#381311 (C++17) No.891 隣接3項間の漸化式

提出ソース

結果

問題	No.891 隣接3項間の漸化式
ユーザー	Haar
提出日時	2019-09-20 21:37:41
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	2 ms / 2,000 ms
コード長	7,678 bytes
コンパイル時間	2,146 ms
コンパイル使用メモリ	204,760 KB
実行使用メモリ	6,944 KB
最終ジャッジ日時	2024-09-14 16:51:26
合計ジャッジ時間	3,592 ms
ジャッジサーバーID （参考情報）	judge5 / judge6

このコードへのチャレンジ
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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 6,812 KB
testcase_01	AC	2 ms 6,940 KB
testcase_02	AC	2 ms 6,944 KB
testcase_03	AC	2 ms 6,940 KB
testcase_04	AC	2 ms 6,940 KB
testcase_05	AC	2 ms 6,940 KB
testcase_06	AC	2 ms 6,944 KB
testcase_07	AC	2 ms 6,940 KB
testcase_08	AC	2 ms 6,944 KB
testcase_09	AC	2 ms 6,940 KB
testcase_10	AC	2 ms 6,944 KB
testcase_11	AC	2 ms 6,944 KB
testcase_12	AC	2 ms 6,944 KB
testcase_13	AC	2 ms 6,940 KB
testcase_14	AC	2 ms 6,940 KB
testcase_15	AC	2 ms 6,940 KB
testcase_16	AC	2 ms 6,940 KB
testcase_17	AC	2 ms 6,944 KB
testcase_18	AC	2 ms 6,944 KB
testcase_19	AC	2 ms 6,940 KB
testcase_20	AC	2 ms 6,944 KB
testcase_21	AC	2 ms 6,940 KB
testcase_22	AC	2 ms 6,944 KB
testcase_23	AC	2 ms 6,944 KB
testcase_24	AC	2 ms 6,944 KB
testcase_25	AC	2 ms 6,940 KB
testcase_26	AC	2 ms 6,940 KB
testcase_27	AC	2 ms 6,940 KB
testcase_28	AC	2 ms 6,940 KB
testcase_29	AC	2 ms 6,944 KB
testcase_30	AC	2 ms 6,944 KB
testcase_31	AC	2 ms 6,944 KB
testcase_32	AC	2 ms 6,940 KB
testcase_33	AC	2 ms 6,940 KB
testcase_34	AC	2 ms 6,940 KB
testcase_35	AC	2 ms 6,940 KB
testcase_36	AC	2 ms 6,940 KB
testcase_37	AC	2 ms 6,940 KB
testcase_38	AC	2 ms 6,940 KB
testcase_39	AC	2 ms 6,944 KB
testcase_40	AC	2 ms 6,944 KB
testcase_41	AC	2 ms 6,940 KB

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ソースコード

raw source code

#include <bits/stdc++.h>
#define LLI long long int
#define FOR(v, a, b) for(LLI v = (a); v < (b); ++v)
#define FORE(v, a, b) for(LLI v = (a); v <= (b); ++v)
#define REP(v, n) FOR(v, 0, n)
#define REPE(v, n) FORE(v, 0, n)
#define REV(v, a, b) for(LLI v = (a); v >= (b); --v)
#define ALL(x) (x).begin(), (x).end()
#define RALL(x) (x).rbegin(), (x).rend()
#define ITR(it, c) for(auto it = (c).begin(); it != (c).end(); ++it)
#define RITR(it, c) for(auto it = (c).rbegin(); it != (c).rend(); ++it)
#define EXIST(c,x) ((c).find(x) != (c).end())
#define fst first
#define snd second
#define popcount __builtin_popcount
#define UNIQ(v) (v).erase(unique(ALL(v)), (v).end())
#define bit(i) (1LL<<(i))

#ifdef DEBUG
#include <misc/C++/Debug.cpp>
#else
#define dump(...) ((void)0)
#endif

