#include <math.h>
#include <stdio.h>
#include <iostream.h>
#include <stdlib.h>
#define EPS 3.0e-14
#define MAXIT 10

long double gammln(long double xx)
{
	double x,y,tmp,ser;
	static double cof[6]={76.18009172947146,-86.50532032941677,24.01409824083091,-1.231739572450155,0.1208650973866179e-2,-0.5395239384953e-5};
	int j;
	y=x=xx;
	tmp=x+5.5;
	tmp-=(x+0.5)*log(tmp);
	ser=1.000000000190015;
	for (j=0;j<=5;j++) ser +=cof[j]/++y;
	return -tmp+log(2.5066282746310005*ser/x);
}

void gaulag(double x[], double w[], int n, float alf)
{
	long double gammln(long double xx);
	//void nrerror(char error_text[]);
	int i,its,j;
	long double ai;
	double p1,p2,p3,pp,z,z1;
	
	for (i=1;i<=n;i++)
	{
		if (i==1)
		{
			z=(1+alf)*(3+0.92*alf)/(1+2.4*n+1.8*alf);
		}
		else if (i==2)
		{
			z+=(15+6.25*alf)/(1+0.9*alf+2.5*n);
		}
		else 
		{
			ai=i-2;
			z+=((1+2.55*ai)/(1.9*ai)+1.26*ai*alf/(1+3.5*ai))*(z-x[i-2])/(1+0.3*alf);
		}
		for (its=1;its<=MAXIT;its++)
		{
			p1=1;
			p2=0;
			for (j=1;j<=n;j++)
			{
				p3=p2;
				p2=p1;
				p1=((2*j-1+alf-z)*p2-(j-1+alf)*p3)/j;
			}
			pp=(n*p1-(n+alf)*p2)/z;
			z1=z;
			z=z1-p1/pp;
			if (fabs(z-z1) <= EPS) break;
		}
		if (its > MAXIT) {printf("Zu viele Iterationen in gaulag\n");exit(1);}
		x[i]=z;
		w[i]=-exp(gammln(alf+n)-gammln((long double)n))/(pp*n*p2);
	}
}

void main()
{
	FILE *stream;
	int n,i;
	int j;
	double s;
	float alf;
	char datei[50];
	printf("n: "); scanf("%d",&n);
	printf("alpha: "); scanf("%f",&alf);
	printf("Ausgabedateiname: "); scanf("%s",datei);
	if ((stream=fopen(datei,"w"))==NULL)
		{
			printf("Kann Datei nicht öffnen!!!");
			exit(1);
		}
	double x[100];double w[100];
	gaulag(x,w,n,alf);
	for (i=1;i<=n;i++) {
	printf("%d: x %lf w %lf\n",i,x[i],w[i]);
	fprintf(stream,"%d: x %lf w %lf\n",i,x[i],w[i]);}
	s=0;
	for (j=1;j<=n;j++)
	{
		s+=w[j]*(1/(1-exp(-x[j])));
	}
	printf("Ergebinis: %lf\n",s);
	fprintf(stream,"Ergebinis: %lf",s);
}