#955589 (C++17) No.1073 無限すごろく

提出ソース

結果

問題	No.1073 無限すごろく
ユーザー	CleyL
提出日時	2024-02-25 16:13:19
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	8,192 bytes
コンパイル時間	1,704 ms
コンパイル使用メモリ	137,372 KB
実行使用メモリ	6,676 KB
最終ジャッジ日時	2024-02-25 16:13:22
合計ジャッジ時間	3,479 ms
ジャッジサーバーID （参考情報）	judge12 / judge14

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 6,676 KB
testcase_01	AC	2 ms 6,676 KB
testcase_02	AC	2 ms 6,676 KB
testcase_03	AC	1 ms 6,676 KB
testcase_04	AC	2 ms 6,676 KB
testcase_05	AC	2 ms 6,676 KB
testcase_06	AC	2 ms 6,676 KB
testcase_07	AC	1 ms 6,676 KB
testcase_08	AC	2 ms 6,676 KB
testcase_09	AC	1 ms 6,676 KB
testcase_10	AC	2 ms 6,676 KB
testcase_11	AC	2 ms 6,676 KB
testcase_12	AC	2 ms 6,676 KB
testcase_13	AC	1 ms 6,676 KB
testcase_14	AC	2 ms 6,676 KB
testcase_15	AC	2 ms 6,676 KB
testcase_16	AC	1 ms 6,676 KB
testcase_17	AC	2 ms 6,676 KB
testcase_18	AC	2 ms 6,676 KB
testcase_19	AC	1 ms 6,676 KB
testcase_20	AC	1 ms 6,676 KB
testcase_21	AC	2 ms 6,676 KB
testcase_22	AC	2 ms 6,676 KB
testcase_23	AC	2 ms 6,676 KB
testcase_24	AC	2 ms 6,676 KB
testcase_25	AC	2 ms 6,676 KB
testcase_26	AC	1 ms 6,676 KB
testcase_27	AC	1 ms 6,676 KB
testcase_28	AC	2 ms 6,676 KB
testcase_29	AC	2 ms 6,676 KB
testcase_30	AC	2 ms 6,676 KB
testcase_31	AC	1 ms 6,676 KB
testcase_32	AC	2 ms 6,676 KB

権限があれば一括ダウンロードができます

ソースコード

raw source code

#line 2 "/home/sakflat/CP/_library/cpp/template/template.cpp"

//yukicoder@cpp17

#include <iostream>
#include <iomanip>

#include <algorithm>

#include <cmath>
#include <cctype>
#include <climits>
#include <cassert>

#include <string>
#include <vector>
#include <set>
#include <stack>
#include <queue>
#include <map>

#include <random>

#include <bitset>

#include <complex>

#include <utility>

#include <numeric>

#include <functional>


using namespace std;
using ll = long long;
using P = pair<ll,ll>;


const ll MOD = 998244353;
const ll MODx = 1000000007;
const int INF = (1<<30)-1;
const ll LINF = (1LL<<62LL)-1;
const double EPS = (1e-10);


P ar4[4] = {{0,1},{0,-1},{1,0},{-1,0}};
P ar8[8] = {{-1,-1},{-1,0},{-1,1},{0,-1},{0,1},{1,-1},{1,0},{1,1}};


template <typename T> vector<T> make_vector(size_t a, T b) { return vector<T>(a, b); }
template <typename... Ts> auto make_vector(size_t a, Ts... ts) { return vector<decltype(make_vector(ts...))>(a, make_vector(ts...)); }
 
/*
確認ポイント
cout << fixed << setprecision(n) << 小数計算//n桁の小数表記になる

計算量は変わらないが楽できるシリーズ
min(max)_element(iter,iter)で一番小さい(大きい)値のポインタが帰ってくる
count(iter,iter,int)でintがiterからiterの間にいくつあったかを取得できる
*/

/* comment outed because can cause bugs
__attribute__((constructor))
void initial() {
  cin.tie(0);
  ios::sync_with_stdio(false);
}
*/
#line 2 "/home/sakflat/CP/_library/cpp/template/basic.cpp"