#define gcd __gcd

using namespace std;
template <class T> constexpr T lcm(T m, T n){return m/gcd(m,n)*n;}

template <typename I> void join(ostream &ost, I s, I t, string d=" "){for(auto i=s; i!=t; ++i){if(i!=s)ost<<d; ost<<*i;}ost<<endl;}
template <typename T> istream& operator>>(istream &is, vector<T> &v){for(auto &a : v) is >> a; return is;}

template <typename T, typename U> bool chmin(T &a, const U &b){return (a>b ? a=b, true : false);}
template <typename T, typename U> bool chmax(T &a, const U &b){return (a<b ? a=b, true : false);}
template <typename T, size_t N, typename U> void fill_array(T (&a)[N], const U &v){fill((U*)a, (U*)(a+N), v);}

struct Init{
  Init(){
    cin.tie(0);
    ios::sync_with_stdio(false);
  }
}init;

template <uint32_t M> class ModInt{
public:
  uint64_t val;
  ModInt(): val(0){}
  ModInt(int64_t n){
    if(n >= M) val = n % M;
    else if(n < 0) val = n % M + M;
    else val = n;
  }
  
  inline constexpr ModInt operator+(const ModInt &a) const {return ModInt((val+a.val)%M);}
  inline constexpr ModInt operator-(const ModInt &a) const {return ModInt((val-a.val+M)%M);}
  inline constexpr ModInt operator*(const ModInt &a) const {return ModInt((val*a.val)%M);}
  inline constexpr ModInt operator/(const ModInt &a) const {return ModInt((val*a.inv().val)%M);}
  
  inline constexpr ModInt& operator=(const ModInt &a){val = a.val; return *this;}
  inline constexpr ModInt& operator+=(const ModInt &a){if((val += a.val) >= M) val -= M; return *this;}
  inline constexpr ModInt& operator-=(const ModInt &a){if(val < a.val) val += M; val -= a.val; return *this;}
  inline constexpr ModInt& operator*=(const ModInt &a){(val *= a.val) %= M; return *this;}
  inline constexpr ModInt& operator/=(const ModInt &a){(val *= a.inv().val) %= M; return *this;}

  inline constexpr bool operator==(const ModInt &a) const {return val==a.val;}
  inline constexpr bool operator!=(const ModInt &a) const {return val!=a.val;}

  inline constexpr ModInt& operator++(){*this += 1; return *this;}
  inline constexpr ModInt& operator--(){*this -= 1; return *this;}

  inline constexpr ModInt operator++(int){ModInt t = *this; *this += 1; return t;}
  inline constexpr ModInt operator--(int){ModInt t = *this; *this -= 1; return t;}
  
  inline constexpr static ModInt power(LLI n, LLI p){
    ModInt ret = 1, e = n;
    for(; p; e *= e, p >>= 1) if(p&1) ret *= e;
    return ret;
  }

  inline constexpr ModInt power(LLI p) const {return power(val,p);}
  
  inline constexpr ModInt inv() const {
    int64_t a = val, b = M, u = 1, v = 0;

    while(b){
      int64_t t = a/b;
      a -= t*b; swap(a,b);
      u -= t*v; swap(u,v);
    }
    u %= M;
    if(u < 0) u += M;
    
    return u;
  }
};

template <uint32_t M> ModInt<M> operator-(const ModInt<M> &a){return M-a.val;}

template <uint32_t M> ModInt<M> operator+(int64_t a, const ModInt<M> &b){return ModInt<M>(ModInt<M>(a)+b.val);}
template <uint32_t M> ModInt<M> operator-(int64_t a, const ModInt<M> &b){return ModInt<M>(ModInt<M>(a)-b.val);}
template <uint32_t M> ModInt<M> operator*(int64_t a, const ModInt<M> &b){return ModInt<M>(ModInt<M>(a)*b.val);}
template <uint32_t M> ModInt<M> operator/(int64_t a, const ModInt<M> &b){return ModInt<M>(ModInt<M>(a)/b.val);}

template <uint32_t M> istream& operator>>(istream &is, ModInt<M> &a){is >> a.val; return is;}
template <uint32_t M> ostream& operator<<(ostream &os, const ModInt<M> &a){ os << a.val; return os;}

using mint = ModInt<1000000007>;

template <typename T, int N> struct SquareMatrix{
  array<array<T,N>,N> matrix;

