結果

問題 No.463 魔法使いのすごろく🎲
コンテスト
ユーザー koyumeishi
提出日時 2016-12-14 03:27:57
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 39 ms / 2,000 ms
コード長 7,479 bytes
コンパイル時間 1,313 ms
コンパイル使用メモリ 121,568 KB
実行使用メモリ 5,248 KB
最終ジャッジ日時 2024-11-30 06:59:40
合計ジャッジ時間 2,886 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge4
このコードへのチャレンジ
（要ログイン）
ファイルパターン 結果
sample AC * 3
other AC * 36
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 # 

#include <iostream>
#include <vector>
#include <cstdio>
#include <sstream>
#include <map>
#include <string>
#include <algorithm>
#include <queue>
#include <cmath>
#include <functional>
#include <set>
#include <ctime>
#include <random>
#include <chrono>
#include <cassert>
#include <tuple>
#include <utility>
using namespace std;

namespace {
  using Integer = long long; //__int128;
  template<class T, class S> istream& operator >> (istream& is, pair<T,S>& p){return is >> p.first >> p.second;}
  template<class T> istream& operator >> (istream& is, vector<T>& vec){for(T& val: vec) is >> val; return is;}
  template<class T> istream& operator ,  (istream& is, T& val){ return is >> val;}
  template<class T, class S> ostream& operator << (ostream& os, const pair<T,S>& p){return os << p.first << " " << p.second;}
  template<class T> ostream& operator << (ostream& os, const vector<T>& vec){for(size_t i=0; i<vec.size(); i++) os << vec[i] << (i==vec.size()-1?"":" "); return os;}
  template<class T> ostream& operator ,  (ostream& os, const T& val){ return os << " " << val;}

  template<class H> void print(const H& head){ cout << head; }
  template<class H, class ... T> void print(const H& head, const T& ... tail){ cout << head << " "; print(tail...); }
  template<class ... T> void println(const T& ... values){ print(values...); cout << endl; }

  template<class H> void eprint(const H& head){ cerr << head; }
  template<class H, class ... T> void eprint(const H& head, const T& ... tail){ cerr << head << " "; eprint(tail...); }
  template<class ... T> void eprintln(const T& ... values){ eprint(values...); cerr << endl; }

  class range{ Integer start_, end_, step_; public: struct range_iterator{ Integer val, step_; range_iterator(Integer v, Integer step) : val(v), step_(step) {} Integer operator * (){return val;} void operator ++ (){val += step_;} bool operator != (range_iterator& x){return step_ > 0 ? val < x.val : val > x.val;} }; range(Integer len) : start_(0), end_(len), step_(1) {} range(Integer start, Integer end) : start_(start), end_(end), step_(1) {} range(Integer start, Integer end, Integer step) : start_(start), end_(end), step_(step) {} range_iterator begin(){ return range_iterator(start_, step_); } range_iterator   end(){ return range_iterator(  end_, step_); } };

  inline string operator "" _s (const char* str, size_t size){ return move(string(str)); }
  constexpr Integer my_pow(Integer x, Integer k, Integer z=1){return k==0 ? z : k==1 ? z*x : (k&1) ? my_pow(x*x,k>>1,z*x) : my_pow(x*x,k>>1,z);}
  constexpr Integer my_pow_mod(Integer x, Integer k, Integer M, Integer z=1){return k==0 ? z%M : k==1 ? z*x%M : (k&1) ? my_pow_mod(x*x%M,k>>1,M,z*x%M) : my_pow_mod(x*x%M,k>>1,M,z);}
  constexpr unsigned long long operator "" _ten (unsigned long long value){ return my_pow(10,value); }

  inline int k_bit(Integer x, int k){return (x>>k)&1;} //0-indexed

  mt19937 mt(chrono::duration_cast<chrono::nanoseconds>(chrono::steady_clock::now().time_since_epoch()).count());

  template<class T> string join(const vector<T>& v, const string& sep){ stringstream ss; for(size_t i=0; i<v.size(); i++){ if(i>0) ss << sep; ss << v[i]; } return ss.str(); }

  inline string operator * (string s, int k){ string ret; while(k){ if(k&1) ret += s; s += s; k >>= 1; } return ret; }
}
constexpr long long mod = 9_ten + 7;

using real = double;


//A[n*p]*b[p*1] = x[n*1]
vector<vector<real> > gaussian_elimination(vector<vector<real> > &A, vector<vector<real> > &x){
  bool valid = true;
  int rank=0;
  int n = A.size();
  int p = A[0].size();
  vector< vector<real> > R = A;
  for(int i=0; i<n; i++){
    R[i].insert(R[i].end(), x[i].begin(), x[i].end());
  }
  int m = R[0].size();  //p + x[0].size()

  //print(R);

