import java.util.Scanner;
class HW2p7
{
  static double pdfOld=-1.;
  static double xOld=0.;
  public static void main(String[] args)
  {
    Scanner sc=new Scanner(System.in);
//**********************************************************************
//                                                                     *
//     Get the number of histories desired                             *
//                                                                     *
//**********************************************************************
    while(true)
    {
      System.out.println("\n Number of bins?");
      int nbin=sc.nextInt();
      System.out.println("\n Lower limit of bins?");
      double a=sc.nextDouble();
      System.out.println("\n Upper limit of bins?");
      double b=sc.nextDouble();
      double dx=(b-a)/(double)nbin;
      int n=0;
      System.out.println("\n Number of histories?");
      int ntry=sc.nextInt();
      if(ntry < 0)System.exit(0);
      if(ntry >0)n=ntry;
//**********************************************************************
//                                                                     *
//     Initialize the two bins we will be collecting information in.   *
//                                                                     *
//**********************************************************************
      double[] total_score=new double[nbin];
      double[] total_squared=new double[nbin];
//**********************************************************************
//                                                                     *
//     For each history:                                               *
//                                                                     *
//**********************************************************************
      for(int ihistory=0;ihistory<n;ihistory++)
      {
//**********************************************************************
//                                                                     *
//       Call getX get the x value for this history                    *
//                                                                     *
//**********************************************************************
        double x=getX();
//**********************************************************************
//                                                                     *
//       Contribute to the average and average_squared bins            *
//                                                                     *
//**********************************************************************
        int ibin=(int)((x-a)/dx);
        if(ibin>-1 && ibin < nbin)
        {
          total_score[ibin]+=1.;
          total_squared[ibin]+=1.*1.;
        }
      }
//**********************************************************************
//                                                                     *
//     After all histories have been run:                              *
//                                                                     *
//       Find the estimate of the average                              *
//                                                                     *
//**********************************************************************
      for(int i=0;i<nbin;i++)
      {
        double xhat=total_score[i]/n/(b-a);
        double x2hat=total_squared[i]/n/(b-a);
//**********************************************************************
//                                                                     *
//       Find the sample variance and sample standard deviation        *
//                                                                     *
//**********************************************************************
        double sample_variance=(double)n/(double)(n-1)*(x2hat-xhat*xhat);
        double sample_sd=Math.sqrt(sample_variance);
//**********************************************************************
//                                                                     *
//       Find the mean variance and mean standard deviation            *
//                                                                     *
//**********************************************************************
        double mean_variance=sample_variance/(double)(n-1);
        double mean_sd=Math.sqrt(mean_variance);
//**********************************************************************
//                                                                     *
//       Print out the results for this run                            *
//                                                                     *
//**********************************************************************
        System.out.printf(" For = %1$9d (%2$6.2f,%3$6.2f) ==> %4$10.5f +/- %5$10.5f  (%6$6.3f percent)\n",
        (i+1),i*dx,(i+1)*dx,xhat*nbin,mean_sd*nbin,mean_sd/xhat*100.);
      }
    }
  }
//**********************************************************************
//**********************************************************************
  static double  getX()
  {
    double a=0.;
    double b=Math.PI;
    double xtry=Math.random()*(b-a)+a;
    double ret=xtry;
    double pdfNew=2.*xtry+Math.sin(xtry);
//**********************************************************************
//                                                                     *
// Rule 1 if new PDF is greater, go to it                              *
//                                                                     *
//**********************************************************************
    if(pdfNew>pdfOld)
    {
      ret=xtry;
      pdfOld=pdfNew;
    }
    else
    {
//**********************************************************************
//                                                                     *
// Rule 2 if not, go to new PDF with probability pdfNew/pdfOld         *
//                                                                     *
//**********************************************************************
      if(Math.random()<pdfNew/pdfOld)
      {
        ret=xtry;
        pdfOld=pdfNew;
      }
      else
      {
//**********************************************************************
//                                                                     *
// Rule 3 Otherwise, stay with the old value of x/                     *
//                                                                     *
//**********************************************************************
        ret=xOld;
      }
    }
    xOld=ret;
    return ret;
  }
}