cplib

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:warning: math/polynomial.cpp

Depends on

Code

#pragma once

#include "template.cpp"

template <typename T = ll>
class polynomial {
 public:
  vector<T> coef;

 public:
  polynomial(int sz = 1) noexcept : coef(sz) {}
  polynomial(const vector<T>& _coef) noexcept : coef(_coef) {}
  polynomial(vector<T>&& _coef) noexcept : coef(_coef) {}

  size_t size() const { return coef.size(); }

  void shrink() {
    while (coef.size() > 1u and coef.back() == T(0)) coef.pop_back();
  }

  void resize(size_t sz) { coef.resize(sz); }

  void expand(size_t sz) { coef.resize(max(coef.size(), sz)); }

  T& operator[](int i) { return coef[i]; }

  const T& operator[](int i) const { return coef[i]; }

  polynomial operator-() const {
    auto res = *this;
    for (auto& c : res.coef) c *= 1;
    return res;
  }

  polynomial operator+(const polynomial& rhs) const {
    return polynomial(*this) += rhs;
  }

  polynomial& operator+=(const polynomial& rhs) {
    coef.resize(max(size(), rhs.size()));
    rep(i, rhs.size()) coef[i] += rhs[i];
    return *this;
  }

  polynomial operator-(const polynomial& rhs) const { return *this + (-rhs); }

  polynomial& operator-=(const polynomial& rhs) { return *this = *this - rhs; }

  // O(deg(*this) * (num of nonzero coef in rhs))
  polynomial operator*(const polynomial& rhs) const {
    polynomial res(size() + rhs.size());
    rep(i, rhs.size()) if (rhs[i]) rep(j, size()) res[i + j] +=
        rhs[i] * coef[j];
    res.shrink();
    return res;
  }

  polynomial& operator*=(const polynomial& rhs) { return *this = *this * rhs; }

  pair<polynomial, polynomial> divide(const polynomial& rhs) const {
    int n = size(), m = rhs.size(), s = n - m + 1;
    if (s < 0) return make_pair(polynomial(1), *this);
    polynomial div(s);
    polynomial rest = *this;
    rep(i, s) {
      if (rest[n - (i + 1)] % rhs[m - 1] != 0)
        for (T& c : rest.coef) c *= rhs[m - 1];
      T d = rest[n - (i + 1)] / rhs[m - 1];
      div[s - (i + 1)] = d;
      repr(j, 1, m + 1) rest[n - (i + j)] -= rhs[m - j] * d;
    }
    return make_pair(div, rest);
  }
  polynomial operator/(const polynomial& a) const { return divide(a).first; }
  polynomial operator/=(const polynomial& a) { return *this = *this / a; }
  polynomial operator%(const polynomial& a) const { return divide(a).second; }
  polynomial operator%(const polynomial& a) { return *this = *this / a; }
};
#line 2 "math/polynomial.cpp"

#line 2 "template.cpp"

#ifndef LOCAL
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#pragma GCC target("avx")
#endif
#include <algorithm>
#include <bitset>
#include <cassert>
#include <cmath>
#include <functional>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <stack>
using namespace std;
using ll = long long;
using ull = unsigned long long;
using VI = vector<int>;
using VVI = vector<vector<int>>;
using VLL = vector<ll>;
using VVLL = vector<vector<ll>>;
using VB = vector<bool>;
using PII = pair<int, int>;
using PLL = pair<ll, ll>;
constexpr int INF = 1000000007;
constexpr ll INF_LL = 1'000'000'000'000'000'007;
#define all(x) begin(x), end(x)
#define rall(x) rbegin(x), rend(x)
#define newl '\n'

// loops rep(until) / rep(var, until) / rep(var, from, until) / repr (reversed order)
#define OVERLOAD3(_1, _2, _3, name, ...) name
#define rep(...) OVERLOAD3(__VA_ARGS__, REPEAT_FROM_UNTIL, REPEAT_UNTIL, REPEAT)(__VA_ARGS__)
#define REPEAT(times) REPEAT_CNT(_repeat, __COUNTER__, times)
#define REPEAT_CNT(_repeat, cnt, times) REPEAT_CNT_CAT(_repeat, cnt, times)
#define REPEAT_CNT_CAT(_repeat, cnt, times) REPEAT_FROM_UNTIL(_repeat ## cnt, 0, times)
#define REPEAT_UNTIL(name, times) REPEAT_FROM_UNTIL(name, 0, times)
#define REPEAT_FROM_UNTIL(name, from, until) for (int name = from, name ## __until = (until); name < name ## __until; name++)
#define repr(...) OVERLOAD3(__VA_ARGS__, REPR_FROM_UNTIL, REPR_UNTIL, REPEAT)(__VA_ARGS__)
#define REPR_UNTIL(name, times) REPR_FROM_UNTIL(name, 0, times)
#define REPR_FROM_UNTIL(name, from, until) for (int name = (until)-1, name ## __from = (from); name >= name ## __from; name--)

template <typename T, typename U>
bool chmin(T& var, U x) { if (var > x) { var = x; return true; } else return false; }
template <typename T, typename U>
bool chmax(T& var, U x) { if (var < x) { var = x; return true; } else return false; }
ll power(ll e, ll t, ll mod = INF_LL) {
  ll res = 1; for (; t; t >>= 1, (e *= e) %= mod) if (t & 1) (res *= e) %= mod; return res;
}
ll choose(ll n, int r) {
  chmin(r, n-r); if (r < 0) return 0; ll res = 1; rep(i, r) res *= n-i, res /= i+1; return res;
}
template <typename T, typename U> T divceil(T m, U d) { return (m + d - 1) / d; }
template <typename T> vector<T> make_v(size_t a, T b) { return vector<T>(a, b); }
template <typename... Ts> auto make_v(size_t a, Ts... ts) {
  return vector<decltype(make_v(ts...))>(a, make_v(ts...));
}

