結果

問題 No.931 Multiplicative Convolution
ユーザー risujirohrisujiroh
提出日時 2019-10-02 04:11:25
言語 C++14
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 84 ms / 2,000 ms
コード長 4,754 bytes
コンパイル時間 1,877 ms
コンパイル使用メモリ 183,300 KB
実行使用メモリ 7,316 KB
最終ジャッジ日時 2024-10-11 02:39:28
合計ジャッジ時間 4,632 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge3
このコードへのチャレンジ
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 2 ms
6,816 KB
testcase_01 AC 2 ms
6,816 KB
testcase_02 AC 2 ms
6,816 KB
testcase_03 AC 2 ms
6,816 KB
testcase_04 AC 2 ms
6,816 KB
testcase_05 AC 2 ms
6,820 KB
testcase_06 AC 3 ms
6,816 KB
testcase_07 AC 10 ms
6,816 KB
testcase_08 AC 84 ms
7,316 KB
testcase_09 AC 71 ms
7,228 KB
testcase_10 AC 81 ms
7,192 KB
testcase_11 AC 71 ms
7,132 KB
testcase_12 AC 48 ms
6,820 KB
testcase_13 AC 82 ms
7,104 KB
testcase_14 AC 84 ms
7,316 KB
testcase_15 AC 84 ms
7,312 KB
testcase_16 AC 82 ms
7,108 KB
権限があれば一括ダウンロードができます
コンパイルメッセージ
main.cpp:11:20: warning: use of 'auto' in parameter declaration only available with '-std=c++20' or '-fconcepts'
   11 |   constexpr ModInt(auto x) : v(x >= 0 ? x % P : (P - -x % P) % P) {}
      |                    ^~~~
main.cpp:38:9: warning: use of 'auto' in parameter declaration only available with '-std=c++20' or '-fconcepts'
   38 |   M pow(auto n) const {
      |         ^~~~
main.cpp:44:22: warning: use of 'auto' in parameter declaration only available with '-std=c++20' or '-fconcepts'
   44 |   friend M operator*(auto l, M r) { return M(l) *= r; }
      |                      ^~~~
main.cpp:45:22: warning: use of 'auto' in parameter declaration only available with '-std=c++20' or '-fconcepts'
   45 |   friend M operator/(auto l, M r) { return M(l) /= r; }
      |                      ^~~~
main.cpp:46:22: warning: use of 'auto' in parameter declaration only available with '-std=c++20' or '-fconcepts'
   46 |   friend M operator+(auto l, M r) { return M(l) += r; }
      |                      ^~~~
main.cpp:47:22: warning: use of 'auto' in parameter declaration only available with '-std=c++20' or '-fconcepts'
   47 |   friend M operator-(auto l, M r) { return M(l) -= r; }
      |                      ^~~~
main.cpp:50:26: warning: use of 'auto' in parameter declaration only available with '-std=c++20' or '-fconcepts'
   50 |   friend bool operator==(auto l, M r) { return M(l) == r; }
      |                          ^~~~
main.cpp:51:26: warning: use of 'auto' in parameter declaration only available with '-std=c++20' or '-fconcepts'
   51 |   friend bool operator!=(auto l, M r) { return !(l == r); }
      |                          ^~~~

ソースコード

diff # 

#include <bits/stdc++.h>
using namespace std;
using lint = long long;
template<class T = int> using V = vector<T>;
template<class T = int> using VV = V< V<T> >;

template<unsigned P> struct ModInt {
  using M = ModInt;
  unsigned v;
  constexpr ModInt() : v(0) {}
  constexpr ModInt(auto x) : v(x >= 0 ? x % P : (P - -x % P) % P) {}
  constexpr ModInt(unsigned _v, int) : v(_v) {}
  static constexpr unsigned p() { return P; }
  M operator+() const { return *this; }
  M operator-() const { return {v ? P - v : 0, 0}; }
  explicit operator bool() const noexcept { return v; }
  bool operator!() const noexcept { return !(bool)*this; }
  M operator*(M r) const { return M(*this) *= r; }
  M operator/(M r) const { return M(*this) /= r; }
  M operator+(M r) const { return M(*this) += r; }
  M operator-(M r) const { return M(*this) -= r; }
  bool operator==(M r) const { return v == r.v; }
  bool operator!=(M r) const { return !(*this == r); }
  M& operator*=(M r) { v = (uint64_t)v * r.v % P; return *this; }
  M& operator/=(M r) { return *this *= r.inv(); }
  M& operator+=(M r) { if ((v += r.v) >= P) v -= P; return *this; }
  M& operator-=(M r) { if ((v += P - r.v) >= P) v -= P; return *this; }
  M inv() const {
    int a = v, b = P, x = 1, u = 0;
    while (b) {
      int q = a / b;
      swap(a -= q * b, b);
      swap(x -= q * u, u);
    }
    assert(a == 1);
    return x;
  }
  M pow(auto n) const {
    if (n < 0) return pow(-n).inv();
    M res = 1;
    for (M a = *this; n; a *= a, n >>= 1) if (n & 1) res *= a;
    return res;
  }
  friend M operator*(auto l, M r) { return M(l) *= r; }
  friend M operator/(auto l, M r) { return M(l) /= r; }
  friend M operator+(auto l, M r) { return M(l) += r; }
  friend M operator-(auto l, M r) { return M(l) -= r; }
  friend ostream& operator<<(ostream& os, M r) { return os << r.v; }
  friend istream& operator>>(istream& is, M& r) { lint x; is >> x; r = x; return is; }
  friend bool operator==(auto l, M r) { return M(l) == r; }
  friend bool operator!=(auto l, M r) { return !(l == r); }
};
using Mint = ModInt<998244353>;

