i, m){
		int _b;
		cin >> _b;
		b[i] = _b;
	}
	fps f{1};
	f *= a;
	f *= b;
	rep(i, n+m-1){
		cout << f[i] << " \n"[i == n+m-1];
	}
}

#line 1 "verify/yosupo/convolution_mod.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/convolution_mod"

#line 1 "template/template.hpp"
# include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ull = unsigned long long;
const double pi = acos(-1);
template<class T>constexpr T inf() { return ::std::numeric_limits<T>::max(); }
template<class T>constexpr T hinf() { return inf<T>() / 2; }
template <typename T_char>T_char TL(T_char cX) { return tolower(cX); }
template <typename T_char>T_char TU(T_char cX) { return toupper(cX); }
template<class T> bool chmin(T& a,T b) { if(a > b){a = b; return true;} return false; }
template<class T> bool chmax(T& a,T b) { if(a < b){a = b; return true;} return false; }
int popcnt(unsigned long long n) { int cnt = 0; for (int i = 0; i < 64; i++)if ((n >> i) & 1)cnt++; return cnt; }
int d_sum(ll n) { int ret = 0; while (n > 0) { ret += n % 10; n /= 10; }return ret; }
int d_cnt(ll n) { int ret = 0; while (n > 0) { ret++; n /= 10; }return ret; }
ll gcd(ll a, ll b) { if (b == 0)return a; return gcd(b, a%b); };
ll lcm(ll a, ll b) { ll g = gcd(a, b); return a / g*b; };
ll MOD(ll x, ll m){return (x%m+m)%m; }
ll FLOOR(ll x, ll m) {ll r = (x%m+m)%m; return (x-r)/m; }
template<class T> using dijk = priority_queue<T, vector<T>, greater<T>>;
# define all(qpqpq)           (qpqpq).begin(),(qpqpq).end()
# define UNIQUE(wpwpw)        (wpwpw).erase(unique(all((wpwpw))),(wpwpw).end())
# define LOWER(epepe)         transform(all((epepe)),(epepe).begin(),TL<char>)
# define UPPER(rprpr)         transform(all((rprpr)),(rprpr).begin(),TU<char>)
# define rep(i,upupu)         for(ll i = 0, i##_len = (upupu);(i) < (i##_len);(i)++)
# define reps(i,opopo)        for(ll i = 1, i##_len = (opopo);(i) <= (i##_len);(i)++)
# define len(x)                ((ll)(x).size())
# define bit(n)               (1LL << (n))
# define pb push_back
# define eb emplace_back
# define exists(c, e)         ((c).find(e) != (c).end())

struct INIT{
	INIT(){
		std::ios::sync_with_stdio(false);
		std::cin.tie(0);
		cout << fixed << setprecision(20);
	}
}INIT;

namespace mmrz {
	void solve();
}

int main(){
	mmrz::solve();
}
#line 2 "math/modint.hpp"

#line 5 "math/modint.hpp"

template <std::uint_fast64_t Modulus> class modint {
	using u64 = std::uint_fast64_t;
public:
	u64 a;
	constexpr modint(const u64 x = 0) noexcept : a(x % Modulus) {}
	constexpr u64 &value() noexcept { return a; }
	constexpr const u64 &value() const noexcept { return a; }
	constexpr modint operator+(const modint rhs) const noexcept {
		return modint(*this) += rhs;
	}
	constexpr modint operator-(const modint rhs) const noexcept {
		return modint(*this) -= rhs;
	}
	constexpr modint operator*(const modint rhs) const noexcept {
		return modint(*this) *= rhs;
	}
	constexpr modint operator/(const modint rhs) const noexcept {
		return modint(*this) /= rhs;
	}
	constexpr modint &operator+=(const modint rhs) noexcept {
		a += rhs.a;
		if (a >= Modulus) {
			a -= Modulus;
		}
		return *this;
	}
	constexpr modint &operator-=(const modint rhs) noexcept {
		if (a < rhs.a) {
			a += Modulus;
		}
		a -= rhs.a;
		return *this;
	}
	constexpr modint &operator*=(const modint rhs) noexcept {
		a = a * rhs.a % Modulus;
		return *this;
	}
	constexpr modint &operator/=(modint rhs) noexcept {
		u64 exp = Modulus - 2;
		while (exp) {
			if (exp % 2) {
				*this *= rhs;
			}
			rhs *= rhs;
			exp /= 2;
		}
		return *this;
	}

	constexpr modint& operator++() noexcept {
		if (++a == Modulus) a = 0;
		return *this;
	}
	constexpr modint operator++(int) noexcept {
		modint tmp(*this);
		++(*this);
		return tmp;
	}
	constexpr modint& operator--() noexcept {
		if (a == 0) a = Modulus;
		--a;
		return *this;
	}
	constexpr modint operator--(int) noexcept {
		modint tmp(*this);
		--(*this);
		return tmp;
	}

	friend std::ostream& operator<<(std::ostream& os, const modint& rhs) {
		os << rhs.a;
		return os;
	}
};
#line 5 "verify/yosupo/convolution_mod.test.cpp"
using mint998 = modint<998244353>;
#line 1 "math/formal_power_series.hpp"

template<typename mint998>
struct formal_power_series : vector<mint998> {
	using vector<mint998>::vector;
	using FPS = formal_power_series;

	FPS &operator+=(const FPS &r){
		if(r.size() > this->size()){
			this->resize(r.size());
		}
		for(size_t i = 0;i < r.size();i++){
			(*this)[i] += r[i];
		}
		return *this;
	}

