public class Position {

    final   int startDAY = 28800; //Sekunden seit Mitternacht um 8:00(Dienstbeginn)
    private int sec;              //Sekunden seit Mitternacht eines Eintrages
    private double longitude;     //geographische Länge (Dezimalgrad 15.0-17.0)
    private double latitude;      //geographische Breite (Dezimalgrad 47.0-49.0)

    public Position(double longitude, double latitude){
        this.sec       = startDAY;
        this.longitude = longitude;
        this.latitude  = latitude;
    }


    private static double min(double a, double b){
        if(a <= b){
            return a;
        }else{
            return b;
        }
    }


    private static double max(double a, double b){
        if(a >= b){
            return a;
        }else{
            return b;
        }
    }


    private static double pow(double val){
        return val*val;
    }


    // Returns true if (and only if) longitude and latitude of this position (the current object) differ from
    // longitude and latitude of x by at most eps.
    public boolean isClose(Position x, double eps) {
        //eps^2 = a^2(lon) + b^2(lat)
        double aa = pow( max(x.longitude, this.longitude) - min(x.longitude, this.longitude));
        double bb = pow( max(x.latitude, this.latitude) - min(x.latitude, this.latitude));
        System.out.println("dist: " + Math.sqrt(aa+bb) + ", eps: " + eps + ", maxLon: " + max(x.longitude, this.longitude) + ", maxLat: " + max(x.latitude, this.latitude));
        return ( pow(eps) >= aa + bb );
    }

    // Returns true if (and only if) longitude and latitude of this position (the current object) differ from
    // longitude and latitude of any element in xs by at most eps.
    public boolean isCloseToPath(Position[] xs, double eps) {
        for(Position pos : xs){
            if(!this.isClose(pos, eps)){
                return false;
            }
        }
        return true;
    }

    // Parameter xs contains the positions of a tour. A tour is regarded as being stopped at a position in the array
    // if this position is close (difference at most eps) to each of the following 4 positions in the array.
    // The method returns the time (in seconds since midnight) of the first stop (lowest index in the array),
    // or -1 if there is no stop.
    public static int isStopped(Position[] xs, double eps) {
        for(int i=1; i<xs.length; i++){
            int count = 1;
            if( xs[i-1].isClose(xs[i], eps) && ((i-1)+4) < xs.length ){
                for(int x=1; x<=4; x++){
                    if(xs[i-1].isClose(xs[i+x], eps)){
                        count++;
                    }
                    if(count == 4){
                        return xs[i-1].sec;
                    }
                }
            }
        }
        return -1;
    }

    // Returns true if (and only if) the time of each position in xs is higher than that of each other position at a
    // lower index.
    public static boolean chronologic(Position[] xs) {
        for(int i=1; i<xs.length; i++){
            if(xs[i-1].sec > xs[i].sec){
                return false;
            }
        }
        return true;
    }


    // Just for testing ...
    public static void main(String[] args) {
        //**isClose**
        System.out.println("**isClose**");
        Position one = new Position(4,5);
        Position two_1 = new Position(2,3);
        Position two_2 = new Position(2,7);
        Position two_3 = new Position(6,3);
        Position two_4 = new Position(6,7);

        //square(8) = 2.828427....
        //kreis(viertel)
        System.out.println("#1:\t" + one.isClose(two_1, 2.829));        //true
        System.out.println("#2:\t" + one.isClose(two_2, 2.829));        //true
        System.out.println("#3:\t" + one.isClose(two_3, 2.829));        //true
        System.out.println("#4:\t" + one.isClose(two_4, 2.829));        //true

        System.out.println();
        System.out.println("------------");
        System.out.println();

        //**isCloseToPath**
        System.out.println("**isCloseToPath**");
        Position[] xs_1 = new Position[4];
        Position[] xs_2 = new Position[5];
        Position two_5  = new Position(6,8);

        xs_1[0] = two_1;
        xs_1[1] = two_2;
        xs_1[2] = two_3;
        xs_1[3] = two_4;

        System.out.println("#1:\t" + one.isCloseToPath(xs_1, 2.829));   //true

        xs_2[0] = two_1;
        xs_2[1] = two_2;
        xs_2[2] = two_3;
        xs_2[3] = two_4;
        xs_2[4] = two_5;

        System.out.println("#2:\t" + one.isCloseToPath(xs_2, 2.829));   //false

        System.out.println();
        System.out.println("------------");
        System.out.println();

        //**isStopped**
        System.out.println("**isStopped**");
        Position[] test1 = new Position[7];
        Position[] test2 = new Position[2];
        Position p1 = new Position(1, 1.5);
        p1.sec = 1;
        Position p2 = new Position(1, 2);
        p2.sec = 2;
        Position p3 = new Position(1, 2.1);
        p3.sec = 3;
        Position p4 = new Position(1, 2.2);
        p4.sec = 4;
        Position p5 = new Position(1, 2.3);
        p5.sec = 5;
        Position p6 = new Position(1, 2.4);
        p6.sec = 6;
        Position p7 = new Position(3, 4);
        p7.sec = 7;

        test2[0] = p2;
        test2[1] = p1;

        test1[0] = p1;
        test1[1] = p2;
        test1[2] = p3;
        test1[3] = p4;
        test1[4] = p5;
        test1[5] = p6;
        test1[6] = p7;

        System.out.println("#1:\t" + isStopped(test1, 0.5));    // 2
        System.out.println("#2:\t" + isStopped(test2, 0.5));    //-1

        System.out.println();
        System.out.println("------------");
        System.out.println();

        //**chronologic**
        System.out.println("**chronologic**");
        System.out.println("#1:\t" + chronologic(test1));       // true
        System.out.println("#2:\t" + chronologic(test2));       // false
    }
}