competitive-programming-library
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test/yosupo/convolution_mod.test.cpp
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- Last update: 2023-06-25 16:24:15+09:00
- Problem: https://judge.yosupo.jp/problem/convolution_mod
Depends on
- basic/template.hpp
- basic/type_traits.hpp
- NumberTheoreticTransform
(math/NumberTheoreticTransform.hpp)
- StaticModInt
(math/StaticModInt.hpp)
Code
#define PROBLEM "https://judge.yosupo.jp/problem/convolution_mod"
#include "../../math/NumberTheoreticTransform.hpp"
#include "../../basic/template.hpp"
int n, m;
std::vector<int> a, b;
int main() {
scanf("%d%d", &n, &m);
a.resize(n);
b.resize(m);
rep(i, n) scanf("%d", a.data() + i);
rep(i, m) scanf("%d", b.data() + i);
std::vector<StaticModInt<998244353>> c =
NumberTheoreticTransform::convolution<998244353>(a, b);
rep(i, n + m - 1) printf((i == n + m ? "%d\n" : "%d "), c[i]);
}#line 1 "test/yosupo/convolution_mod.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/convolution_mod"
#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 "basic/type_traits.hpp"
class ModInt__Base {};
class StaticModInt__Base : ModInt__Base {};
class DynamicModInt__Base : ModInt__Base {};
template <class T>
class is_ModInt : public std::is_base_of<ModInt__Base, T> {};
template <class T>
constexpr bool is_ModInt_v = is_ModInt<T>::value;
template <class T>
class is_StaticModInt : public std::is_base_of<StaticModInt__Base, T> {};
template <class T>
constexpr bool is_StaticModInt_v = is_StaticModInt<T>::value;
template <class T>
class is_DynamicModInt : public std::is_base_of<DynamicModInt__Base, T> {};
template <class T>
constexpr bool is_DynamicModInt_v = is_DynamicModInt<T>::value;
#line 4 "math/StaticModInt.hpp"
template <int modulo>
class StaticModInt : StaticModInt__Base {
uint value;
static constexpr int inv1000000007[] = {0, 1, 500000004, 333333336,
250000002, 400000003, 166666668, 142857144,
125000001, 111111112, 700000005},
inv998244353[] = {0, 1, 499122177, 332748118,
748683265, 598946612, 166374059, 855638017,
873463809, 443664157, 299473306};
public:
static constexpr int mod_value = modulo;
constexpr StaticModInt() : value(0) {}
template <class T, std::enable_if_t<!std::is_convertible<T, StaticModInt>::value,
std::nullptr_t> = nullptr>
constexpr StaticModInt(T value = 0) : value(value % modulo) {
if (this->value < 0) this->value += modulo;
}
inline constexpr StaticModInt inv() const {
if constexpr (modulo == 1000000007) {
if (*this <= 10) return inv1000000007[*this];
} else if constexpr (modulo == 998244353) {
if (*this <= 10) return inv998244353[*this];
}
return mypow(*this, modulo - 2);
}
inline constexpr StaticModInt pow(lint k) const { return mypow(*this, k); }
inline constexpr operator int() const { return value; }
inline constexpr StaticModInt& operator+=(const StaticModInt& x) {
value = value + x.value;
if (value >= modulo) value -= modulo;
return *this;
}
inline constexpr StaticModInt& operator++() {
if (value == modulo - 1)
value = 0;
else
value++;
return *this;
}
inline constexpr StaticModInt operator++(int) {
StaticModInt res = *this;
++*this;
return res;
}
inline constexpr StaticModInt operator-() const { return StaticModInt(0) -= *this; }
inline constexpr StaticModInt& operator-=(const StaticModInt& x) {
if (value < x.value) value += modulo;
value -= x.value;
return *this;
}
inline constexpr StaticModInt& operator--() {
if (value == 0)
value = modulo - 1;
else
value--;
return *this;
}
inline constexpr StaticModInt operator--(int) {
StaticModInt res = *this;
--*this;
return res;
}
inline constexpr StaticModInt& operator*=(const StaticModInt& x) {
value = (ulint)value * x.value % modulo;
return *this;
}
inline constexpr StaticModInt& operator/=(const StaticModInt& rhs) {
return *this *= rhs.inv();
}
template <class T>
constexpr StaticModInt operator+(const T& rhs) const {
return StaticModInt(*this) += rhs;
