C++ Library for Competitive Programming
/*
* @title 数学/畳み込み/subset convolution
*
* verification-helper: PROBLEM https://judge.yosupo.jp/problem/subset_convolution
*/
#include <iostream>
#include <vector>
#include "emthrm/math/convolution/subset_convolution.hpp"
#include "emthrm/math/modint.hpp"
int main() {
using ModInt = emthrm::MInt<998244353>;
constexpr int kMaxN = 20;
int n;
std::cin >> n;
std::vector<ModInt> a(1 << n), b(1 << n);
for (int i = 0; i < (1 << n); ++i) {
std::cin >> a[i];
}
for (int i = 0; i < (1 << n); ++i) {
std::cin >> b[i];
}
const std::vector<ModInt> c = emthrm::subset_convolution<kMaxN>(a, b);
for (int i = 0; i < (1 << n); ++i) {
std::cout << c[i] << " \n"[i + 1 == (1 << n)];
}
return 0;
}
#line 1 "test/math/convolution/subset_convolution.test.cpp"
/*
* @title 数学/畳み込み/subset convolution
*
* verification-helper: PROBLEM https://judge.yosupo.jp/problem/subset_convolution
*/
#include <iostream>
#include <vector>
#line 1 "include/emthrm/math/convolution/subset_convolution.hpp"
#include <array>
#include <bit>
#include <cassert>
#include <utility>
#line 9 "include/emthrm/math/convolution/subset_convolution.hpp"
namespace emthrm {
template <int MaxN, typename T>
std::vector<T> subset_convolution(
const std::vector<T>& f, const std::vector<T>& g) {
using Polynomial = std::array<T, MaxN + 1>;
assert(std::has_single_bit(f.size()) && f.size() == g.size());
const int n = std::countr_zero(f.size());
assert(n <= MaxN);
const int domain_size = 1 << n;
const auto ranked_zeta_transform =
[n, domain_size](const std::vector<T>& f) -> std::vector<Polynomial> {
std::vector a(domain_size, Polynomial{});
for (int i = 0; i < domain_size; ++i) {
a[i][std::popcount(static_cast<unsigned int>(i))] = f[i];
}
for (int bit = 1; bit < domain_size; bit <<= 1) {
for (int i = 0; i < domain_size; ++i) {
if ((i & bit) == 0) {
for (int degree = 0; degree <= n; ++degree) {
a[i | bit][degree] += a[i][degree];
}
}
}
}
return a;
};
std::vector<Polynomial> a = ranked_zeta_transform(f);
const std::vector<Polynomial> b = ranked_zeta_transform(g);
for (int i = 0; i < domain_size; ++i) {
// Hadamard product
for (int degree_of_a = n; degree_of_a >= 0; --degree_of_a) {
const T tmp = std::exchange(a[i][degree_of_a], T{});
for (int degree_of_b = 0; degree_of_a + degree_of_b <= n; ++degree_of_b) {
a[i][degree_of_a + degree_of_b] += tmp * b[i][degree_of_b];
}
}
}
for (int bit = 1; bit < domain_size; bit <<= 1) {
for (int i = 0; i < domain_size; ++i) {
if ((i & bit) == 0) {
for (int degree = 0; degree <= n; ++degree) {
a[i | bit][degree] -= a[i][degree];
}
}
}
}
std::vector<T> c(domain_size);
for (int i = 0; i < domain_size; ++i) {
c[i] = a[i][std::popcount(static_cast<unsigned int>(i))];
}
return c;
}
} // namespace emthrm
#line 1 "include/emthrm/math/modint.hpp"
#ifndef ARBITRARY_MODINT
#line 6 "include/emthrm/math/modint.hpp"
#endif
#include <compare>
#line 9 "include/emthrm/math/modint.hpp"
// #include <numeric>
#line 12 "include/emthrm/math/modint.hpp"
namespace emthrm {
#ifndef ARBITRARY_MODINT
template <unsigned int M>
struct MInt {
unsigned int v;
constexpr MInt() : v(0) {}
constexpr MInt(const long long x) : v(x >= 0 ? x % M : x % M + M) {}
static constexpr MInt raw(const int x) {
MInt x_;
x_.v = x;
return x_;
}
static constexpr int get_mod() { return M; }
static constexpr void set_mod(const int divisor) {
assert(std::cmp_equal(divisor, M));
}
static void init(const int x) {
inv<true>(x);
fact(x);
fact_inv(x);
}
template <bool MEMOIZES = false>
static MInt inv(const int n) {
// assert(0 <= n && n < M && std::gcd(n, M) == 1);
static std::vector<MInt> inverse{0, 1};
const int prev = inverse.size();
if (n < prev) return inverse[n];
if constexpr (MEMOIZES) {
// "n!" and "M" must be disjoint.