  //foward
  //row
  for(int i=0; i<n; i++){

    //pivot
    int pivot_row = i;
    real pivot_val = fabs(R[i][i]);
    //choose pivot row
    for(int j=i+1; j<n; j++){
      if(pivot_val < fabs(R[j][i])){
        pivot_row = j;
        pivot_val = fabs(R[j][i]);
      }
    }
    if(pivot_row != i){
      swap(R[i], R[pivot_row]);
    }

    if(pivot_val <= 1e-9){
      
      continue;
    }

    rank++;

    {
      real divisor = 1.0/R[i][i];
      //A[i][j] == 0, such that (0 <= j < i)
      for(int j=i; j<m; j++){
        R[i][j] *= divisor;
      }
    }
    
    for(int j=i+1; j<n; j++){
      real divisor = R[j][i]; // R[j][i]/R[i][i], but R[i][i] is 1.0
      for(int k=i; k<m; k++){
        R[j][k] -= R[i][k] * divisor;
      }
    }
  }

  //backward
  //row
  for(int i=n-1; i>=0; i--){
    for(int j=i-1; j>=0; j--){
      real c = R[j][i];
      for(int k=i; k<m; k++){
        R[j][k] -= R[i][k] * c;
      }
    }
  }

  for(int i=0; i<n; i++){
    bool row_valid = false;
    for(int j=i; j<m; j++){
      if(fabs(R[i][j]) <= 1e-9){
        R[i][j] = 0.0;
      }else if(j<p){
        row_valid = true;
      }
    }
    if(row_valid == false && R[i][n] != 0.0){
      valid = false;
    }
  }
  //print(R);
  // cerr << "rank is " << rank << endl;
  // cerr << (valid?"valid":"invalid, no solutions") << endl;

  return R;
}


int main(){
  int n,m;
  cin >> n,m;

  vector<long long> c(n, 0);
  for(int i=1; i<n-1; i++){
    cin >> c[i];
  }

  vector<vector<real>> M(n, vector<real>(n, 0.0));
  for(auto i : range(n) ){
    if(i<n-1) for(int k : range(1,m+1)){
      int p = i+k;
      if( p > n-1 ){
        p = n-1-(p-n+1);
      }
      M[i][p] += (real)1.0/m;
    }
    if(i==n-1){
      M[i][i] = 1.0;
    }
  }

  vector<vector<real>> I(n-1, vector<real>(n-1, 0.0));
  for(auto i : range(n-1) ){
    I[i][i] = 1.0;
  }
  vector<vector<real>> Q(n-1, vector<real>(n-1, 0.0));
  for(auto i : range(n-1) ){
    for(auto j : range(n-1) ){
      Q[i][j] = I[i][j] - M[i][j];
    }
  }

  auto P_ = gaussian_elimination(Q,I);
  vector<vector<real>> P(n-1, vector<real>(n-1, 0.0));
  for(auto i : range(n-1) ){
    for(auto j : range(n-1) ){
      P[i][j] = P_[i][j+n-1];
    }
  }

  eprintln(join(P, "\n"));

  vector<real> EE(n-1, 0);
  for(int i : range(n-1)){
    //EE[i] -= c[i];
    for(int j : range(0, n-1)){
      EE[i] += P[i][j] * c[j];
    }
  }

  EE.push_back(0.0);

  eprintln("exp : " , join(EE, " "));

  real ans = EE[0];
  for(int i=1; i<=m; i++){
    ans = min(ans, EE[i]);
  }

  //eprintln(ans);

  for(int p=1; p<n; p++){
    vector<vector<real>> ii(p, vector<real>(p, 0.0));
    vector<vector<real>> qq(p, vector<real>(p, 0.0));
    for(auto i : range(p) ){
      ii[i][i] = 1.0;
      qq[i][i] = 1.0;
    }
    for(int i=0; i<p-m; i++){
      for(int j=0; j<p; j++){
        qq[i][j] -= M[i][j];
      }
    }

    auto p_ = gaussian_elimination(qq, ii);
    for(int i : range(p)){
      for(int j : range(p)){
        qq[i][j] = p_[i][j+p];
      }
    }

    //eprintln(join(qq, "\n"));

    real ee = 0.0;
    for(int j: range(p)){
      ee += qq[0][j] * c[j];
    }

    //eprintln(ee);

    ans = min(ans, ee + EE[p]);

    eprintln( p , ans);
  }

  vector<vector<double>> dp(2, vector<double>(n, 1e18));
  dp[0] = dp[1] = EE;
  for(int i=n-1; i>n-1-m; i--){
    dp[1][i] = c[i];
  }
  for(int i=n-1-m; i>=0; i--){
    for(int k=1; k<=m; k++){
      int p = i+k;
      dp[1][i] = min(dp[1][i], EE[p]  + c[i]);
    }
    double tmp = 0.0;
    for(int k=1; k<=m; k++){
      int p = i+k;
      tmp += dp[1][p] + c[i];
    }
    tmp *= 1.0/m;

    dp[1][i] = min(tmp, dp[1][i]);
  }
  eprintln(dp[1]);
  ans = min(ans, dp[1][0]);


  printf("%.16f\n", (double)ans);

  return 0;
}
0