#354120 (C++14) No.658 テトラナッチ数列 Hard

提出ソース

結果

問題	No.658 テトラナッチ数列 Hard
ユーザー	fumiphys
提出日時	2019-06-26 17:45:14
言語	C++14 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	345 ms / 2,000 ms
コード長	6,643 bytes
コンパイル時間	1,854 ms
コンパイル使用メモリ	176,052 KB
実行使用メモリ	4,384 KB
最終ジャッジ日時	2023-09-07 13:00:58
合計ジャッジ時間	3,995 ms
ジャッジサーバーID （参考情報）	judge15 / judge11

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テストケース

テストケース表示

入力	結果	実行時間実行使用メモリ
testcase_00	AC	2 ms 4,380 KB
testcase_01	AC	2 ms 4,380 KB
testcase_02	AC	1 ms 4,376 KB
testcase_03	AC	3 ms 4,380 KB
testcase_04	AC	129 ms 4,376 KB
testcase_05	AC	146 ms 4,376 KB
testcase_06	AC	186 ms 4,380 KB
testcase_07	AC	196 ms 4,376 KB
testcase_08	AC	233 ms 4,384 KB
testcase_09	AC	345 ms 4,384 KB
testcase_10	AC	335 ms 4,380 KB

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ソースコード

raw source code

// includes
#include <bits/stdc++.h>

// macros
#define ll long long int
#define pb emplace_back
#define mk make_pair
#define pq priority_queue
#define FOR(i, a, b) for(int i=(a);i<(b);++i)
#define rep(i, n) FOR(i, 0, n)
#define rrep(i, n) for(int i=((int)(n)-1);i>=0;i--)
#define irep(itr, st) for(auto itr = (st).begin(); itr != (st).end(); ++itr)
#define irrep(itr, st) for(auto itr = (st).rbegin(); itr != (st).rend(); ++itr)
#define vrep(v, i) for(int i = 0; i < (v).size(); i++)
#define all(x) (x).begin(),(x).end()
#define sz(x) ((int)(x).size())
#define UNIQUE(v) v.erase(unique(v.begin(), v.end()), v.end())
#define FI first
#define SE second
#define dump(a, n) for(int i = 0; i < n; i++)cout << a[i] << "\n "[i + 1 != n];
#define dump2(a, n, m) for(int i = 0; i < n; i++)for(int j = 0; j < m; j++)cout << a[i][j] << "\n "[j + 1 != m];
#define bit(n) (1LL<<(n))
#define INT(n) int n; cin >> n;
#define LL(n) ll n; cin >> n;
#define DOUBLE(n) double n; cin >> n;
using namespace std;

//  types
typedef pair<int, int> P;
typedef pair<ll, int> Pl;
typedef pair<ll, ll> Pll;
typedef pair<double, double> Pd;
typedef complex<double> cd;
 
// constants
const int inf = 1e9;
const ll linf = 1LL << 50;
const double EPS = 1e-10;
const int mod = 1e9 + 7;
const int dx[4] = {-1, 0, 1, 0};
const int dy[4] = {0, -1, 0, 1};

// solve
template <class T>bool chmax(T &a, const T &b){if(a < b){a = b; return 1;} return 0;}
template <class T>bool chmin(T &a, const T &b){if(a > b){a = b; return 1;} return 0;}
template <typename T> istream &operator>>(istream &is, vector<T> &vec){for(auto &v: vec)is >> v; return is;}
template <typename T> ostream &operator<<(ostream &os, const vector<T>& vec){for(int i = 0; i < vec.size(); i++){ os << vec[i]; if(i + 1 != vec.size())os << " ";} return os;}
template <typename T> ostream &operator<<(ostream &os, const set<T>& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;}
template <typename T> ostream &operator<<(ostream &os, const unordered_set<T>& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;}
template <typename T> ostream &operator<<(ostream &os, const multiset<T>& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;}
template <typename T> ostream &operator<<(ostream &os, const unordered_multiset<T>& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;}
template <typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &p){os << p.first << " " << p.second; return os;}
template <typename T1, typename T2> ostream &operator<<(ostream &os, const map<T1, T2> &mp){for(auto itr = mp.begin(); itr != mp.end(); ++itr){ os << itr->first << ":" << itr->second; auto titr = itr; if(++titr != mp.end())os << " "; } return os;}
template <typename T1, typename T2> ostream &operator<<(ostream &os, const unordered_map<T1, T2> &mp){for(auto itr = mp.begin(); itr != mp.end(); ++itr){ os << itr->first << ":" << itr->second; auto titr = itr; if(++titr != mp.end())os << " "; } return os;}

