C++ Library for Competitive Programming
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/* * @title 数学/畳み込み/集合冪級数の指数 * * verification-helper: PROBLEM https://judge.yosupo.jp/problem/exp_of_set_power_series */ #include <iostream> #include <vector> #include "emthrm/math/convolution/exp_of_set_power_series.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> b(1 << n); for (int i = 0; i < (1 << n); ++i) { std::cin >> b[i]; } const std::vector<ModInt> c = emthrm::exp_of_set_power_series<kMaxN>(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/exp_of_set_power_series.test.cpp" /* * @title 数学/畳み込み/集合冪級数の指数 * * verification-helper: PROBLEM https://judge.yosupo.jp/problem/exp_of_set_power_series */ #include <iostream> #include <vector> #line 1 "include/emthrm/math/convolution/exp_of_set_power_series.hpp" #include <algorithm> #include <bit> #include <cassert> #include <iterator> #line 9 "include/emthrm/math/convolution/exp_of_set_power_series.hpp" #line 1 "include/emthrm/math/convolution/subset_convolution.hpp" #include <array> #line 7 "include/emthrm/math/convolution/subset_convolution.hpp" #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 11 "include/emthrm/math/convolution/exp_of_set_power_series.hpp" namespace emthrm { template <int MaxN, typename T> std::vector<T> exp_of_set_power_series(const std::vector<T>& f) { assert(std::has_single_bit(f.size()) && f[0] == 0); const int n = std::countr_zero(f.size()); assert(n <= MaxN); std::vector<T> exponential{1}; exponential.reserve(1 << n); for (int i = 0; i < n; ++i) { std::ranges::copy(subset_convolution<MaxN>( exponential, std::vector(std::next(f.begin(), 1 << i), std::next(f.begin(), 1 << (i + 1)))), std::back_inserter(exponential)); } return exponential; } } // 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/exp_of_set_power_series.test.cpp" int main() { using ModInt = emthrm::MInt<998244353>; constexpr int kMaxN = 20; int n; std::cin >> n; std::vector<ModInt> b(1 << n); for (int i = 0; i < (1 << n); ++i) { std::cin >> b[i]; } const std::vector<ModInt> c = emthrm::exp_of_set_power_series<kMaxN>(b); for (int i = 0; i < (1 << n); ++i) { std::cout << c[i] << " \n"[i + 1 == (1 << n)]; } return 0; }