}
template <class T>
constexpr StaticModInt& operator+=(const T& rhs) {
return operator+=(StaticModInt(rhs));
}
template <class T>
constexpr StaticModInt operator-(const T& rhs) const {
return StaticModInt(*this) -= rhs;
}
template <class T>
constexpr StaticModInt& operator-=(const T& rhs) {
return operator-=(StaticModInt(rhs));
}
template <class T>
constexpr StaticModInt operator*(const T& rhs) const {
return StaticModInt(*this) *= rhs;
}
template <class T>
constexpr StaticModInt& operator*=(const T& rhs) {
return operator*=(StaticModInt(rhs));
}
template <class T>
constexpr StaticModInt operator/(const T& rhs) const {
return StaticModInt(*this) /= rhs;
}
template <class T>
constexpr StaticModInt& operator/=(const T& rhs) {
return operator/=(StaticModInt(rhs));
}
static StaticModInt primitive_root() {
if constexpr (modulo == 1012924417) return 5;
if constexpr (modulo == 924844033) return 5;
if constexpr (modulo == 998244353) return 3;
if constexpr (modulo == 1224736769) return 3;
if constexpr (modulo == 167772161) return 3;
if constexpr (modulo == 469762049) return 3;
if constexpr (modulo == 1107296257) return 10;
int p = 0;
std::mt19937 mt(0);
std::uniform_int_distribution<> uid(1, modulo - 1);
if (p) return p;
// use naive factorize due to file size limit
std::vector<int> vec;
int tmp = modulo - 1;
for (int i = 2; i * i <= tmp; i++) {
if (tmp % i == 0) {
vec.emplace_back(i);
do {
tmp /= i;
} while (tmp % i == 0);
}
}
if (tmp != 1) vec.emplace_back(tmp);
while (true) {
p = uid(mt);
bool f = true;
for (const auto& i : vec) {
if (mypow(StaticModInt(p), (modulo - 1) / i) == 1) {
f = false;
break;
}
}
if (f) return p;
}
}
};
template <int modulo, class Stream>
Stream& operator>>(Stream& ist, StaticModInt<modulo>& x) {
lint a;
ist >> a;
x = a;
return ist;
}
template <int modulo, class Stream>
Stream& operator<<(Stream& ost, const StaticModInt<modulo>& x) {
ost << int(x);
return ost;
}
#if __cplusplus < 201703L
template <int modulo>
constexpr int StaticModInt<modulo>::inv1000000007[];
template <int modulo>
constexpr int StaticModInt<modulo>::inv998244353[];
#endif
/**
* @title StaticModInt
*/
#line 4 "math/NumberTheoreticTransform.hpp"
// 1012924417, 5, 2^21
// 924844033, 5, 2^21
// 998244353, 3, 2^23
// 1224736769, 3, 2^24
// 167772161, 3, 2^25
// 1107296257, 10, 2^25
// 469762049, 3, 2^26
class NumberTheoreticTransform {
static int constexpr friendly_limit(int p) { return __builtin_ffs(p - 1) - 1; }
public:
template <int modulo>
static void ntt(std::vector<StaticModInt<modulo>>& a, bool inverse,
int size = -1) { // size should be one of powers of two
if (size == -1) size = a.size();
if (size == 1) return;
a.resize(size);
const StaticModInt<modulo> root = StaticModInt<modulo>::primitive_root().pow(
inverse ? modulo - 1 - (modulo - 1) / size : (modulo - 1) / size);
std::vector<StaticModInt<modulo>> b(size);
StaticModInt<modulo> r_p = root;
for (int i = size >> 1, w = 1; w < size; i >>= 1, w <<= 1) {
StaticModInt<modulo> r_pp = 1;
for (int j = 0; j < i; j++, r_pp *= r_p) {
for (int k = 0; k < w; k++) {
b[k + ((w * j) << 1)] = a[k + w * j] + a[k + w * j + (size >> 1)];
b[k + ((w * j) << 1) + w] = r_pp * (a[k + w * j] - a[k + w * j + (size >> 1)]);
}
}
std::swap(a, b);
r_p *= r_p;
}
}
private:
template <class T, int modulo>
static std::vector<StaticModInt<modulo>> internal_convolution(const std::vector<T>& f_,
const std::vector<T>& g_) {
std::vector<StaticModInt<modulo>> f(f_.size()), g(g_.size());
rep(i, f_.size()) f[i] = f_[i];
rep(i, g_.size()) g[i] = g_[i];
return internal_convolution(std::move(f), std::move(g));
}
template <int modulo>
static std::vector<StaticModInt<modulo>> internal_convolution(
const std::vector<StaticModInt<modulo>>& f, const std::vector<StaticModInt<modulo>>& g) {
auto f_ = f, g_ = g;
return internal_convolution(std::move(f_), std::move(g_));
}
template <int modulo>
static std::vector<StaticModInt<modulo>> internal_convolution(