template<typename T>
T extgcd(T a, T b, T &x, T &y){ 
  T d = a;
  if(b != 0){
    d = extgcd(b, a % b, y, x);
    y -= (a / b) * x;
  }else{
    x = 1, y = 0;
  }
  return d;
}

template <typename T>
T modinv(T a, T m){
  long long x = 0, y = 0;
  extgcd<long long>(a, m, x, y);
  x %= m;
  if(x < 0)x += m;
  return x;
}

template <int MOD = int(1e9+7)>
struct LMatrix{
  vector<vector<long long>> v;
  int n, m;
  LMatrix(int n_, int m_ = -1): n(n_), m(m_){
    if(m < 0)m = n;
    v.resize(n);
    for(int i = 0; i < n; i++)v[i].resize(m);
  }
  void identity(){
    assert(n == m);
    for(int i = 0; i < n; i++){
      for(int j = 0; j < n; j++){
        v[i][j] = (i == j ? 1: 0);
      }
    }
  }
  vector<long long> &operator[](size_t i){
    return v[i];
  }
  const vector<long long> &operator[](size_t i) const{
    return v[i];
  }
  LMatrix operator*(const LMatrix &r) const{
    assert(m == r.n);
    int l = r.m;
    LMatrix res(n, l);
    for(int i = 0; i < n; i++){
      for(int j = 0; j < l; j++){
        res.v[i][j] = 0;
        for(int k = 0; k < m; k++){
          res.v[i][j] = (res.v[i][j] + v[i][k] * r.v[k][j] % MOD) % MOD;
        }
      }
    }
    return res;
  }
  LMatrix operator+(const LMatrix &r) const{
    assert(n == r.n);
    assert(m == r.m);
    LMatrix res(n, m);
    for(int i = 0; i < n; i++){
      for(int j = 0; j < m; j++){
        res[i][j] = (v[i][j] + r[i][j]) % MOD;
      }
    }
    return res;
  }
  LMatrix operator-(const LMatrix &r) const{
    assert(n == r.n);
    assert(m == r.m);
    LMatrix res(n, m);
    for(int i = 0; i < n; i++){
      for(int j = 0; j < m; j++){
        res[i][j] = (v[i][j] - r[i][j]) % MOD;
        if(res[i][j] < 0)res[i][j] += MOD;
      }
    }
    return res;
  }
  template <typename T>
  LMatrix operator*(T a) const{
    LMatrix res = *this;
    for(int i = 0; i < n; i++){
      for(int j = 0; j < n; j++){
        res[i][j] = a * res[i][j] % MOD;
      }
    }
    return res;
  }
  LMatrix inv2() const{
    assert(n == 2 && m == 2);
    long long det = v[0][0] * v[1][1] % MOD - v[0][1] * v[1][0] % MOD;
    if(det < 0)det += MOD;
    assert(det != 0);
    LMatrix res(2, 2);
    long long inv = modinv(det, (long long)MOD);
    res[0][0] = v[1][1];
    res[1][1] = v[0][0];
    res[1][0] = - v[1][0];
    res[0][1] = - v[0][1];
    for(int i = 0; i < n; i++){
      for(int j = 0; j < m; j++){
        res[i][j] %= MOD;
        res[i][j] = res[i][j] * inv % MOD;
        if(res[i][j] < 0)res[i][j] += MOD;
      }
    }
    return res;
  }
};

template <typename T, int MOD = int(1e9+7)>
LMatrix<MOD> operator*(T a, const LMatrix<MOD> b){
  return b * a;
}

template <int MOD = int(1e9+7)>
LMatrix<MOD> powerm(LMatrix<MOD> &a, long long n){
  long long tmp = n;
  LMatrix<MOD> curr = a;
  LMatrix<MOD> res(a.n);
  res.identity();
  while(tmp){
    if(tmp % 2 == 1){
      res = res * curr;
    }
    curr = curr * curr;
    tmp /= 2;
  }
  return res;
}

int main(int argc, char const* argv[])
{
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout << fixed << setprecision(20);
  INT(q);
  LMatrix<17> lm(4, 4);
  rep(i, 4)lm[0][i] = 1; rep(i, 3)lm[i+1][i] = 1;
  rep(i, q){
    LL(n);
    if(n < 5){
      if(n == 4)cout << 1 << endl;
      else cout << 0 << endl;
      continue;
    }
    auto LM = powerm<17>(lm, n - 4);
    cout << LM[0][0] << endl;
  }
  return 0;
}

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結果

テストケース

ソースコード