#line 2 "/home/sakflat/CP/_library/cpp/math/binary-power-method.cpp"

template <typename T>
T uPow(T z,T n, T mod){
  T ans = 1;
  while(n != 0){
    if(n%2){
      ans*=z;
      if(mod)ans%=mod;
    }
    n >>= 1;
    z*=z;
    if(mod)z%=mod;
  }
  return ans;
}

#line 2 "/home/sakflat/CP/_library/cpp/data-structure/mod-int/mod-int.cpp"

template <int mod>
struct ModInt{
  int n;
  ModInt():n(0){}
  ModInt(long long n_):n(n_ >= 0 ? n_%mod : mod - ((-n_)%mod) ){}
  ModInt(int n_):n(n_ >= 0 ? n_%mod : mod - ((-n_)%mod) ){}

  ModInt &operator+=(const ModInt &p){
    if((n+=p.n) >= mod)n-=mod;
    return *this;
  }
  ModInt &operator-=(const ModInt &p){
    n+=mod-p.n;
    if(n >= mod)n-=mod;
    return *this;
  }
  ModInt &operator*=(const ModInt &p){
    n = (int) ((1LL*n*p.n)%mod);
    return *this;
  }
  ModInt &operator/=(const ModInt &p){
    *this *= p.inverse();
    return *this;
  }
  ModInt operator-() const {return ModInt(-n);}
  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 n==p.n;}
  bool operator<(const ModInt &p) const {return n<p.n;}
  bool operator>(const ModInt &p) const {return n>p.n;}
  bool operator>=(const ModInt &p) const {return n>=p.n;}
  bool operator<=(const ModInt &p) const {return n<=p.n;}
  bool operator!=(const ModInt &p) const {return n!=p.n;}

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

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

  int getMod() const {
    return mod;
  }

  friend ostream &operator<<(ostream &os, const ModInt &p){
    return os << p.n;
  }
  friend istream &operator>>(istream &is, ModInt &a){
    int64_t t;
    is >> t;
    a = ModInt<mod> ((long long)t);
    return (is);

  }
};
using mint = ModInt<MODx>;
#line 1 "/home/sakflat/CP/_library/cpp/math/matrix.cpp"
template <typename T>
struct mat{
  vector<vector<T>> x;
  int h,w;
  mat():x(vector<vector<T>>()){}
  mat(int h,int w):x(vector<vector<T>>(h,vector<T>(w))),h(h),w(w){}
  mat(int h,int w, T c):x(vector<vector<T>>(h,vector<T>(w,c))),h(h),w(w){}
  mat(vector<vector<T>> A):x(A),h(A.size()),w(A[0].size()){}
  vector<T>& operator[](int i){return x[i];}

  void resize(int h, int w){
    x.assign(h, vector<T>(w, 0));
  }

  mat base(){
    return mat(h,w,0);
  }

  mat& operator*=(mat& y){
    mat<T> ret(h,y.w,0);
    if(w != y.h){
      for(int i = 0; h > i; i++){
        for(int j = 0; y.w > j; j++){
          ret[i][j] = -1;
        }
      }
    }else{
      for(int i = 0; h > i; i++){
        for(int j = 0; y.w > j; j++){
          for(int k = 0; w > k; k++){
            ret[i][j] = ret[i][j] + x[i][k]*y[k][j];
          }
        }
      }
    }
    for(int i = 0; h > i; i++){
      x[i].resize(y.w);
    }
    w = y.w;
    for(int i = 0; h > i; i++){
      for(int j = 0; y.w > j; j++){
        x[i][j] = ret[i][j];
      }
    }
    return *this;
  }

  mat& operator*=(T v){
    for(int i = 0; h > i; i++){
      for(int j = 0; w > j; j++){
        x[i][j] *= v;
      }
    }
    return *this;
  }

  mat operator*(mat& y){return mat(*this) *= y;}
  mat operator*(T y){return mat(*this) *= y;}


