結果

問題 No.931 Multiplicative Convolution
ユーザー ei1333333ei1333333
提出日時 2019-11-23 00:18:11
言語 C++17
(gcc 13.2.0 + boost 1.83.0)
結果
AC  
実行時間 65 ms / 2,000 ms
コード長 7,283 bytes
コンパイル時間 2,564 ms
コンパイル使用メモリ 215,844 KB
実行使用メモリ 9,364 KB
最終ジャッジ日時 2024-04-19 14:07:10
合計ジャッジ時間 4,161 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge2
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
5,248 KB
testcase_01 AC 2 ms
5,376 KB
testcase_02 AC 2 ms
5,376 KB
testcase_03 AC 1 ms
5,376 KB
testcase_04 AC 2 ms
5,376 KB
testcase_05 AC 2 ms
5,376 KB
testcase_06 AC 2 ms
5,376 KB
testcase_07 AC 9 ms
5,376 KB
testcase_08 AC 65 ms
9,236 KB
testcase_09 AC 49 ms
9,288 KB
testcase_10 AC 62 ms
9,248 KB
testcase_11 AC 50 ms
9,312 KB
testcase_12 AC 38 ms
6,532 KB
testcase_13 AC 64 ms
9,160 KB
testcase_14 AC 65 ms
9,360 KB
testcase_15 AC 65 ms
9,364 KB
testcase_16 AC 63 ms
9,152 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

#include <bits/stdc++.h>

using namespace std;


using int64 = long long;
const int mod = 998244353;

const int64 infll = (1LL << 62) - 1;
const int inf = (1 << 30) - 1;

struct IoSetup {
  IoSetup() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
    cerr << fixed << setprecision(10);
  }
} iosetup;


template< typename T1, typename T2 >
ostream &operator<<(ostream &os, const pair< T1, T2 > &p) {
  os << p.first << " " << p.second;
  return os;
}

template< typename T1, typename T2 >
istream &operator>>(istream &is, pair< T1, T2 > &p) {
  is >> p.first >> p.second;
  return is;
}

template< typename T >
ostream &operator<<(ostream &os, const vector< T > &v) {
  for(int i = 0; i < (int) v.size(); i++) {
    os << v[i] << (i + 1 != v.size() ? " " : "");
  }
  return os;
}

template< typename T >
istream &operator>>(istream &is, vector< T > &v) {
  for(T &in : v) is >> in;
  return is;
}

template< typename T1, typename T2 >
inline bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); }

template< typename T1, typename T2 >
inline bool chmin(T1 &a, T2 b) { return a > b && (a = b, true); }

template< typename T = int64 >
vector< T > make_v(size_t a) {
  return vector< T >(a);
}

template< typename T, typename... Ts >
auto make_v(size_t a, Ts... ts) {
  return vector< decltype(make_v< T >(ts...)) >(a, make_v< T >(ts...));
}

template< typename T, typename V >
typename enable_if< is_class< T >::value == 0 >::type fill_v(T &t, const V &v) {
  t = v;
}

template< typename T, typename V >
typename enable_if< is_class< T >::value != 0 >::type fill_v(T &t, const V &v) {
  for(auto &e : t) fill_v(e, v);
}

template< typename F >
struct FixPoint : F {
  FixPoint(F &&f) : F(forward< F >(f)) {}

  template< typename... Args >
  decltype(auto) operator()(Args &&... args) const {
    return F::operator()(*this, forward< Args >(args)...);
  }
};

template< typename F >
inline decltype(auto) MFP(F &&f) {
  return FixPoint< F >{forward< F >(f)};
}

template< typename Mint >
struct NumberTheoreticTransformFriendlyModInt {

  vector< int > rev;
  vector< Mint > rts;
  int base, max_base;
  Mint root;

  NumberTheoreticTransformFriendlyModInt() : base(1), rev{0, 1}, rts{0, 1} {
    const int mod = Mint::get_mod();
    assert(mod >= 3 && mod % 2 == 1);
    auto tmp = mod - 1;
    max_base = 0;
    while(tmp % 2 == 0) tmp >>= 1, max_base++;
    root = 2;
    while(root.pow((mod - 1) >> 1) == 1) root += 1;
    assert(root.pow(mod - 1) == 1);
    root = root.pow((mod - 1) >> max_base);
  }

  void ensure_base(int nbase) {
    if(nbase <= base) return;
    rev.resize(1 << nbase);
    rts.resize(1 << nbase);
    for(int i = 0; i < (1 << nbase); i++) {
      rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1));
    }
    assert(nbase <= max_base);
    while(base < nbase) {
      Mint z = root.pow(1 << (max_base - 1 - base));
      for(int i = 1 << (base - 1); i < (1 << base); i++) {
        rts[i << 1] = rts[i];
        rts[(i << 1) + 1] = rts[i] * z;
      }
      ++base;
    }
  }


