結果

問題 No.2529 Treasure Hunter
コンテスト
ユーザー ochiaigawa
提出日時 2023-11-03 23:21:52
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 18 ms / 2,000 ms
コード長 5,534 bytes
コンパイル時間 2,416 ms
コンパイル使用メモリ 215,880 KB
最終ジャッジ日時 2025-02-17 18:53:24
ジャッジサーバーID
（参考情報） 		judge5 / judge5
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 * 1
other AC * 22
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>
#include <atcoder/modint>
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
using namespace std;
using mint = atcoder::modint998244353;
template <typename T> class Matrix {
  public:
    Matrix() {}
    explicit Matrix(int N) : Matrix(N, N) {}
    explicit Matrix(int H, int W) : mat(H, vector<T>(W)) {}
    int height() const {
      return (int) mat.size();
    }
    int width() const {
      return (int) mat[0].size();
    }
    const std::vector<T> &operator[](int k) const {
      return mat[k];
    }
    std::vector<T> &operator[](int k) { 
      return mat[k];
    }
    static inline Matrix I(int N) {
      Matrix ret(N);
      for(int i = 0; i < N; i++) ret[i][i] = T(1);
      return ret;
    }
    Matrix &operator+=(const Matrix &other) {
      int H = height();
      int W = width();
      assert(H == other.height() && W == other.width());
      for(int i = 0; i < H; i++) {
        for(int j = 0; j < W; j++) {
          (*this)[i][j] += other[i][j];
        }
      }
      return (*this);
    }
    Matrix &operator+=(T X) {
      int H = height();
      int W = width();
      for(int i = 0; i < H; i++) {
        for(int j = 0; j < W; j++) {
          mat[i][j] += X;
        }
      }
      return (*this);
    }
    Matrix &operator-=(const Matrix &other) {
      int H = height();
      int W = width();
      assert(H == other.height() && W == other.width());
      for(size_t i = 0; i < H; i++) {
        for(size_t j = 0; j < W; j++) {
          (*this)[i][j] -= other[i][j];
        }
      }
      return (*this);
    }
    Matrix &operator-=(T X) {
      int H = height();
      int W = width();
      for(int i = 0; i < H; i++) {
        for(int j = 0; j < W; j++) {
          mat[i][j] -= X;
        }
      }
      return (*this);
    }
    Matrix &operator*=(T X) {
      int H = height();
      int W = width();
      for(int i = 0; i < H; i++) {
        for(int j = 0; j < W; j++) {
          mat[i][j] *= X;
        }
      }
      return (*this);
    }
    Matrix &operator/=(T X) {
      int H = height();
      int W = width();
      for(int i = 0; i < H; i++) {
        for(int j = 0; j < W; j++) {
          mat[i][j] /= X;
        }
      }
      return (*this);
    }
    Matrix operator+(const Matrix &other) const {
      return (Matrix(*this) += other);
    }
    Matrix operator+(T X) const {
      return (Matrix(*this) += X);
    }
    Matrix operator-(const Matrix &other) const {
      return (Matrix(*this) -= other);
    }
    Matrix operator-(T X) const {
      return (Matrix(*this) -= X);
    }
    Matrix operator*(T X) const {
      return (Matrix(*this) *= X);
    }
    Matrix operator/(T X) const {
      return (Matrix(*this) /= X);
    }

    Matrix mat_mul(Matrix &other) {
      int h0 = height();
      int w0 = width();
      int h1 = other.height();
      int w1 = other.width();
      assert(w0 == h1);
      vector<vector<T>> ret(h0, vector<T>(w1, T(0)));
      for(int i = 0; i < h0; i++) {
        for(int j = 0; j < w1; j++) {
          for(int k = 0; k < w0; k++) {
            ret[i][j] += (*this)[i][k] * other[k][j];
          }
        }
      }
      this->mat.swap(ret);
      return (*this);
    }
    Matrix pow(long long k) const {
      Matrix A = (*this);
      assert(height() == width());
      Matrix ret = Matrix::I(height());
      while(k) {
        if(k & 1) {
          ret.mat_mul(A);
        }
        A.mat_mul(A);
        k >>= 1LL;
      }
      return ret;
    }
    Matrix sum() {
      Matrix A = (*this);
      T ret = 0;
      int h = height();
      int w = width();
      for(int i = 0; i < h; i++) {
        for(int j = 0; j < w; j++) {
          ret += A[i][j];
        }
      }
      return T(ret);
    }

  private:
    std::vector<std::vector<T>> mat;
};

void solve() {
  int N, M;
  cin >> M >> N;
  if(M <= 3) {
    Matrix<mint> m(3);
    m[0][0] = 1;
    m[1][0] = M;
    m[2][0] = 0;
    m[0][1] = 1;
    m[1][1] = M - 1;
    m[2][1] = 0;
    m[0][2] = 0;
    m[1][2] = 0;
    m[2][2] = 0;
    Matrix<mint> p = m.pow(N - 1);
    vector<mint> v = {1, M, 0};
    mint ans = 0;
    for(int i = 0; i < 3; i++) {
      for(int j = 0; j < 3; j++) {
        ans += p[i][j] * v[j];
      }
    }
    cout << ans.val() << '\n';
  } else if(M % 2 == 0) {
    Matrix<mint> m(3);
    m[0][0] = 1;
    m[1][0] = M;
    m[2][0] = mint(M) * (M / 2 - 2) + M / 2;
    m[0][1] = 1;
    m[1][1] = M - 1;
    m[2][1] = mint(M - 2) * (M / 2 - 2) + (M - 1) / 2;
    m[0][2] = 1;
    m[1][2] = M - 2;
    m[2][2] = mint(M - 3) * (M - 2) / 2 - (M - 4);
    Matrix<mint> p = m.pow(N - 1);
    vector<mint> v = {1, M, mint(M - 3) * (M - 2) / 2 + (M - 3)};
    mint ans = 0;
    for(int i = 0; i < 3; i++) {
      for(int j = 0; j < 3; j++) {
        ans += p[i][j] * v[j];
      }
    }
    cout << ans.val() << '\n';
  } else {
    Matrix<mint> m(3);
    m[0][0] = 1;
    m[1][0] = M;
    m[2][0] = mint(M) * (M / 2 - 1);
    m[0][1] = 1;
    m[1][1] = M - 1;
    m[2][1] = mint(M - 2) * (M / 2 - 1);
    m[0][2] = 1;
    m[1][2] = M - 2;
    m[2][2] = mint(M - 3) * (M - 2) / 2 - (M - 4);
    Matrix<mint> p = m.pow(N - 1);
    vector<mint> v = {1, M, mint(M - 3) * (M - 2) / 2 + (M - 3)};
    mint ans = 0;
    for(int i = 0; i < 3; i++) {
      for(int j = 0; j < 3; j++) {
        ans += p[i][j] * v[j];
      }
    }
    cout << ans.val() << '\n';
  }
}

int main() {
  cin.tie(0); cout.tie(0);
  ios::sync_with_stdio(false);
  int T;
  cin >> T;
  while(T--) {
    solve();
  }
  return 0;
}
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