	FPS &operator+=(const mint998 &v){
		if(this->empty())this->resize(1);
		(*this)[0] += v;
		return *this;
	}

	FPS &operator-=(const FPS &r){
		if(r.size() > this->size()){
			this->resize(r.size());
		}
		for(size_t i = 0;i < r.size();i++){
			(*this)[i] -= r[i];
		}
		return *this;
	}

	FPS &operator-=(const mint998 &v){
		if(this->empty())this->resize(1);
		(*this)[0] -= v;
		return *this;
	}

	FPS &operator*=(const FPS &g){
		size_t N = std::bit_ceil(this->size() + g.size() - 1);

		vector<mint998> F(N, 0), G(N, 0);

		for (size_t i = 0; i < this->size(); i++){
			F[i] = (*this)[i];
		}
		for (size_t i = 0; i < g.size(); i++){
			G[i] = g[i];
		}

		DFT(F);
		DFT(G);

		vector<mint998> FG(N);
		for (size_t i = 0; i < N; i++){
			FG[i] = F[i] * G[i];
		}
		IDFT(FG);

		FPS fg(this->size() + g.size() - 1);
		for (size_t i = 0; i < fg.size(); i++){
			fg[i] = FG[i];
		}
		return *this = fg;
	}

	FPS &operator*=(const mint998 &v){
		for(size_t k = 0;k < this->size();k++){
			(*this)[k] *= v;
			return *this;
		}
	}

	FPS operator+(const FPS &r) const { return FPS(*this) += r; }
	FPS operator+(const mint998 &v) const { return FPS(*this) += v; }
	FPS operator-(const FPS &r) const { return FPS(*this) -= r; }
	FPS operator-(const mint998 &v) const { return FPS(*this) -= v; }
	FPS operator*(const FPS &r) const { return FPS(*this) *= r; }
	FPS operator*(const mint998 &v) const { return FPS(*this) *= v; }
	FPS operator-() const {
		FPS ret(this->size());
		for(size_t i = 0;i < this->size();i++){
			ret[i] = -(*this)[i];
		}
		return ret;
	}

	void shrink(){
		while(this->size() && this->back() == mint998(0))this->pop_back();
	}

	mint998 eval(mint998 x) const {
		mint998 r = 0, w = 1;
		for(auto &v : *this){
			r += w*v;
			w *= x;
		}
		return r;
	}
};

#line 2 "math/power.hpp"

#include <type_traits>

template<typename T>
concept NotPrimitiveInt =
	!(std::is_same_v<T, int> ||
		std::is_same_v<T, long> ||
		std::is_same_v<T, long long> ||
		std::is_same_v<T, unsigned> ||
		std::is_same_v<T, unsigned long> ||
		std::is_same_v<T, unsigned long long>);

template<NotPrimitiveInt T>
T power(T n, long long k) {
	T ret = 1;
	while(k > 0) {
		if(k & 1)ret *= n;
		n = n*n;
		k >>= 1;
	}
	return ret;
}

long long power(long long n, long long k, long long p) {
	long long ret = 1;
	while(k > 0){
		if(k & 1)ret = ret*n % p;
		n = n*n % p;
		k >>= 1;
	}
	return ret;
}
#line 103 "math/formal_power_series.hpp"

vector<vector<mint998>> zeta_table;

mint998 zeta(size_t n, int i){
	i += n;
	i %= n;
	if(zeta_table.empty()){
		zeta_table.resize(24);
		mint998 r = power<mint998>(3,119);
		for(int j = 23;j >= 0;j--){
			zeta_table[j].resize(1);
			zeta_table[j][0] = r;
			r *= r;
		}
	}
	int N_2 = __builtin_ctz(n);
	if(zeta_table[N_2].size() == 1){
		mint998 r = zeta_table[N_2][0];
		zeta_table[N_2][0] = 1;
		zeta_table[N_2].resize(n);
		for(size_t j = 1;j < n;j++){
			zeta_table[N_2][j] = r * zeta_table[N_2][j-1];
			if(j == n-1){
				assert((zeta_table[N_2][j] * r).a == 1);
			}
		}
	}
	return zeta_table[N_2][i];
}

void DFT(vector<mint998> &f, bool inverse = false){
	size_t N = f.size();
	if(N == 1)return;

	size_t n = N >> 1;

	vector<mint998> f0(n), f1(n);
	for (size_t i = 0; i < n; i++){
		f0[i] = f[2 * i];
		f1[i] = f[2 * i + 1];
	}

	DFT(f0, inverse);
	DFT(f1, inverse);

	for (size_t i = 0; i < n; i++){
		f[i] = f0[i] + (inverse ? zeta(N, -i) : zeta(N, i)) * f1[i];
		f[n + i] = f0[i] + (inverse ? zeta(N, -n - i) : zeta(N, n + i)) * f1[i];
	}
}

void IDFT(vector<mint998> &f){
	DFT(f, true);
	size_t N = f.size();
	for (mint998 &a : f){
		a /= N;
	}
}
#line 7 "verify/yosupo/convolution_mod.test.cpp"
using fps = formal_power_series<mint998>;

using namespace mmrz;

void mmrz::solve(){
	int n, m;
	cin >> n >> m;
	fps a(n), b(m);
	rep(i, n){
		int _a;
		cin >> _a;
		a[i] = _a;
	}
	rep(i, m){
		int _b;
		cin >> _b;
		b[i] = _b;
	}
	fps f{1};
	f *= a;
	f *= b;
	rep(i, n+m-1){
		cout << f[i] << " \n"[i == n+m-1];
	}
}

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