C++ Library for Competitive Programming
View the Project on GitHub emthrm/cp-library
/* * @title 数学/多項式 * * verification-helper: IGNORE * verification-helper: PROBLEM https://judge.yosupo.jp/problem/division_of_polynomials */ #include <iostream> #include "emthrm/math/modint.hpp" #include "emthrm/math/polynomial.hpp" int main() { using ModInt = emthrm::MInt<998244353>; int n, m; std::cin >> n >> m; emthrm::Polynomial<ModInt> f(n - 1), g(m - 1); for (int i = 0; i < n; ++i) { std::cin >> f[i]; } for (int i = 0; i < m; ++i) { std::cin >> g[i]; } auto [q, r] = f.divide(g); q.shrink(); r.shrink(); const int u = (q == emthrm::Polynomial<ModInt>{0} ? 0 : q.degree() + 1); const int v = (r == emthrm::Polynomial<ModInt>{0} ? 0 : r.degree() + 1); std::cout << u << ' ' << v << '\n'; for (int i = 0; i < u; ++i) { std::cout << q[i]; if (i + 1 < u) std::cout << ' '; } std::cout << '\n'; for (int i = 0; i < v; ++i) { std::cout << r[i]; if (i + 1 < v) std::cout << ' '; } std::cout << '\n'; return 0; }
#line 1 "test/math/polynomial.test.cpp" /* * @title 数学/多項式 * * verification-helper: IGNORE * verification-helper: PROBLEM https://judge.yosupo.jp/problem/division_of_polynomials */ #include <iostream> #line 1 "include/emthrm/math/modint.hpp" #ifndef ARBITRARY_MODINT # include <cassert> #endif #include <compare> #line 9 "include/emthrm/math/modint.hpp" // #include <numeric> #include <utility> #include <vector> 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 1 "include/emthrm/math/polynomial.hpp" #include <algorithm> #include <cassert> #include <functional> #include <initializer_list> #include <iterator> #include <numeric> #line 12 "include/emthrm/math/polynomial.hpp" namespace emthrm { template <typename T> struct Polynomial { std::vector<T> coef; explicit Polynomial(const int deg = 0) : coef(deg + 1, 0) {} explicit Polynomial(const std::vector<T>& coef) : coef(coef) {} Polynomial(const std::initializer_list<T> init) : coef(init.begin(), init.end()) {} template <typename InputIter> explicit Polynomial(const InputIter first, const InputIter last) : coef(first, last) {} inline const T& operator[](const int term) const { return coef[term]; } inline T& operator[](const int term) { return coef[term]; } using Mult = std::function<std::vector<T>(const std::vector<T>&, const std::vector<T>&)>; static void set_mult(const Mult mult) { get_mult() = mult; } void resize(const int deg) { coef.resize(deg + 1, 0); } void shrink() { while (coef.size() > 1 && coef.back() == 0) coef.pop_back(); } int degree() const { return std::ssize(coef) - 1; } Polynomial& operator=(const std::vector<T>& coef_) { coef = coef_; return *this; } Polynomial& operator=(const Polynomial& x) = default; Polynomial& operator+=(const Polynomial& x) { const int deg_x = x.degree(); if (deg_x > degree()) resize(deg_x); for (int i = 0; i <= deg_x; ++i) { coef[i] += x[i]; } return *this; } Polynomial& operator-=(const Polynomial& x) { const int deg_x = x.degree(); if (deg_x > degree()) resize(deg_x); for (int i = 0; i <= deg_x; ++i) { coef[i] -= x[i]; } return *this; } Polynomial& operator*=(const T x) { for (T& e : coef) e *= x; return *this; } Polynomial& operator*=(const Polynomial& x) { return *this = get_mult()(coef, x.coef); } Polynomial& operator/=(const T x) { assert(x != 0); return *this *= static_cast<T>(1) / x; } std::pair<Polynomial, Polynomial> divide(Polynomial x) const { x.shrink(); Polynomial rem = *this; const int n = rem.degree(), m = x.degree(), deg = n - m; if (deg < 0) return {Polynomial{0}, rem}; Polynomial quo(deg); for (int i = 0; i <= deg; ++i) { quo[deg - i] = rem[n - i] / x[m]; for (int j = 0; j <= m; ++j) { rem[n - i - j] -= x[m - j] * quo[deg - i]; } } rem.resize(deg); return {quo, rem}; } Polynomial& operator/=(const Polynomial& x) { return *this = divide(x).first; } Polynomial& operator%=(const Polynomial& x) { return *this = divide(x).second; } Polynomial& operator<<=(const int n) { coef.insert(coef.begin(), n, 0); return *this; } bool operator==(Polynomial x) const { x.shrink(); Polynomial y = *this; y.shrink(); return x.coef == y.coef; } Polynomial operator+() const { return *this; } Polynomial operator-() const { Polynomial res = *this; for (T& e : res.coef) e = -e; return res; } Polynomial operator+(const Polynomial& x) const { return Polynomial(*this) += x; } Polynomial operator-(const Polynomial& x) const { return Polynomial(*this) -= x; } Polynomial operator*(const T x) const { return Polynomial(*this) *= x; } Polynomial operator*(const Polynomial& x) const { return Polynomial(*this) *= x; } Polynomial operator/(const T x) const { return Polynomial(*this) /= x; } Polynomial operator/(const Polynomial& x) const { return Polynomial(*this) /= x; } Polynomial operator%(const Polynomial& x) const { return Polynomial(*this) %= x; } Polynomial operator<<(const int n) const { return Polynomial(*this) <<= n; } T horner(const T x) const { return std::accumulate( coef.rbegin(), coef.rend(), static_cast<T>(0), [x](const T l, const T r) -> T { return l * x + r; }); } Polynomial differential() const { const int deg = degree(); assert(deg >= 0); Polynomial res(std::max(deg - 1, 0)); for (int i = 1; i <= deg; ++i) { res[i - 1] = coef[i] * i; } return res; } Polynomial pow(int exponent) const { Polynomial res{1}, base = *this; for (; exponent > 0; exponent >>= 1) { if (exponent & 1) res *= base; base *= base; } return res; } Polynomial translate(const T c) const { const int n = coef.size(); std::vector<T> fact(n, 1), inv_fact(n, 1); for (int i = 1; i < n; ++i) { fact[i] = fact[i - 1] * i; } inv_fact[n - 1] = static_cast<T>(1) / fact[n - 1]; for (int i = n - 1; i > 0; --i) { inv_fact[i - 1] = inv_fact[i] * i; } std::vector<T> g(n), ex(n); for (int i = 0; i < n; ++i) { g[i] = coef[i] * fact[i]; } std::reverse(g.begin(), g.end()); T pow_c = 1; for (int i = 0; i < n; ++i) { ex[i] = pow_c * inv_fact[i]; pow_c *= c; } const std::vector<T> conv = get_mult()(g, ex); Polynomial res(n - 1); for (int i = 0; i < n; ++i) { res[i] = conv[n - 1 - i] * inv_fact[i]; } return res; } private: static Mult& get_mult() { static Mult mult = [](const std::vector<T>& a, const std::vector<T>& b) -> std::vector<T> { const int n = a.size(), m = b.size(); std::vector<T> res(n + m - 1, 0); for (int i = 0; i < n; ++i) { for (int j = 0; j < m; ++j) { res[i + j] += a[i] * b[j]; } } return res; }; return mult; } }; } // namespace emthrm #line 12 "test/math/polynomial.test.cpp" int main() { using ModInt = emthrm::MInt<998244353>; int n, m; std::cin >> n >> m; emthrm::Polynomial<ModInt> f(n - 1), g(m - 1); for (int i = 0; i < n; ++i) { std::cin >> f[i]; } for (int i = 0; i < m; ++i) { std::cin >> g[i]; } auto [q, r] = f.divide(g); q.shrink(); r.shrink(); const int u = (q == emthrm::Polynomial<ModInt>{0} ? 0 : q.degree() + 1); const int v = (r == emthrm::Polynomial<ModInt>{0} ? 0 : r.degree() + 1); std::cout << u << ' ' << v << '\n'; for (int i = 0; i < u; ++i) { std::cout << q[i]; if (i + 1 < u) std::cout << ' '; } std::cout << '\n'; for (int i = 0; i < v; ++i) { std::cout << r[i]; if (i + 1 < v) std::cout << ' '; } std::cout << '\n'; return 0; }