template<unsigned P, unsigned g> void ntt(V< ModInt<P> >& a, bool inv = false) {
  int n = a.size();
  assert(__builtin_popcount(n) == 1);
  int j = 0;
  for (int i = 1; i < n; ++i) {
    int w = n >> 1;
    while (j >= w) j -= w, w >>= 1;
    j += w;
    if (i < j) swap(a[i], a[j]);
  }
  assert((P - 1) % n == 0);
  auto xi = ModInt<P>(g).pow((P - 1) / n);
  if (inv) xi = xi.inv();
  for (int k = 0; 1 << k < n; ++k) {
    const int w = 1 << k;
    const auto dt = xi.pow(n >> k + 1);
    for (int s = 0; s < n; s += 2 * w) {
      ModInt<P> t = 1;
      for (int i = s; i < s + w; ++i) {
        auto p = a[i], q = a[i + w] * t;
        a[i] = p + q, a[i + w] = p - q;
        t *= dt;
      }
    }
  }
}
template<unsigned P, unsigned g = 6420> V< ModInt<P> > multiply(const V< ModInt<P> >& a, const V< ModInt<P> >& b) {
  if (a.empty() or b.empty()) return {};
  int sz = a.size() + b.size() - 1, n = 1 << __lg(2 * sz - 1);
  auto _a = a, _b = b;
  _a.resize(n), _b.resize(n);
  ntt<P, g>(_a), ntt<P, g>(_b);
  for (int i = 0; i < n; ++i) _a[i] *= _b[i];
  ntt<P, g>(_a, true);
  _a.resize(sz);
  const auto inv_n = ModInt<P>(n).inv();
  for (auto&& e : _a) e *= inv_n;
  return _a;
}

lint tmod(lint a, lint p) { return (a %= p) < 0 ? a + p : a; }
lint mod_pow(lint a, lint n, lint p) {
  assert(n >= 0);
  a = tmod(a, p);
  lint res = 1;
  while (n) {
    if (n & 1) (res *= a) %= p;
    (a *= a) %= p;
    n >>= 1;
  }
  return res;
}

template<class Z> map<Z, int> factorize(Z n) {
  map<Z, int> res;
  for (Z i = 2; i * i <= n; ++i) while (n % i == 0) ++res[i], n /= i;
  if (n != 1) ++res[n];
  return res;
}
template<class Z> Z rng(Z a, Z b) {
  static mt19937 mt(chrono::steady_clock::now().time_since_epoch().count());
  return uniform_int_distribution<Z>(a, b - 1)(mt);
}
lint primitive_root(lint p) {
  auto mp = factorize(p - 1);
  while (true) {
    lint g = rng(1LL, p);
    bool ok = true;
    for (const auto& e : mp) {
      if (mod_pow(g, (p - 1) / e.first, p) == 1) {
        ok = false;
        break;
      }
    }
    if (!ok) continue;
    return g;
  }
}

int main() {
  cin.tie(nullptr); ios::sync_with_stdio(false);
  lint p; cin >> p;
  V<Mint> a(p), b(p);
  for (int i = 1; i < p; ++i) cin >> a[i];
  for (int i = 1; i < p; ++i) cin >> b[i];

  lint g = primitive_root(p);
  V<Mint> na(p - 1), nb(p - 1);
  lint t = 1;
  for (int i = 0; i < p - 1; ++i) {
    na[i] = a[t];
    nb[i] = b[t];
    (t *= g) %= p;
  }
  
  auto nc = multiply(na, nb);
  V<Mint> c(p);
  t = 1;
  for (int i = 0; i < (int)nc.size(); ++i) {
    c[t] += nc[i];
    (t *= g) %= p;
  }
  for (int i = 1; i < p; ++i) {
    cout << c[i] << " \n"[i == p - 1];
  }
}
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