//test centralni limitni vety 
#define ndata 1000000 //pocet simulaci
#define nbins 100 //pocet binu
#define pi  3.1415926535897932384626433832795

int run(int N)  //N = kolik nah. prom. U(0,1) secist
{
        double x;
        double y[ndata];  //histogram souctu 
        double x_gauss[nbins],y_gauss[nbins]; //predikce CLT - gausian
        double delta; //sirka binu
        double x_min,x_max;   //minimalni a maximalni hodnota - meze histogramu
        double mu,sigma; //ocekavana hodnota a st dev. gausianu
        int i,k;
        
        printf("N = %d\n",N);
        TRandom3 *gRandom = new TRandom3(); // vytvori generator nahodnych cisel
        x_min=0;  //min. histogramu
        x_max=N;  //max. histogramu
        TH1D *hist = new TH1D("data", "histogram", nbins, x_min, x_max);
        mu=N/2.0; //ocekavana hodnota - predpoved CLT
        sigma=sqrt(N/12.0); //st dev. - predpoved CLT
        printf("mu = %lf\n",mu);
        printf("sigma = %lf\n",sigma);
        
        for(i = 0; i < ndata; i++) 
        {
          y[i]=0; 
          for(k = 0; k < N; k++)
          {
               x=gRandom->Rndm(); //generovani nah. prom. U(0,1)
               y[i]=y[i]+x; //suma N nah. prom. U(0,1)
             } //k
          } //i
               
        delta=(x_max-x_min)/(double)nbins; //vypocet sirky binu 
        printf("delta (bin width) = %lf\n",delta);     
        for(i = 0; i < nbins; i++) //vypocet predikce CLT  (gausianu)
        {
          x_gauss[i]=x_min+i*delta;
          y_gauss[i]=ndata*delta*1.0/(sqrt(2.0*pi)*sigma)*exp(-pow(x_gauss[i]-mu,2)/(2.0*pow(sigma,2)));
        }
        TCanvas *c0 = new TCanvas("c0", "mean",5,5,1200,800); //definice okna
        TH1D *hist = new TH1D("hist", "histogram",nbins,x_min,x_max);//definice histogramu
        for(i = 0; i < ndata; i++) hist->Fill(y[i]);//naplneni histogramu
        TGraph *g0= new TGraph(nbins,x_gauss,y_gauss);//definice grafu s gausianem
        hist->Draw(); //vykresleni histogramu
        g0->SetLineColor(2);//barva cary grafu
        hist->SetTitle("histogram + CLT prediction"); //nadpis grafu
        hist->GetXaxis()->SetTitle("y");  //popis osy y
        hist->GetXaxis()->CenterTitle();
        hist->GetYaxis()->SetTitle("pocet pripadu");  //popis osy y
        hist->GetYaxis()->CenterTitle();
		//hist->GetHistogram()->SetMinimum(-20.);
		hist->SetMinimum(0);
        hist->Draw(); //vykresleni histogramu
        g0->Draw("L");     //nakresli graf        
        return(0);
}