  SquareMatrix(): matrix(){}
  SquareMatrix(const T &val){
    REP(i,N) matrix[i].fill(val);
  }
  SquareMatrix(const SquareMatrix<T,N> &) = default;
  SquareMatrix(SquareMatrix<T,N> &&) = default;
  SquareMatrix(initializer_list<initializer_list<T>> list){
    int i = 0;
    ITR(it1,list){
      int j = 0;
      ITR(it2,*it1){
        matrix[i][j] = *it2;
        ++j;
      }
      ++i;
    }
  }

  bool operator==(const SquareMatrix<T,N> &val) const {
    return matrix == val.matrix;
  }

  bool operator!=(const SquareMatrix<T,N> &val) const {
    return !(*this == val);
  }

  SquareMatrix& operator=(const SquareMatrix &) = default;

  SquareMatrix& operator+=(const SquareMatrix &val){
    REP(i,N) REP(j,N) matrix[i][j] = matrix[i][j] + val[i][j];
    return *this;
  }

  SquareMatrix& operator-=(const SquareMatrix &val){
    REP(i,N) REP(j,N) matrix[i][j] = matrix[i][j] - val[i][j];
    return *this;
  }

  SquareMatrix& operator*=(const SquareMatrix &val){
    array<array<T,N>,N> temp = {};
    REP(i,N) REP(j,N) REP(k,N) temp[i][j] = temp[i][j] + matrix[i][k] * val[k][j];
    swap(matrix, temp);
    return *this;
  }

  inline const auto& operator[](size_t i) const {return matrix[i];}
  inline auto& operator[](size_t i){return matrix[i];}
  inline int size() const {return N;}
  
  static SquareMatrix<T,N> make_unit(){
    SquareMatrix<T,N> ret;
    REP(i,N) ret[i][i] = 1;
    return ret;
  }

  SquareMatrix<T,N> transpose() const {
    SquareMatrix<T,N> ret;
    REP(i,N) REP(j,N) ret[i][j] = matrix[j][i];
    return ret;
  }
 
  void show(int w = 10) const {
#ifdef DEBUG
    cerr << "⎛" << string((w+1)*N, ' ') << "⎞" << endl;
    REP(i,N){
      cerr << "⎜";
      REP(j,N) cerr << setw(w) << matrix[i][j] << " ";
      cerr << "⎟";
      cerr << endl;
    }
    cerr << "⎝" << string((w+1)*N, ' ') << "⎠" << endl;
#endif
  }
};

template <typename T, int N> SquareMatrix<T,N> operator+(const SquareMatrix<T,N> &a, const SquareMatrix<T,N> &b){auto ret = a; ret += b; return ret;}
template <typename T, int N> SquareMatrix<T,N> operator-(const SquareMatrix<T,N> &a, const SquareMatrix<T,N> &b){auto ret = a; ret -= b; return ret;}
template <typename T, int N> SquareMatrix<T,N> operator*(const SquareMatrix<T,N> &a, const SquareMatrix<T,N> &b){auto ret = a; ret *= b; return ret;}

template <typename T, int N> SquareMatrix<T,N> power(SquareMatrix<T,N> a, uint64_t p){
  if(p == 0) return SquareMatrix<T,N>::make_unit();
  if(p == 1) return a;
  
  SquareMatrix<T,N> temp = power(a, p/2);
  auto ret = temp * temp;

  if(p%2) ret *= a;
 
  return ret;
}

template <typename T, int N> vector<T> operator*(const SquareMatrix<T,N> &a, const vector<T> &b){
  vector<T> ret(N);

  REP(i,N){
    REP(j,N){
      ret[i] += a[i][j] * b[j];
    }
  }

  return ret;
}

template <typename T, int N> vector<T> operator*(const vector<T> &b, const SquareMatrix<T,N> &a){
  vector<T> ret(N);

  REP(i,N){
    REP(j,N){
      ret[j] += b[i] * a[i][j];
    }
  }

  return ret;
}

using M = SquareMatrix<mint,2>;


int main(){
  mint a,b;
  int n;
  while(cin >> a >> b >> n){
    if(n == 0){
      cout << 0 << endl;
    }else if(n == 1){
      cout << 1 << endl;
    }else{
    
      M m = {{a,b},{1,0}};

      m = power(m, n-1);

      mint ans = m[0][0];
      cout << ans << endl;
    }
  }




  return 0;
}

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結果

テストケース

ソースコード