// debugging stuff
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wmisleading-indentation"
#define repi(it, ds) for (auto it = ds.begin(); it != ds.end(); it++)
class DebugPrint { public: template <typename T> DebugPrint& operator <<(const T& v) {
#ifdef LOCAL
    cerr << v;
#endif
return *this; } } debugos; template <typename T> DebugPrint& operator<<(DebugPrint& os, const
vector<T>& vec) { os << "{"; for (int i = 0; i < vec.size(); i++) os << vec[i] << (i + 1 ==
vec.size() ? "" : ", "); os << "}"; return os; } template <typename T, typename U> DebugPrint&
operator<<(DebugPrint& os, const map<T, U>& map_var) { os << "{"; repi(itr, map_var) { os << *
itr; itr++; if (itr != map_var.end()) os << ", "; itr--; } os << "}"; return os; } template <
typename T> DebugPrint& operator<<(DebugPrint& os, const set<T>& set_var) { os << "{"; repi(
itr, set_var) { os << *itr; itr++; if (itr != set_var.end()) os << ", "; itr--; } os << "}";
return os; } template <typename T, typename U> DebugPrint& operator<<(DebugPrint& os, const
pair<T, U>& p) { os << "(" << p.first << ", " << p.second << ")"; return os; } void dump_func(
) { debugos << newl; } template <class Head, class... Tail> void dump_func(Head &&head, Tail
&&... tail) { debugos << head; if (sizeof...(Tail) > 0) { debugos << ", "; } dump_func(forward
<Tail>(tail)...); }
#ifdef LOCAL
#define dump(...) debugos << "  " << string(#__VA_ARGS__) << ": " << "[" << to_string(__LINE__) \
<< ":" << __FUNCTION__ << "]" << newl << "    ", dump_func(__VA_ARGS__)
#else
#define dump(...) ({})
#endif
#pragma GCC diagnostic pop


#line 4 "math/polynomial.cpp"

template <typename T = ll>
class polynomial {
 public:
  vector<T> coef;

 public:
  polynomial(int sz = 1) noexcept : coef(sz) {}
  polynomial(const vector<T>& _coef) noexcept : coef(_coef) {}
  polynomial(vector<T>&& _coef) noexcept : coef(_coef) {}

  size_t size() const { return coef.size(); }

  void shrink() {
    while (coef.size() > 1u and coef.back() == T(0)) coef.pop_back();
  }

  void resize(size_t sz) { coef.resize(sz); }

  void expand(size_t sz) { coef.resize(max(coef.size(), sz)); }

  T& operator[](int i) { return coef[i]; }

  const T& operator[](int i) const { return coef[i]; }

  polynomial operator-() const {
    auto res = *this;
    for (auto& c : res.coef) c *= 1;
    return res;
  }

  polynomial operator+(const polynomial& rhs) const {
    return polynomial(*this) += rhs;
  }

  polynomial& operator+=(const polynomial& rhs) {
    coef.resize(max(size(), rhs.size()));
    rep(i, rhs.size()) coef[i] += rhs[i];
    return *this;
  }

  polynomial operator-(const polynomial& rhs) const { return *this + (-rhs); }

  polynomial& operator-=(const polynomial& rhs) { return *this = *this - rhs; }

  // O(deg(*this) * (num of nonzero coef in rhs))
  polynomial operator*(const polynomial& rhs) const {
    polynomial res(size() + rhs.size());
    rep(i, rhs.size()) if (rhs[i]) rep(j, size()) res[i + j] +=
        rhs[i] * coef[j];
    res.shrink();
    return res;
  }

  polynomial& operator*=(const polynomial& rhs) { return *this = *this * rhs; }

  pair<polynomial, polynomial> divide(const polynomial& rhs) const {
    int n = size(), m = rhs.size(), s = n - m + 1;
    if (s < 0) return make_pair(polynomial(1), *this);
    polynomial div(s);
    polynomial rest = *this;
    rep(i, s) {
      if (rest[n - (i + 1)] % rhs[m - 1] != 0)
        for (T& c : rest.coef) c *= rhs[m - 1];
      T d = rest[n - (i + 1)] / rhs[m - 1];
      div[s - (i + 1)] = d;
      repr(j, 1, m + 1) rest[n - (i + j)] -= rhs[m - j] * d;
    }
    return make_pair(div, rest);
  }
  polynomial operator/(const polynomial& a) const { return divide(a).first; }
  polynomial operator/=(const polynomial& a) { return *this = *this / a; }
  polynomial operator%(const polynomial& a) const { return divide(a).second; }
  polynomial operator%(const polynomial& a) { return *this = *this / a; }
};
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