  void ntt(vector< Mint > &a) {
    const int n = (int) a.size();
    assert((n & (n - 1)) == 0);
    int zeros = __builtin_ctz(n);
    ensure_base(zeros);
    int shift = base - zeros;
    for(int i = 0; i < n; i++) {
      if(i < (rev[i] >> shift)) {
        swap(a[i], a[rev[i] >> shift]);
      }
    }
    for(int k = 1; k < n; k <<= 1) {
      for(int i = 0; i < n; i += 2 * k) {
        for(int j = 0; j < k; j++) {
          Mint z = a[i + j + k] * rts[j + k];
          a[i + j + k] = a[i + j] - z;
          a[i + j] = a[i + j] + z;
        }
      }
    }
  }


  void intt(vector< Mint > &a) {
    const int n = (int) a.size();
    ntt(a);
    reverse(a.begin() + 1, a.end());
    Mint inv_sz = Mint(1) / n;
    for(int i = 0; i < n; i++) a[i] *= inv_sz;
  }

  vector< Mint > multiply(vector< Mint > a, vector< Mint > b) {
    int need = a.size() + b.size() - 1;
    int nbase = 1;
    while((1 << nbase) < need) nbase++;
    ensure_base(nbase);
    int sz = 1 << nbase;
    a.resize(sz, 0);
    b.resize(sz, 0);
    ntt(a);
    ntt(b);
    Mint inv_sz = Mint(1) / sz;
    for(int i = 0; i < sz; i++) {
      a[i] *= b[i] * inv_sz;
    }
    reverse(a.begin() + 1, a.end());
    ntt(a);
    a.resize(need);
    return a;
  }
};

template< int mod >
struct ModInt {
  int x;

  ModInt() : x(0) {}

  ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}

  ModInt &operator+=(const ModInt &p) {
    if((x += p.x) >= mod) x -= mod;
    return *this;
  }

  ModInt &operator-=(const ModInt &p) {
    if((x += mod - p.x) >= mod) x -= mod;
    return *this;
  }

  ModInt &operator*=(const ModInt &p) {
    x = (int) (1LL * x * p.x % mod);
    return *this;
  }

  ModInt &operator/=(const ModInt &p) {
    *this *= p.inverse();
    return *this;
  }

  ModInt operator-() const { return ModInt(-x); }

  ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }

  ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }

  ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }

  ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }

  bool operator==(const ModInt &p) const { return x == p.x; }

  bool operator!=(const ModInt &p) const { return x != p.x; }

  ModInt inverse() const {
    int a = x, b = mod, u = 1, v = 0, t;
    while(b > 0) {
      t = a / b;
      swap(a -= t * b, b);
      swap(u -= t * v, v);
    }
    return ModInt(u);
  }

  ModInt pow(int64_t n) const {
    ModInt ret(1), mul(x);
    while(n > 0) {
      if(n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }

  friend ostream &operator<<(ostream &os, const ModInt &p) {
    return os << p.x;
  }

  friend istream &operator>>(istream &is, ModInt &a) {
    int64_t t;
    is >> t;
    a = ModInt< mod >(t);
    return (is);
  }

  static int get_mod() { return mod; }
};

using modint = ModInt< mod >;

int64_t mod_pow(int64_t x, int64_t n, int64_t mod) {
  int64_t ret = 1;
  while(n > 0) {
    if(n & 1) (ret *= x) %= mod;
    (x *= x) %= mod;
    n >>= 1;
  }
  return ret;
}

map< int64_t, int > prime_factor(int64_t n) {
  map< int64_t, int > ret;
  for(int64_t i = 2; i * i <= n; i++) {
    while(n % i == 0) {
      ret[i]++;
      n /= i;
    }
  }
  if(n != 1) ret[n] = 1;
  return (ret);
}

int main() {
  int P;
  cin >> P;
  vector< modint > A(P), B(P);
  for(int i = 1; i < P; i++) cin >> A[i];
  for(int i = 1; i < P; i++) cin >> B[i];

  if(P == 2) {
    cout << A[1] * B[1] << endl;
    return 0;
  }

  int root = 2;
  auto d = prime_factor(P - 1);
  for(; root < P; root++) {
    bool ok = true;
    for(const auto &p : d) {
      const uint q = p.first;
      const uint per = (P - 1) / q;
      if(mod_pow(root, per, P) == 1) {
        ok = false;
        break;
      }
    }
    if(ok) { break; }
  }


  vector< modint > C(P - 1), D(P - 1);
  int tap = 1;
  for(int i = 0; i < P - 1; i++) {
    C[i] = A[tap];
    D[i] = B[tap];
    (tap *= root) %= P;
  }
  NumberTheoreticTransformFriendlyModInt< modint > ntt;
  auto E = ntt.multiply(C, D);
  tap = 1;
  vector< modint > F(P - 1);
  for(int i = 0; i < E.size(); i++) {
    F[tap - 1] += E[i];
    (tap *= root) %= P;
  }
  cout << F << endl;
}
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