結果

問題 No.1879 How many matchings?
ユーザー torisasami4
提出日時 2022-03-18 22:56:38
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 10 ms / 2,000 ms
コード長 8,785 bytes
コンパイル時間 2,616 ms
コンパイル使用メモリ 232,108 KB
最終ジャッジ日時 2025-01-28 10:35:26
ジャッジサーバーID
（参考情報） 		judge1 / judge1
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ファイルパターン 結果
other AC * 15
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ソースコード

diff #
プレゼンテーションモードにする

#pragma GCC optimize("Ofast,no-stack-protector,unroll-loops,fast-math")
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define pb(...) emplace_back(__VA_ARGS__)
#define mp(a, b) make_pair(a, b)
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
#define lscan(x) scanf("%I64d", &x)
#define lprint(x) printf("%I64d", x)
#define rep(i, n) for (ll i = 0; i < (n); i++)
#define rep2(i, n) for (ll i = (ll)n - 1; i >= 0; i--)
#define REP(i, l, r) for (ll i = l; i < (r); i++)
#define REP2(i, l, r) for (ll i = (ll)r - 1; i >= (l); i--)
#define siz(x) (ll) x.size()
template <class T>
using rque = priority_queue<T, vector<T>, greater<T>>;
template <class T>
bool chmin(T &a, const T &b) {
    if (b < a) {
        a = b;
        return 1;
    }
    return 0;
}
template <class T>
bool chmax(T &a, const T &b) {
    if (b > a) {
        a = b;
        return 1;
    }
    return 0;
}
template <class T>
void print(vector<T> a) {
    if (a.empty())
        cout << '\n';
    else {
        for (int i = 0; i < a.size(); i++)
            cout << a[i] << (i + 1 == a.size() ? '\n' : ' ');
    }
}
// __int128_t gcd(__int128_t a, __int128_t b) {
//     if (a == 0)
//         return b;
//     if (b == 0)
//         return a;
//     __int128_t cnt = a % b;
//     while (cnt != 0) {
//         a = b;
//         b = cnt;
//         cnt = a % b;
//     }
//     return b;
// }
long long extGCD(long long a, long long b, long long &x, long long &y) {
    if (b == 0) {
        x = 1;
        y = 0;
        return a;
    }
    long long d = extGCD(b, a % b, y, x);
    y -= a / b * x;
    return d;
}
struct UnionFind {
    vector<ll> data;
    int num;
    UnionFind(int sz) {
        data.assign(sz, -1);
        num = sz;
    }
    bool unite(int x, int y) {
        x = find(x), y = find(y);
        if (x == y)
            return (false);
        if (data[x] > data[y])
            swap(x, y);
        data[x] += data[y];
        data[y] = x;
        num--;
        return (true);
    }
    int find(int k) {
        if (data[k] < 0)
            return (k);
        return (data[k] = find(data[k]));
    }
    ll size(int k) {
        return (-data[find(k)]);
    }
    bool same(int x, int y) {
        return find(x) == find(y);
    }
    int operator[](int k) {
        return find(k);
    }
};
template <int mod>
struct Mod_Int {
    int x;
    Mod_Int() : x(0) {
    }
    Mod_Int(long long y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {
    }
    static int get_mod() {
        return mod;
    }
    Mod_Int &operator+=(const Mod_Int &p) {
        if ((x += p.x) >= mod)
            x -= mod;
        return *this;
    }
    Mod_Int &operator-=(const Mod_Int &p) {
        if ((x += mod - p.x) >= mod)
            x -= mod;
        return *this;
    }
    Mod_Int &operator*=(const Mod_Int &p) {
        x = (int)(1LL * x * p.x % mod);
        return *this;
    }
    Mod_Int &operator/=(const Mod_Int &p) {
        *this *= p.inverse();
        return *this;
    }
    Mod_Int &operator++() {
        return *this += Mod_Int(1);
    }
    Mod_Int operator++(int) {
        Mod_Int tmp = *this;
        ++*this;
        return tmp;
    }
    Mod_Int &operator--() {
        return *this -= Mod_Int(1);
    }
    Mod_Int operator--(int) {
        Mod_Int tmp = *this;
        --*this;
        return tmp;
    }
    Mod_Int operator-() const {
        return Mod_Int(-x);
    }
    Mod_Int operator+(const Mod_Int &p) const {
        return Mod_Int(*this) += p;
    }
    Mod_Int operator-(const Mod_Int &p) const {
        return Mod_Int(*this) -= p;
    }
    Mod_Int operator*(const Mod_Int &p) const {
        return Mod_Int(*this) *= p;
    }
    Mod_Int operator/(const Mod_Int &p) const {
        return Mod_Int(*this) /= p;
    }
    bool operator==(const Mod_Int &p) const {
        return x == p.x;
    }
    bool operator!=(const Mod_Int &p) const {
        return x != p.x;
    }
    Mod_Int inverse() const {
        assert(*this != Mod_Int(0));
        return pow(mod - 2);
    }
    Mod_Int pow(long long k) const {
        Mod_Int now = *this, ret = 1;
        for (; k > 0; k >>= 1, now *= now) {
            if (k & 1)
                ret *= now;
        }
        return ret;
    }
    friend ostream &operator<<(ostream &os, const Mod_Int &p) {
        return os << p.x;
    }
    friend istream &operator>>(istream &is, Mod_Int &p) {
        long long a;
        is >> a;
        p = Mod_Int<mod>(a);
        return is;
    }
};
ll mpow2(ll x, ll n, ll mod) {
    ll ans = 1;
    x %= mod;
    while (n != 0) {
        if (n & 1)
            ans = ans * x % mod;
        x = x * x % mod;
        n = n >> 1;
    }
    return ans;
}
ll modinv2(ll a, ll mod) {
    ll b = mod, u = 1, v = 0;
    while (b) {
        ll t = a / b;
        a -= t * b;
        swap(a, b);
        u -= t * v;
        swap(u, v);
    }
    u %= mod;
    if (u < 0)
        u += mod;
    return u;
}
constexpr int mod = 1000000007;
// constexpr int mod = 998244353;
// constexpr int mod = 31607;
using mint = Mod_Int<mod>;
mint mpow(mint x, ll n) {
    mint ans = 1;
    while (n != 0) {
        if (n & 1)
            ans *= x;
        x *= x;
        n = n >> 1;
    }
    return ans;
}
// ----- 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);
  }
};
mint fib(ll k) {
    Matrix<mint> a(2), b(2, 1);
    a[0][0] = 1, a[0][1] = 1, a[1][0] = 1, b[0][0] = 1, b[1][0] = 0;
    a ^= k;
    a *= b;
    return a[1][0];
}
// ----- library -------
int main() {
    ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
    cout << fixed << setprecision(15);
    ll n;
    cin >> n;
    if(n & 1) {
        mint ans = ((fib(n / 2 + 3) + fib(n / 2 + 1)) * (n / 2 + 2) - fib(n / 2 + 2)) / 5;
        ans += ((fib(n / 2 + 2) + fib(n / 2)) * (n / 2 + 1) - fib(n / 2 + 1)) / 5;
        cout << ans << endl;
    }
    else
        cout << fib(n / 2 + 1) << endl;
}
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