class MexicanWave {

    public static void main(String[] args) {
// ( jak nie trudno się domyślić funkcja to x^2)
        double[] x = {-2,1,2,4 };
        double[]y = {3, 1, -3, 8};

//chcemy znaleźć wartość w x = 2
        double y2 = lagrangeInterpolation(x,y,0);
        System.out.println("x = 2 -> y = "+y2);

    }

    public static double lagrangeInterpolation(double[] xs, double[] ys, double x ){
        double t;
        double y = 0.0;

        for(int k = 0; k< xs.length; k++){
            StringBuilder builder = new StringBuilder();
            StringBuilder builder1 = new StringBuilder();
            builder.append(k+1).append(": ");
            t = 1.0;
            for(int j = 0; j < xs.length ; j++){
                if(j != k ){
                    builder.append(String.format("(x-%.0f)/(%.0f-%.0f)*", xs[j], xs[k], xs[j]));
                    builder1.append(String.format("(x-x%d)/(x%d-x%d)*", (j+1), (k+1), (j+1)));
                    t = t * ((x-xs[j])/(xs[k]-xs[j]));
                }
            }
            System.out.println(builder.toString());
            System.out.println(builder1.toString());
            System.out.println();
            y += t*ys[k];
        }
        return y;
    }


}