結果

問題 No.2874 Gunegune Tree
コンテスト
ユーザー hos.lyric
提出日時 2024-09-06 22:06:49
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 2 ms / 2,000 ms
コード長 5,669 bytes
コンパイル時間 1,287 ms
コンパイル使用メモリ 112,480 KB
実行使用メモリ 6,944 KB
最終ジャッジ日時 2024-09-06 22:08:05
合計ジャッジ時間 2,135 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge4
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 30
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 <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <functional>
#include <iostream>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

using namespace std;

using Int = long long;

template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << "(" << a.first << ", " << a.second << ")"; };
template <class T> ostream &operator<<(ostream &os, const vector<T> &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; }
template <class T> void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; }
template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; }
template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; }
#define COLOR(s) ("\x1b[" s "m")

////////////////////////////////////////////////////////////////////////////////
template <unsigned M_> struct ModInt {
  static constexpr unsigned M = M_;
  unsigned x;
  constexpr ModInt() : x(0U) {}
  constexpr ModInt(unsigned x_) : x(x_ % M) {}
  constexpr ModInt(unsigned long long x_) : x(x_ % M) {}
  constexpr ModInt(int x_) : x(((x_ %= static_cast<int>(M)) < 0) ? (x_ + static_cast<int>(M)) : x_) {}
  constexpr ModInt(long long x_) : x(((x_ %= static_cast<long long>(M)) < 0) ? (x_ + static_cast<long long>(M)) : x_) {}
  ModInt &operator+=(const ModInt &a) { x = ((x += a.x) >= M) ? (x - M) : x; return *this; }
  ModInt &operator-=(const ModInt &a) { x = ((x -= a.x) >= M) ? (x + M) : x; return *this; }
  ModInt &operator*=(const ModInt &a) { x = (static_cast<unsigned long long>(x) * a.x) % M; return *this; }
  ModInt &operator/=(const ModInt &a) { return (*this *= a.inv()); }
  ModInt pow(long long e) const {
    if (e < 0) return inv().pow(-e);
    ModInt a = *this, b = 1U; for (; e; e >>= 1) { if (e & 1) b *= a; a *= a; } return b;
  }
  ModInt inv() const {
    unsigned a = M, b = x; int y = 0, z = 1;
    for (; b; ) { const unsigned q = a / b; const unsigned c = a - q * b; a = b; b = c; const int w = y - static_cast<int>(q) * z; y = z; z = w; }
    assert(a == 1U); return ModInt(y);
  }
  ModInt operator+() const { return *this; }
  ModInt operator-() const { ModInt a; a.x = x ? (M - x) : 0U; return a; }
  ModInt operator+(const ModInt &a) const { return (ModInt(*this) += a); }
  ModInt operator-(const ModInt &a) const { return (ModInt(*this) -= a); }
  ModInt operator*(const ModInt &a) const { return (ModInt(*this) *= a); }
  ModInt operator/(const ModInt &a) const { return (ModInt(*this) /= a); }
  template <class T> friend ModInt operator+(T a, const ModInt &b) { return (ModInt(a) += b); }
  template <class T> friend ModInt operator-(T a, const ModInt &b) { return (ModInt(a) -= b); }
  template <class T> friend ModInt operator*(T a, const ModInt &b) { return (ModInt(a) *= b); }
  template <class T> friend ModInt operator/(T a, const ModInt &b) { return (ModInt(a) /= b); }
  explicit operator bool() const { return x; }
  bool operator==(const ModInt &a) const { return (x == a.x); }
  bool operator!=(const ModInt &a) const { return (x != a.x); }
  friend std::ostream &operator<<(std::ostream &os, const ModInt &a) { return os << a.x; }
};
////////////////////////////////////////////////////////////////////////////////

constexpr unsigned MO = 998244353;
using Mint = ModInt<MO>;

using Pair = pair<Mint, Mint>;
Pair operator+(const Pair &a, const Pair &b) { return make_pair(a.first + b.first, a.second + b.second); }
Pair operator-(const Pair &a, const Pair &b) { return make_pair(a.first - b.first, a.second - b.second); }
Pair operator*(const Pair &a, const Pair &b) { return make_pair(a.first * b.first, a.first * b.second + a.second * b.first); }
Pair operator*(const Pair &a, Mint k) { return make_pair(a.first * k, a.second * k); }
Pair operator*(Mint k, const Pair &a) { return make_pair(k * a.first, k * a.second); }
Pair &operator+=(Pair &a, const Pair &b) { return a = a + b; }
Pair &operator-=(Pair &a, const Pair &b) { return a = a - b; }
Pair &operator*=(Pair &a, const Pair &b) { return a = a * b; }
Pair &operator*=(Pair &a, Mint k) { return a = a * k; }
constexpr Pair ZERO(0, 0);


constexpr int U = 5;

struct Mat {
  Pair a[U][U];
  Mat() : a{} {}
};

Mat operator*(const Mat &a, const Mat &b) {
  const int n = U;
  Mat c;
  for (int i = 0; i < n; ++i) for (int k = 0; k < n; ++k) for (int j = 0; j < n; ++j) {
    c.a[i][j] += a.a[i][k] * b.a[k][j];
  }
  return c;
}

Mat A;
Mat power(int e) {
  if (e == 0) {
    Mat ret;
    for (int u = 0; u < U; ++u) ret.a[u][u] = Pair(1, 0);
    return ret;
  }
  Mat res = power(e >> 1);
  res = res * res;
  if (e & 1) {
    return res * A;
  } else {
    return res;
  }
}

int main() {
  for (int u = 0; u < 5; ++u) {
    int denom = 0;
    for (int v = 0; v < 5; ++v) if (abs(u - v) <= 1) ++denom;
    for (int v = 0; v < 5; ++v) if (abs(u - v) <= 1) A.a[u][v] = Mint(denom).inv() * Pair(1, (1 <= v && v <= 3) ? 1 : 0);
  }
  
  int N;
  for (; ~scanf("%d", &N); ) {
    const Mat B = power(N - 1);
    Pair ans = ZERO;
    for (int u = 0; u < U; ++u) for (int v = 0; v < U; ++v) {
      ans += Mint(5).inv() * Pair(1, ((1 <= u && u <= 3) ? 1 : 0)) * B.a[u][v];
    }
    printf("%u\n", ans.second.x);
  }
  return 0;
}
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