結果

問題 No.526 フィボナッチ数列の第N項をMで割った余りを求める
コンテスト
ユーザー sibasyun
提出日時 2024-05-02 22:05:41
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 9 ms / 2,000 ms
コード長 5,312 bytes
コンパイル時間 2,135 ms
コンパイル使用メモリ 199,220 KB
最終ジャッジ日時 2025-02-21 10:41:53
ジャッジサーバーID
（参考情報） 		judge5 / judge5
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ファイルパターン 結果
sample AC * 3
other AC * 12
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/all>
#include <iostream>
#include <iomanip>
#include <math.h>

using namespace std;
// using namespace atcoder;
// using mint = modint998244353;
// using mint = modint1000000007;
using vi = vector<int>;
using vvi = vector<vector<int>>;
using ll = long long;
template <class T> using max_heap = priority_queue<T>;
template <class T> using min_heap = priority_queue<T, vector<T>, greater<>>;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define rep2(i, f, n) for (int i = (int) f; i < (int)(n); i++)
#define repd(i, n, l) for (int i = (int) n; i >= (int) l; i--)

const ll inf = ll(1e9+7);

// from noshi91's library

#include <cstdint>

class runtime_modint {
  using u64 = std::uint_fast64_t;

  static u64 &mod() {
    static u64 mod_ = 0;
    return mod_;
  }

public:
  u64 a;

  runtime_modint(const u64 x = 0) : a(x % get_mod()) {}
  u64 &value() noexcept { return a; }
  const u64 &value() const noexcept { return a; }
  runtime_modint operator+(const runtime_modint rhs) const {
    return runtime_modint(*this) += rhs;
  }
  runtime_modint operator-(const runtime_modint rhs) const {
    return runtime_modint(*this) -= rhs;
  }
  runtime_modint operator*(const runtime_modint rhs) const {
    return runtime_modint(*this) *= rhs;
  }
  runtime_modint operator/(const runtime_modint rhs) const {
    return runtime_modint(*this) /= rhs;
  }
  runtime_modint &operator+=(const runtime_modint rhs) {
    a += rhs.a;
    if (a >= get_mod()) {
      a -= get_mod();
    }
    return *this;
  }
  runtime_modint &operator-=(const runtime_modint rhs) {
    if (a < rhs.a) {
      a += get_mod();
    }
    a -= rhs.a;
    return *this;
  }
  runtime_modint &operator*=(const runtime_modint rhs) {
    a = a * rhs.a % get_mod();
    return *this;
  }
  runtime_modint &operator/=(runtime_modint rhs) {
    u64 exp = get_mod() - 2;
    while (exp) {
      if (exp % 2) {
        *this *= rhs;
      }
      rhs *= rhs;
      exp /= 2;
    }
    return *this;
  }

  static void set_mod(const u64 x) { mod() = x; }
  static u64 get_mod() { return mod(); }
};

// from ei1333's library
template< class T >
struct Matrix {
  vector< vector< T > > A;

  Matrix() {}

  Matrix(size_t n, size_t m) : A(n, vector< T >(m, 0)) {}

  Matrix(size_t n) : A(n, vector< T >(n, 0)) {};

  size_t height() const {
    return (A.size());
  }

  size_t width() const {
    return (A[0].size());
  }

  inline const vector< T > &operator[](int k) const {
    return (A.at(k));
  }

  inline vector< T > &operator[](int k) {
    return (A.at(k));
  }

  static Matrix I(size_t n) {
    Matrix mat(n);
    for(int i = 0; i < n; i++) mat[i][i] = 1;
    return (mat);
  }

  Matrix &operator+=(const Matrix &B) {
    size_t n = height(), m = width();
    assert(n == B.height() && m == B.width());
    for(int i = 0; i < n; i++)
      for(int j = 0; j < m; j++)
        (*this)[i][j] += B[i][j];
    return (*this);
  }

  Matrix &operator-=(const Matrix &B) {
    size_t n = height(), m = width();
    assert(n == B.height() && m == B.width());
    for(int i = 0; i < n; i++)
      for(int j = 0; j < m; j++)
        (*this)[i][j] -= B[i][j];
    return (*this);
  }

  Matrix &operator*=(const Matrix &B) {
    size_t n = height(), m = B.width(), p = width();
    assert(p == B.height());
    vector< vector< T > > C(n, vector< T >(m, 0));
    for(int i = 0; i < n; i++)
      for(int j = 0; j < m; j++)
        for(int k = 0; k < p; k++)
          C[i][j] = (C[i][j] + (*this)[i][k] * B[k][j]);
    A.swap(C);
    return (*this);
  }

  Matrix &operator^=(long long k) {
    Matrix B = Matrix::I(height());
    while(k > 0) {
      if(k & 1) B *= *this;
      *this *= *this;
      k >>= 1LL;
    }
    A.swap(B.A);
    return (*this);
  }

  Matrix operator+(const Matrix &B) const {
    return (Matrix(*this) += B);
  }

  Matrix operator-(const Matrix &B) const {
    return (Matrix(*this) -= B);
  }

  Matrix operator*(const Matrix &B) const {
    return (Matrix(*this) *= B);
  }

  Matrix operator^(const long long k) const {
    return (Matrix(*this) ^= k);
  }

  friend ostream &operator<<(ostream &os, Matrix &p) {
    size_t n = p.height(), m = p.width();
    for(int i = 0; i < n; i++) {
      os << "[";
      for(int j = 0; j < m; j++) {
        os << p[i][j] << (j + 1 == m ? "]\n" : ",");
      }
    }
    return (os);
  }


  T determinant() {
    Matrix B(*this);
    assert(width() == height());
    T ret = 1;
    for(int i = 0; i < width(); i++) {
      int idx = -1;
      for(int j = i; j < width(); j++) {
        if(B[j][i] != 0) idx = j;
      }
      if(idx == -1) return (0);
      if(i != idx) {
        ret *= -1;
        swap(B[i], B[idx]);
      }
      ret *= B[i][i];
      T vv = B[i][i];
      for(int j = 0; j < width(); j++) {
        B[i][j] /= vv;
      }
      for(int j = i + 1; j < width(); j++) {
        T a = B[j][i];
        for(int k = 0; k < width(); k++) {
          B[j][k] -= B[i][k] * a;
        }
      }
    }
    return (ret);
  }
};

int main() {
    int n, m;
    cin >> n >> m;
    runtime_modint::set_mod(m);
    Matrix<runtime_modint> mat(2);
    mat[0][0].a = 1;
    mat[0][1].a = 1;
    mat[1][0].a = 1;
    mat[1][1].a = 0;
    mat.operator^=(n-3);
    cout << (mat[0][0] + mat[0][1]).a << endl;
    return 0;
}
0