#382058 (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	alexara1123
提出日時	2019-09-21 14:41:37
言語	C++14 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	388 ms / 2,000 ms
コード長	5,996 bytes
コンパイル時間	1,134 ms
コンパイル使用メモリ	101,624 KB
実行使用メモリ	5,376 KB
最終ジャッジ日時	2024-09-18 22:25:08
合計ジャッジ時間	3,876 ms
ジャッジサーバーID （参考情報）	judge4 / judge2

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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 5,248 KB
testcase_01	AC	2 ms 5,376 KB
testcase_02	AC	2 ms 5,376 KB
testcase_03	AC	4 ms 5,376 KB
testcase_04	AC	148 ms 5,376 KB
testcase_05	AC	166 ms 5,376 KB
testcase_06	AC	209 ms 5,376 KB
testcase_07	AC	225 ms 5,376 KB
testcase_08	AC	261 ms 5,376 KB
testcase_09	AC	387 ms 5,376 KB
testcase_10	AC	388 ms 5,376 KB

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ソースコード

raw source code

#include <cstdio>
#include <cstdlib>
#include <algorithm>
#include <vector>
#include <cstring>
#include <queue>
#include <set>
#include <unordered_set>
#include <unordered_map>
#include <map>
#include <functional>
#include <cmath>
#include <cassert>
#include <string>
#include <iostream>

using namespace std;
typedef long long ll;
ll MOD = 1000000007;
typedef pair<int, int> P;

template <class T>
ostream &operator<<(ostream &o, const vector<T> &v)
{
   o << "{";
   for (int i = 0; i < (int)v.size(); i++)
      o << (i > 0 ? ", " : "") << v[i];
   o << "}";
   return o;
}

template <int mod>
struct ModInt
{
   int x;

   ModInt() : x(0) {}

   ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}

   ModInt &operator+=(const ModInt &p)
   {
      if ((x += p.x) >= mod)
         x -= mod;
      return *this;
   }

   ModInt &operator-=(const ModInt &p)
   {
      if ((x += mod - p.x) >= mod)
         x -= mod;
      return *this;
   }

   ModInt &operator*=(const ModInt &p)
   {
      x = (int)(1LL * x * p.x % mod);
      return *this;
   }

   ModInt &operator/=(const ModInt &p)
   {
      *this *= p.inverse();
      return *this;
   }

   ModInt operator-() const { return ModInt(-x); }

   ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }

   ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }

   ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }

   ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }

   bool operator==(const ModInt &p) const { return x == p.x; }

   bool operator!=(const ModInt &p) const { return x != p.x; }

   ModInt inverse() const
   {
      int a = x, b = mod, u = 1, v = 0, t;
      while (b > 0)
      {
         t = a / b;
         swap(a -= t * b, b);
         swap(u -= t * v, v);
      }
      return ModInt(u);
   }

   ModInt pow(int64_t n) const
   {
      ModInt ret(1), mul(x);
      while (n > 0)
      {
         if (n & 1)
            ret *= mul;
         mul *= mul;
         n >>= 1;
      }
      return ret;
   }

   friend ostream &operator<<(ostream &os, const ModInt &p)
   {
      return os << p.x;
   }

   friend istream &operator>>(istream &is, ModInt &a)
   {
      int64_t t;
      is >> t;
      a = ModInt<mod>(t);
      return (is);
   }
};

const int mod = 17;
using modint = 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 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()
{
   ios::sync_with_stdio(false);
   cin.tie(0);

   ll q;
   cin >> q;

   Matrix<modint> m(4);
   m[0][0] = 1;
   m[0][1] = 1;
   m[0][2] = 1;
   m[0][3] = 1;
   m[1][0] = 1;
   m[2][1] = 1;
   m[3][2] = 1;
   for (int i = 0; i < q; i++)
   {
      ll n;
      cin >> n;
      auto f = m ^ n;
      cout << f[3][3] << endl;
   }
}

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結果

テストケース

ソースコード