# Python module for calculating the newton polynom from given points
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# Licensed under the GPLv2 License, Version 2.0 (the "License");
# Copyright (c) Sven Vogel

def combine(p0, p1):
    return (p1[1] - p1[0]) / (p0[1] - p0[0])


def combine_n(*points):
    k = len(points) - 1

    if k == 1:
        return combine(points[0], points[1])
    else:
        return (combine_n(points[1:k]) - combine_n(points[0:(k - 1)])) / (points[k][0] - points[0][0])


def newton_polynom(*points):
    for x in range(len(points)):

        print(combine_n(points[0:x]))

        for y in range(x):
            print(format(" * (x - %s)", points[y][0]))


def test():
    newton_polynom([1, 2], [3, 4], [9, -5])