const std::vector<StaticModInt<modulo>>& f, std::vector<StaticModInt<modulo>>&& g) {
auto f_ = f;
return internal_convolution(std::move(f_), std::move(g));
}
template <int modulo>
static std::vector<StaticModInt<modulo>> internal_convolution(
std::vector<StaticModInt<modulo>>& f, const std::vector<StaticModInt<modulo>>&& g) {
auto g_ = g;
return internal_convolution(std::move(f), std::move(g_));
}
template <int modulo>
static std::vector<StaticModInt<modulo>> internal_convolution(
std::vector<StaticModInt<modulo>>&& f, std::vector<StaticModInt<modulo>>&& g) {
size_t target_size = f.size() + g.size() - 1, sz = 1;
while (sz < target_size) sz <<= 1;
f.resize(sz), g.resize(sz);
ntt(f, false), ntt(g, false);
rep(i, f.size()) f[i] *= g[i];
ntt(f, true);
StaticModInt<modulo> inv = StaticModInt<modulo>(sz).inv();
rep(i, f.size()) f[i] *= inv;
f.resize(target_size);
return std::move(f);
}
public:
template <int modulo>
static std::vector<StaticModInt<modulo>> convolution(
const std::vector<StaticModInt<modulo>>& f, const std::vector<StaticModInt<modulo>>& g) {
if (1 << friendly_limit(modulo) >= f.size() + g.size() - 1) {
auto f_ = f, g_ = g;
return internal_convolution<modulo>(std::move(f_), std::move(g_));
} else if (1 << friendly_limit(modulo) + 2 >= f.size() + g.size() - 1) {
int sz = 1 << friendly_limit(modulo) - 1;
std::vector<std::vector<StaticModInt<modulo>>> f_, g_;
for (int i = 0; i * sz < f.size(); i++)
f_.emplace_back(f.begin() + i * sz,
f.begin() + std::min((int)f.size(), (i + 1) * sz));
for (int i = 0; i * sz < g.size(); i++)
g_.emplace_back(g.begin() + i * sz,
g.begin() + std::min((int)g.size(), (i + 1) * sz));
std::vector<StaticModInt<modulo>> res(f.size() + g.size() - 1);
rep(i, f_.size()) {
rep(j, g_.size()) {
auto tmp =
internal_convolution<modulo>(j == g_.size() - 1 ? std::move(f_[i]) : f_[i],
i == f_.size() - 1 ? std::move(g_[j]) : g_[j]);
rep(k, tmp.size()) res[(i + j) * sz + k] += tmp[k];
}
}
return res;
}
constexpr int base1 = 167772161, base2 = 1107296257, base3 = 469762049;
auto re1 = internal_convolution<StaticModInt<modulo>, base1>(f, g);
auto re2 = internal_convolution<StaticModInt<modulo>, base2>(f, g);
auto re3 = internal_convolution<StaticModInt<modulo>, base3>(f, g);
std::vector<StaticModInt<modulo>> res(re1.size());
constexpr int r12 = StaticModInt<base2>(base1).inv();
constexpr int r13 = StaticModInt<base3>(base1).inv();
constexpr int r23 = StaticModInt<base3>(base2).inv();
rep(i, re1.size()) {
re2[i] = StaticModInt<base2>(re2[i] - re1[i]) * r12;
re3[i] = (StaticModInt<base3>(re3[i] - re1[i]) * r13 - re2[i]) * r23;
res[i] = StaticModInt<modulo>(re1[i]) + StaticModInt<modulo>(re2[i]) * base1 +
StaticModInt<modulo>(re3[i]) * base1 * base2;
}
return res;
}
template <int modulo, class T>
static std::vector<StaticModInt<modulo>> convolution(const std::vector<T>& f,
const std::vector<T>& g) {
std::vector<StaticModInt<modulo>> f_(f.size()), g_(g.size());
rep(i, f.size()) f_[i] = f[i];
rep(i, g.size()) g_[i] = g[i];
return convolution(f_, g_);
}
template <class T>
static std::vector<lint> convolution_plain(const std::vector<T>& f, const std::vector<T>& g) {
const int mod1 = 998244353, mod2 = 1224736769;
std::vector<StaticModInt<mod1>> mul1 = internal_convolution<T, mod1>(f, g);
std::vector<StaticModInt<mod2>> mul2 = internal_convolution<T, mod2>(f, g);
std::vector<lint> res(mul1.size());
rep(i, mul1.size()) res[i] = ChineseRem(mul1[i], mod1, mul2[i], mod2).first;
return res;
}
};
/**
* @title NumberTheoreticTransform
*/
#line 4 "test/yosupo/convolution_mod.test.cpp"
int n, m;
std::vector<int> a, b;
int main() {
scanf("%d%d", &n, &m);
a.resize(n);
b.resize(m);
rep(i, n) scanf("%d", a.data() + i);
rep(i, m) scanf("%d", b.data() + i);
std::vector<StaticModInt<998244353>> c =
NumberTheoreticTransform::convolution<998244353>(a, b);
rep(i, n + m - 1) printf((i == n + m ? "%d\n" : "%d "), c[i]);
}