inverse.resize(n + 1);
for (int i = prev; i <= n; ++i) {
inverse[i] = -inverse[M % i] * raw(M / i);
}
return inverse[n];
}
int u = 1, v = 0;
for (unsigned int a = n, b = M; b;) {
const unsigned int q = a / b;
std::swap(a -= q * b, b);
std::swap(u -= q * v, v);
}
return u;
}
static MInt fact(const int n) {
static std::vector<MInt> factorial{1};
if (const int prev = factorial.size(); n >= prev) {
factorial.resize(n + 1);
for (int i = prev; i <= n; ++i) {
factorial[i] = factorial[i - 1] * i;
}
}
return factorial[n];
}
static MInt fact_inv(const int n) {
static std::vector<MInt> f_inv{1};
if (const int prev = f_inv.size(); n >= prev) {
f_inv.resize(n + 1);
f_inv[n] = inv(fact(n).v);
for (int i = n; i > prev; --i) {
f_inv[i - 1] = f_inv[i] * i;
}
}
return f_inv[n];
}
static MInt nCk(const int n, const int k) {
if (n < 0 || n < k || k < 0) [[unlikely]] return MInt();
return fact(n) * (n - k < k ? fact_inv(k) * fact_inv(n - k) :
fact_inv(n - k) * fact_inv(k));
}
static MInt nPk(const int n, const int k) {
return n < 0 || n < k || k < 0 ? MInt() : fact(n) * fact_inv(n - k);
}
static MInt nHk(const int n, const int k) {
return n < 0 || k < 0 ? MInt() : (k == 0 ? 1 : nCk(n + k - 1, k));
}
static MInt large_nCk(long long n, const int k) {
if (n < 0 || n < k || k < 0) [[unlikely]] return MInt();
inv<true>(k);
MInt res = 1;
for (int i = 1; i <= k; ++i) {
res *= inv(i) * n--;
}
return res;
}
constexpr MInt pow(long long exponent) const {
MInt res = 1, tmp = *this;
for (; exponent > 0; exponent >>= 1) {
if (exponent & 1) res *= tmp;
tmp *= tmp;
}
return res;
}
constexpr MInt& operator+=(const MInt& x) {
if ((v += x.v) >= M) v -= M;
return *this;
}
constexpr MInt& operator-=(const MInt& x) {
if ((v += M - x.v) >= M) v -= M;
return *this;
}
constexpr MInt& operator*=(const MInt& x) {
v = (unsigned long long){v} * x.v % M;
return *this;
}
MInt& operator/=(const MInt& x) { return *this *= inv(x.v); }
constexpr auto operator<=>(const MInt& x) const = default;
constexpr MInt& operator++() {
if (++v == M) [[unlikely]] v = 0;
return *this;
}
constexpr MInt operator++(int) {
const MInt res = *this;
++*this;
return res;
}
constexpr MInt& operator--() {
v = (v == 0 ? M - 1 : v - 1);
return *this;
}
constexpr MInt operator--(int) {
const MInt res = *this;
--*this;
return res;
}
constexpr MInt operator+() const { return *this; }
constexpr MInt operator-() const { return raw(v ? M - v : 0); }
constexpr MInt operator+(const MInt& x) const { return MInt(*this) += x; }
constexpr MInt operator-(const MInt& x) const { return MInt(*this) -= x; }
constexpr MInt operator*(const MInt& x) const { return MInt(*this) *= x; }
MInt operator/(const MInt& x) const { return MInt(*this) /= x; }
friend std::ostream& operator<<(std::ostream& os, const MInt& x) {
return os << x.v;
}
friend std::istream& operator>>(std::istream& is, MInt& x) {
long long v;
is >> v;
x = MInt(v);
return is;
}
};
#else // ARBITRARY_MODINT
template <int ID>
struct MInt {
unsigned int v;
constexpr MInt() : v(0) {}
MInt(const long long x) : v(x >= 0 ? x % mod() : x % mod() + mod()) {}
static constexpr MInt raw(const int x) {
MInt x_;
x_.v = x;
return x_;
}
static int get_mod() { return mod(); }
static void set_mod(const unsigned int divisor) { mod() = divisor; }
static void init(const int x) {
inv<true>(x);
fact(x);
fact_inv(x);
}
template <bool MEMOIZES = false>
static MInt inv(const int n) {
// assert(0 <= n && n < mod() && std::gcd(x, mod()) == 1);
static std::vector<MInt> inverse{0, 1};
const int prev = inverse.size();
if (n < prev) return inverse[n];
if constexpr (MEMOIZES) {
// "n!" and "M" must be disjoint.
