#746790 (C++17) No.1879 How many matchings?

• 問題: No.1879 How many matchings?
• ユーザー: HayatoY
• 提出日時: 2022-03-18 22:20:29
• 言語: C++17 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 12 ms / 2,000 ms
• コード長: 6,506 bytes
• コンパイル時間: 1,947 ms
• コンパイル使用メモリ: 204,180 KB
• 最終ジャッジ日時: 2025-01-28 10:27:41
• ジャッジサーバーID （参考情報）: judge5 / judge1

ファイルパターン	結果
other	AC * 15

ソースコード

#include <bits/stdc++.h>
#ifdef __LOCAL
#define DBG(X) cout << #X << " = " << (X) << endl;
#define SAY(X) cout << (X) << endl;
#else
#define DBG(X)
#define SAY(X)
#define NDEBUG
#endif

using namespace std;

typedef int_fast32_t int32;
typedef int_fast64_t int64;

const int32 inf = 1e9+7;
const int32 MOD = 1000000007;
const int64 llinf = 1e18;

#define YES(n) cout << ((n) ? "YES\n" : "NO\n"  )
#define Yes(n) cout << ((n) ? "Yes\n" : "No\n"  )
#define POSSIBLE(n) cout << ((n) ? "POSSIBLE\n" : "IMPOSSIBLE\n"  )
#define ANS(n) cout << (n) << "\n"
#define REP(i,n) for(int64 i=0;i<(n);++i)
#define FOR(i,a,b) for(int64 i=(a);i<(b);i++)
#define FORR(i,a,b) for(int64 i=(a);i>=(b);i--)
#define all(obj) (obj).begin(),(obj).end()
#define rall(obj) (obj).rbegin(),(obj).rend()
#define fi first
#define se second
#define pb(a) push_back(a)
typedef pair<int32,int32> pii;
typedef pair<int64,int64> pll;

template<class T> inline bool chmax(T& a, T b) {
	if (a < b) { a = b; return true; } return false;
}
template<class T> inline bool chmin(T& a, T b) {
	if (a > b) { a = b; return true; } return false;
}

template<int_fast64_t mod>
struct ModInt{
  int_fast64_t x;
  constexpr ModInt(int_fast64_t y = 0):x((y%mod+mod)%mod){}
  constexpr ModInt& operator+=(const ModInt& a){
    if((x += a.x) >= mod) x -= mod;
    return *this;
  }
  constexpr ModInt& operator-=(const ModInt& a){
    if((x -= a.x) < 0)x += mod;
    return *this;
  }
  constexpr ModInt& operator*=(const ModInt& a){
    x = x * a.x % mod;
    return *this;
  }
  constexpr ModInt& operator/=(const ModInt& a){
    *this *= a.inv();
    return *this;
  }
  constexpr ModInt operator-() const {
    return ModInt(-x);
  }
  constexpr ModInt operator+(const ModInt& a) const {
    return ModInt(*this) += a;
  }
  constexpr ModInt operator-(const ModInt& a) const {
    return ModInt(*this) -= a;
  }
  constexpr ModInt operator*(const ModInt& a) const {
    return ModInt(*this) *= a;
  }
  constexpr ModInt operator/(const ModInt& a) const {
    return ModInt(*this) /= a;
  }
  constexpr ModInt operator++(){
    *this += ModInt(1);
    return *this;
  }
  constexpr ModInt operator++(int){
    ModInt old = *this;
    ++*this;
    return old;
  }
  constexpr ModInt operator--(){
    *this -= ModInt(1);
    return *this;
  }
  constexpr ModInt operator--(int){
    ModInt old = *this;
    --*this;
    return old;
  }
  constexpr bool operator==(const ModInt& a) const {
    return x == a.x;
  }
  constexpr bool operator!=(const ModInt& a) const {
    return x != a.x;
  }
  constexpr ModInt pow(int_fast64_t r) const {
    if(!r)return 1;
    ModInt res = pow(r>>1);
    res *= res;
    if(r & 1) res *= *this;
    return res;
  }
  constexpr ModInt inv() const {
    return pow(mod-2);
  }
  friend istream& operator>>(istream& is, ModInt& a){
    int_fast64_t t;
    is >> t;
    a = ModInt(t);
    return is;
  }
  friend ostream& operator<<(ostream& os, const ModInt& a){
    return os << a.x;
  }
};
using mint = ModInt<MOD>;

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 size() const {
     if(A.empty()) return 0;
     assert(A.size() == A[0].size());
     return A.size();
  }

  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(){
	cin.tie(0);
	ios::sync_with_stdio(false);
	int64 n;
	cin >> n;

	Matrix<mint> ft(4,1);
	ft[0][0] = 2;
	ft[1][0] = 3;
	ft[2][0] = 1;
	ft[3][0] = 1;
	Matrix<mint> E(4,4);
	E[0] = {0,1,0,1};
	E[1] = {1,0,0,0};
	E[2] = {0,1,0,0};
	E[3] = {0,0,1,0};
	Matrix<mint> O(4,4);
	O[0] = {1,1,1,1};
	O[1] = {1,0,0,0};
	O[2] = {0,1,0,0};
	O[3] = {0,0,1,0};

	if(n <= 4){
		ANS(ft[4-n][0]);
		return 0;
	}
	auto EO = E * O;
	EO ^= (n-4)/2;
	if(n % 2)EO = O * EO;
	ANS((EO * ft)[0][0]);
	return 0;
}