/**
 * Euclidean calculations on one-dimensional array indices
 */
class Euclid {
    /**
     * Calculate the euclidean distance between two array indices
     *
     * @param current index
     * @param goal index
     * @return the distance from current to goal
     */
    public int distance(int current, int goal) {
        int currentRow = current / width;
        int currentCol = current % height;

        int goalRow = goal / width;
        int goalCol = goal % height;

        return Math.abs(currentRow - goalRow) + Math.abs(currentCol - goalCol);
    }

    /**
     * A string representation of the distance calculation.
     *
     * @param current index
     * @param goal index
     * @return formatted string
     */
    public String distanceString(int current, int goal) {
        return String.format("Distance from %s to %s is %s", current, goal, distance(current, goal));
    }

    // default width
    private int width = 3;

    // default height
    private int height = width;

    // singleton object
    private static Euclid instance;

    /**
     * @return singleton
     */
    Euclid getInstance() {
        return getInstance(width);
    }

    /**
     * @return singleton
     */
   static Euclid getInstance(int n){
        return getInstance(n, n);
    }

    /**
     * @return singleton
     */
    static synchronized Euclid getInstance(int width, int height) {
        if (instance == null){
            instance = new Euclid(width, height);
        }

        return instance;
    }

    // private constructor
    private Euclid(int n) {
        this.width = n;
        this.height = n;
    }

    // private constructor
    private Euclid(int i, int j) {
        this.width = i;
        this.height = j;
    }

    // private constructor
    private Euclid() {}

}