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#include "math/set/set_power_series.hpp"
#pragma once #include <algorithm> #include <array> #include <cassert> #include <vector> #include "subset_convolution.hpp" /** * @brief Set Power Series */ template <typename mint, int N> class SetPowerSeries : public std::vector<mint> { using SPS = SetPowerSeries<mint, N>; using Poly = std::array<mint, N + 1>; public: using std::vector<mint>::vector; using std::vector<mint>::operator=; // -- binary operation with scalar --- SPS& operator+=(const mint& rhs) { if (this->empty()) this->resize(1); (*this)[0] += rhs; return *this; } SPS& operator-=(const mint& rhs) { if (this->empty()) this->resize(1); (*this)[0] -= rhs; return *this; } SPS& operator*=(const mint& rhs) { for (auto& x : *this) x *= rhs; return *this; } SPS& operator/=(const mint& rhs) { return *this *= rhs.inv(); } SPS operator+(const mint& rhs) const { return SPS(*this) += rhs; } SPS operator-(const mint& rhs) const { return SPS(*this) -= rhs; } SPS operator*(const mint& rhs) const { return SPS(*this) *= rhs; } SPS operator/(const mint& rhs) const { return SPS(*this) /= rhs; } // --- binary operation with SPS --- SPS& operator+=(const SPS& rhs) { if (this->size() < rhs.size()) this->resize(rhs.size()); for (int i = 0; i < (int)rhs.size(); ++i) (*this)[i] += rhs[i]; return *this; } SPS& operator-=(const SPS& rhs) { if (this->size() < rhs.size()) this->resize(rhs.size()); for (int i = 0; i < (int)rhs.size(); ++i) (*this)[i] -= rhs[i]; return *this; } SPS& operator*=(const SPS& rhs) { *this = subset_convolution<mint, N>(*this, rhs); return *this; } SPS operator+(const SPS& rhs) const { return SPS(*this) += rhs; } SPS operator-(const SPS& rhs) const { return SPS(*this) -= rhs; } SPS operator*(const SPS& rhs) const { return SPS(*this) *= rhs; } // --- compositions --- SPS exp() const { assert((*this)[0] == mint(0)); const int n = std::bit_width(std::bit_ceil(this->size())) - 1; SPS res(1 << n); res[0] = 1; for (int i = 0; i < n; ++i) { SPS a(this->begin() + (1 << i), this->begin() + (1 << (i + 1))); SPS b(res.begin(), res.begin() + (1 << i)); a *= b; std::copy(a.begin(), a.end(), res.begin() + (1 << i)); } return res; } };
#line 2 "math/set/set_power_series.hpp" #include <algorithm> #include <array> #include <cassert> #include <vector> #line 4 "math/set/subset_convolution.hpp" #line 2 "math/set/zeta_moebius_transform.hpp" #include <bit> #line 5 "math/set/zeta_moebius_transform.hpp" template <typename T> void superset_fzt(std::vector<T>& a) { assert(std::has_single_bit(a.size())); const int n = a.size(); for (int i = 1; i < n; i <<= 1) { for (int j = 0; j < n; ++j) { if (!(j & i)) a[j] += a[j | i]; } } } template <typename T> void superset_fmt(std::vector<T>& a) { assert(std::has_single_bit(a.size())); const int n = a.size(); for (int i = 1; i < n; i <<= 1) { for (int j = 0; j < n; ++j) { if (!(j & i)) a[j] -= a[j | i]; } } } template <typename T> void subset_fzt(std::vector<T>& a) { assert(std::has_single_bit(a.size())); const int n = a.size(); for (int i = 1; i < n; i <<= 1) { for (int j = 0; j < n; ++j) { if (!(j & i)) a[j | i] += a[j]; } } } template <typename T> void subset_fmt(std::vector<T>& a) { assert(std::has_single_bit(a.size())); const int n = a.size(); for (int i = 1; i < n; i <<= 1) { for (int j = 0; j < n; ++j) { if (!