cp-library

C++ Library for Competitive Programming

View the Project on GitHub emthrm/cp-library

:warning: 数学/多項式
(test/math/polynomial.test.cpp)

Depends on

Code

/*
 * @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;
}
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