結果

問題 No.75 回数の期待値の問題
ユーザー Taiki0715
提出日時 2023-08-17 17:19:27
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 24 ms / 5,000 ms
コード長 4,895 bytes
コンパイル時間 3,645 ms
コンパイル使用メモリ 259,288 KB
最終ジャッジ日時 2025-02-16 08:59:13
ジャッジサーバーID
（参考情報） 		judge2 / judge3
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ファイルパターン 結果
sample AC * 4
other AC * 16
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

diff #
プレゼンテーションモードにする

#include <bits/stdc++.h>
using namespace std;
#if __has_include(<atcoder/all>)
#include <atcoder/all>
using namespace atcoder;
template<int mod>istream &operator>>(istream &is,static_modint<mod> &a){long long b;is>>b;a=b;return is;}
istream &operator>>(istream &is,modint &a){long long b;cin>>b;a=b;return is;}
#endif
using ll=long long;
using ull=unsigned long long;
using P=pair<ll,ll>;
template<typename T>using minque=priority_queue<T,vector<T>,greater<T>>;
template<typename T>bool chmax(T &a,const T &b){return (a<b?(a=b,true):false);}
template<typename T>bool chmin(T &a,const T &b){return (a>b?(a=b,true):false);}
template<typename T1,typename T2>istream &operator>>(istream &is,pair<T1,T2>&p){is>>p.first>>p.second;return is;}
template<typename T>istream &operator>>(istream &is,vector<T> &a){for(auto &i:a)is>>i;return is;}
template<typename T1,typename T2>void operator++(pair<T1,T2>&a,int n){a.first++,a.second++;}
template<typename T1,typename T2>void operator--(pair<T1,T2>&a,int n){a.first--,a.second--;}
template<typename T>void operator++(vector<T>&a,int n){for(auto &i:a)i++;}
template<typename T>void operator--(vector<T>&a,int n){for(auto &i:a)i--;}
#define reps(i,a,n) for(int i=(a);i<(n);i++)
#define rep(i,n) reps(i,0,n)
#define all(x) x.begin(),x.end()
#define pcnt(x) __builtin_popcount(x)
ll myceil(ll a,ll b){return (a+b-1)/b;}
#ifdef LOCAL
#include "debug.h"
#else
#define debug(...) static_cast<void>(0)
template<typename T1,typename T2>ostream &operator<<(ostream &os,const pair<T1,T2>&p){os<<p.first<<' '<<p.second;return os;}
#endif
void SOLVE();
int main(){
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  #ifdef LOCAL
  clock_t start=clock();
  #endif
  int testcase=1;
  //cin>>testcase;
  for(int i=0;i<testcase;i++){
    SOLVE();
  }
  #ifdef LOCAL
  cout<<"time:";
  cout<<(clock()-start)/1000;
  cout<<"ms\n";
  #endif
}
template<class T>
struct Matrix{
  vector<vector<T>>A;
  Matrix(int h,int w):A(h,vector<T>(w,0)){}
  Matrix(int n):A(n,vector<T>(n,0)){}
  size_t height()const{return A.size();}
  size_t width()const{return A[0].size();}
  const vector<T> &operator[](int k)const{return (A.at(k));}
  vector<T> &operator[](int k){return (A.at(k));}
  Matrix I(size_t n){
    Matrix m(n);
    rep(i,n)m[i][i]=1;
    return m;
  }
  Matrix &operator+=(const Matrix &B){
    size_t h=height(),w=width();
    assert(h==B.height());
    assert(w==B.width());
    rep(i,h)rep(j,w)(*this)[i][j]+=B[i][j];
    return *this;
  }
  Matrix &operator-=(const Matrix &B){
    size_t h=height(),w=width();
    assert(h==B.height());
    assert(w==B.width());
    rep(i,h)rep(j,w)(*this)[i][j]-=B[i][j];
    return *this;
  }
  Matrix &operator*=(const Matrix &B){
    size_t h=height(),w=B.width(),p=width();
    assert(B.height()==p);
    vector<vector<T>>C(h,vector<T>(w,0));
    rep(i,h)rep(k,p)rep(j,w)C[i][j]=(C[i][j]+(*this)[i][k]*B[k][j]);
    A.swap(C);
    return *this;
  }
  Matrix &operator^=(ll k){
    assert(height()==width());
    assert(k>=0);
    Matrix B=I(height());
    while(k){
      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 ll k)const{
    return (Matrix(*this)^=k);
  }
  T det(){
    Matrix<T>b(*this);
    assert(this->height()==this->width());
    T ret=1;
    rep(i,width()){
      int id=-1;
      reps(j,i,width()){
        if(b[j][i]!=0)id=j;
      }
      if(id==-1)return 0;
      if(i!=id){
        ret*=-1;
        swap(b[i],b[id]);
      }
      ret*=b[i][i];
      T inv=b[i][i].inv();
      rep(j,width()){
        b[i][j]*=inv;
      }
      reps(j,i+1,width()){
        T x=b[j][i];
        rep(k,width()){
          b[j][k]-=b[i][k]*x;
        }
      }
    }
    return ret;
  }
  Matrix inv(){
    assert(this->height()==this->width());
    int n=this->height();
    Matrix<T>b(*this);
    Matrix<T>ret=I(n);
    rep(i,n){
      int id=-1;
      reps(j,i,n){
        if(b[j][i]!=0)id=j;
      }
      assert(id!=-1);
      if(i!=id){
        swap(b[i],b[id]);
        swap(ret[i],ret[id]);
      }
      T inv=(double)1/b[i][i];
      rep(j,n){
        b[i][j]*=inv;
        ret[i][j]*=inv;
      }
      rep(j,n)if(i!=j){
        T x=b[j][i];
        rep(k,n){
          b[j][k]-=b[i][k]*x;
          ret[j][k]-=ret[i][k]*x;
        }
      }
    }
    return ret;
  }
};
void SOLVE(){
  int k;
  cin>>k;
  Matrix<double>mat(k);
  rep(i,k)reps(j,1,7){
    if(i+j<k)mat[i][i+j]+=(double)1/6;
    else if(i+j!=k)mat[i][0]+=(double)1/6;
  }
  Matrix<double>I(k);
  rep(i,k)I[i][i]=1;
  mat=I-mat;
  mat=mat.inv();
  mat*=mat;
  double ans=0;
  reps(i,1,7)if(k-i>=0)ans+=mat[0][k-i]/6;
  cout<<ans<<endl;
}
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