inverse.resize(n + 1);
for (int i = prev; i <= n; ++i) {
inverse[i] = -inverse[mod() % i] * raw(mod() / i);
}
return inverse[n];
}
int u = 1, v = 0;
for (unsigned int a = n, b = mod(); b;) {
const unsigned int q = a / b;
std::swap(a -= q * b, b);
std::swap(u -= q * v, v);
}
return u;
}
static MInt fact(const int n) {
static std::vector<MInt> factorial{1};
if (const int prev = factorial.size(); n >= prev) {
factorial.resize(n + 1);
for (int i = prev; i <= n; ++i) {
factorial[i] = factorial[i - 1] * i;
}
}
return factorial[n];
}
static MInt fact_inv(const int n) {
static std::vector<MInt> f_inv{1};
if (const int prev = f_inv.size(); n >= prev) {
f_inv.resize(n + 1);
f_inv[n] = inv(fact(n).v);
for (int i = n; i > prev; --i) {
f_inv[i - 1] = f_inv[i] * i;
}
}
return f_inv[n];
}
static MInt nCk(const int n, const int k) {
if (n < 0 || n < k || k < 0) [[unlikely]] return MInt();
return fact(n) * (n - k < k ? fact_inv(k) * fact_inv(n - k) :
fact_inv(n - k) * fact_inv(k));
}
static MInt nPk(const int n, const int k) {
return n < 0 || n < k || k < 0 ? MInt() : fact(n) * fact_inv(n - k);
}
static MInt nHk(const int n, const int k) {
return n < 0 || k < 0 ? MInt() : (k == 0 ? 1 : nCk(n + k - 1, k));
}
static MInt large_nCk(long long n, const int k) {
if (n < 0 || n < k || k < 0) [[unlikely]] return MInt();
inv<true>(k);
MInt res = 1;
for (int i = 1; i <= k; ++i) {
res *= inv(i) * n--;
}
return res;
}
MInt pow(long long exponent) const {
MInt res = 1, tmp = *this;
for (; exponent > 0; exponent >>= 1) {
if (exponent & 1) res *= tmp;
tmp *= tmp;
}
return res;
}
MInt& operator+=(const MInt& x) {
if ((v += x.v) >= mod()) v -= mod();
return *this;
}
MInt& operator-=(const MInt& x) {
if ((v += mod() - x.v) >= mod()) v -= mod();
return *this;
}
MInt& operator*=(const MInt& x) {
v = (unsigned long long){v} * x.v % mod();
return *this;
}
MInt& operator/=(const MInt& x) { return *this *= inv(x.v); }
auto operator<=>(const MInt& x) const = default;
MInt& operator++() {
if (++v == mod()) [[unlikely]] v = 0;
return *this;
}
MInt operator++(int) {
const MInt res = *this;
++*this;
return res;
}
MInt& operator--() {
v = (v == 0 ? mod() - 1 : v - 1);
return *this;
}
MInt operator--(int) {
const MInt res = *this;
--*this;
return res;
}
MInt operator+() const { return *this; }
MInt operator-() const { return raw(v ? mod() - v : 0); }
MInt operator+(const MInt& x) const { return MInt(*this) += x; }
MInt operator-(const MInt& x) const { return MInt(*this) -= x; }
MInt operator*(const MInt& x) const { return MInt(*this) *= x; }
MInt operator/(const MInt& x) const { return MInt(*this) /= x; }
friend std::ostream& operator<<(std::ostream& os, const MInt& x) {
return os << x.v;
}
friend std::istream& operator>>(std::istream& is, MInt& x) {
long long v;
is >> v;
x = MInt(v);
return is;
}
private:
static unsigned int& mod() {
static unsigned int divisor = 0;
return divisor;
}
};
#endif // ARBITRARY_MODINT
} // namespace emthrm
#line 12 "test/math/convolution/subset_convolution.test.cpp"
int main() {
using ModInt = emthrm::MInt<998244353>;
constexpr int kMaxN = 20;
int n;
std::cin >> n;
std::vector<ModInt> a(1 << n), b(1 << n);
for (int i = 0; i < (1 << n); ++i) {
std::cin >> a[i];
}
for (int i = 0; i < (1 << n); ++i) {
std::cin >> b[i];
}
const std::vector<ModInt> c = emthrm::subset_convolution<kMaxN>(a, b);
for (int i = 0; i < (1 << n); ++i) {
std::cout << c[i] << " \n"[i + 1 == (1 << n)];
}
return 0;
}