import java.applet.Applet;
import java.awt.event.*;
import java.awt.*;
import java.util.Arrays;

/*This class does some basic mathematical operations*/

public class BasicMath {
    double x,y;

    public static int abs(int n) {
	int nn=(int)(Math.abs(n));
	return(nn);
    }

    public static int cyclicDistance(int a,int b,int n) {
	int n1=abs(a-b);
	int n2=abs(a-b+n);
	int n3=abs(a-b-n);
	int nn=n1;
	if(nn>n2) nn=n2;
	if(nn>n3) nn=n3;
	return(nn);
    }


    /*both x and t are in (0,1).  When t=0, this
      map is the identity. When t=1, this map
      outputs 1/2.*/

    public static double condition(double x,double t) {
	double a=1-t;
	double b=t/2.0;
	double y=a*x+b;
	return(y);
    }



    public static double[] randomList(int n,double t) {
	double[] y=new double[n+1];
	y[0]=0;
	for(int i=1;i<n+1;++i) {
	    double x=condition(Math.random(),t);
	    y[i]=y[i-1]+x;
	}
	for(int i=0;i<n;++i) y[i]=y[i]/y[n];
	return(y);
    }







}