  mat pow(long long n){//正方行列のみ
    mat<T> res(h,w);
    mat<T> ret(h,w,0);
    mat<T> a(h,w);
    for(int i = 0; h > i; i++){
      ret[i][i] = 1;
    }
    for(int i = 0; h > i; i++){
      for(int j = 0; w > j; j++){
        a[i][j] = (*this)[i][j];
      }
    }
    while(n > 0){
      if(n & 1){
        ret *= a;
      }
      a *= a;
      n/=2;
    }
    for(int i = 0; h > i; i++){
      for(int j = 0; w > j; j++){
        res[i][j] = ret[i][j];
      }
    }
    return res;
  }


  // Requirement: h==w
  pair<bool, mat> inv(){
    if(h != w)return {false, base()};
    mat<T> gaussianMat(h, 2*w, 0);
    for(int i = 0; h > i; i++){
      for(int j = 0; w > j; j++){
        gaussianMat[i][j] = (*this)[i][j];
      }
    }
    for(int i = 0; h > i; i++){
      gaussianMat[i][w+i] = 1;
    }

    for(int i = 0; h > i; i++){
      for(int j = i; h > j; j++){
        if(gaussianMat[j][i] != 0){
          swap(gaussianMat[i], gaussianMat[j]);
        }
      }
      T initCoeffient = gaussianMat[i][i];
      if(initCoeffient == 0){
        return {false, base()};
      }
      for(int j = 0; 2*w > j; j++){
        gaussianMat[i][j] /= initCoeffient;
      }
      for(int j = i+1; h > j; j++){
        T deleteCoeffient = gaussianMat[j][i] * -1;
        for(int k = i; 2*w > k; k++){
          gaussianMat[j][k] += deleteCoeffient * gaussianMat[i][k];
        }
      }
    }

    for(int i = 0; h > i; i++){
      if(gaussianMat[i][i] != 1){
        T normarizeCoeffient = gaussianMat[i][i];
        if(normarizeCoeffient == 0)continue;
        for(int j = i; 2*w > j; j++){
          gaussianMat[i][j] /= normarizeCoeffient;
        }
      }
    }

    for(int i = h-1; 0 <= i; i--){
      for(int j = 0; i > j; j++){
        T deleteCoeffient = gaussianMat[j][i] * -1;
        for(int k = i; 2*w > k; k++){
          gaussianMat[j][k] += deleteCoeffient * gaussianMat[i][k];
        }
      }
    }

    mat v(h, w);
    for(int i = 0; h > i; i++){
      for(int j = 0; w > j; j++){
        v[i][j] = gaussianMat[i][j+w];
      }
    }
    return {true, v};
  }

  friend istream &operator>>(istream &is, mat &m){
    for(int i = 0; m.h > i; i++){
      for(int j = 0; m.w > j; j++){
        is>>m.x[i][j];
      }
    }
    return is;
  }

  friend ostream &operator<<(ostream &os, const mat &m){
    for(int i = 0; m.h > i; i++){
      for(int j = 0; m.w > j; j++){
        os << m.x[i][j];
        if(j+1 != m.w)cout << " ";
      }
      if(i+1 != m.h)cout << "\n";
    }
    return os;
  }
};
int main(){
  long long x;cin>>x;
  vector<vector<mint>> k(6, vector<mint>(6, 1));
  vector<vector<mint>> S(6, vector<mint>(1, 1));
  for(int i = 0; 6 > i; i++){
    for(int j = 0; 6 > j; j++){
      k[i][j] = (i <= j ? (mint)1/(mint)6 : 0);
      for(int l = 0; i > l; l++){
        k[i][j] += k[l][j]/6;
      }
    }
  }
  mat<mint> A(k), B(S);
  for(int i = 0; 6 > i; i++){
    B[i][0] = (mint)uPow(7LL, max((long long)i-1, 0LL), MODx)/(mint)uPow(6LL, (long long)i, MODx);
  }
  cout << (A.pow(x/6)*B)[x%6][0] << endl;
  return 0;
}