(j & i)) a[j | i] -= a[j]; } } } #line 6 "math/set/subset_convolution.hpp" template <typename T, std::size_t N> std::array<T, N>& operator+=(std::array<T, N>& lhs, const std::array<T, N>& rhs) { for (int i = 0; i < (int)N; ++i) lhs[i] += rhs[i]; return lhs; } template <typename T, std::size_t N> std::array<T, N>& operator-=(std::array<T, N>& lhs, const std::array<T, N>& rhs) { for (int i = 0; i < (int)N; ++i) lhs[i] -= rhs[i]; return lhs; } template <typename T, int N> std::vector<T> subset_convolution(const std::vector<T>& a, const std::vector<T>& b) { using Poly = std::array<T, N + 1>; const int n = std::bit_ceil(std::max(a.size(), b.size())); // convert to polynomials std::vector<Poly> pa(n), pb(n); for (int i = 0; i < (int)a.size(); ++i) { pa[i][std::popcount((unsigned int)i)] = a[i]; } for (int i = 0; i < (int)b.size(); ++i) { pb[i][std::popcount((unsigned int)i)] = b[i]; } // bitwise or convolution subset_fzt(pa); subset_fzt(pb); for (int i = 0; i < n; ++i) { Poly pc; for (int j = 0; j <= N; ++j) { for (int k = 0; k <= N - j; ++k) { pc[j + k] += pa[i][j] * pb[i][k]; } } pa[i].swap(pc); } subset_fmt(pa); // convert back std::vector<T> ret(n); for (int i = 0; i < n; ++i) { ret[i] = pa[i][std::popcount((unsigned int)i)]; } return ret; } #line 8 "math/set/set_power_series.hpp" /** * @brief Set Power Series */ template <typename mint, int N> class SetPowerSeries : public std::vector<mint> { using SPS = SetPowerSeries<mint, N>; using Poly = std::array<mint, N + 1>; public: using std::vector<mint>::vector; using std::vector<mint>::operator=; // -- binary operation with scalar --- SPS& operator+=(const mint& rhs) { if (this->empty()) this->resize(1); (*this)[0] += rhs; return *this; } SPS& operator-=(const mint& rhs) { if (this->empty()) this->resize(1); (*this)[0] -= rhs; return *this; } SPS& operator*=(const mint& rhs) { for (auto& x : *this) x *= rhs; return *this; } SPS& operator/=(const mint& rhs) { return *this *= rhs.inv(); } SPS operator+(const mint& rhs) const { return SPS(*this) += rhs; } SPS operator-(const mint& rhs) const { return SPS(*this) -= rhs; } SPS operator*(const mint& rhs) const { return SPS(*this) *= rhs; } SPS operator/(const mint& rhs) const { return SPS(*this) /= rhs; } // --- binary operation with SPS --- SPS& operator+=(const SPS& rhs) { if (this->size() < rhs.size()) this->resize(rhs.size()); for (int i = 0; i < (int)rhs.size(); ++i) (*this)[i] += rhs[i]; return *this; } SPS& operator-=(const SPS& rhs) { if (this->size() < rhs.size()) this->resize(rhs.size()); for (int i = 0; i < (int)rhs.size(); ++i) (*this)[i] -= rhs[i]; return *this; } SPS& operator*=(const SPS& rhs) { *this = subset_convolution<mint, N>(*this, rhs); return *this; } SPS operator+(const SPS& rhs) const { return SPS(*this) += rhs; } SPS operator-(const SPS& rhs) const { return SPS(*this) -= rhs; } SPS operator*(const SPS& rhs) const { return SPS(*this) *= rhs; } // --- compositions --- SPS exp() const { assert((*this)[0] == mint(0)); const int n = std::bit_width(std::bit_ceil(this->size())) - 1; SPS res(1 << n); res[0] = 1; for (int i = 0; i < n; ++i) { SPS a(this->begin() + (1 << i), this->begin() + (1 << (i + 1))); SPS b(res.begin(), res.begin() + (1 << i)); a *= b; std::copy(a.begin(), a.end(), res.begin() + (1 << i)); } return res; } };