Recursion baby

finite_differences_recursion.py

pts = [(-1, 1), (0, 1), (1, 0), (2, 2), (3, 3), (4, 2)]

def fd(*points, values=None):
    if values is None:
        values = []
    if len(points) == 2:
        x0, y0 = points[0]
        x1, y1 = points[1]
        val = (y1 - y0) / (x1 - x0)
        values.append(val)
        return val, values
    num = (fd(*points[1:], values=values)[0] - fd(*points[:-1], values=values)[0])
    denom = (points[1:][-1][0] - points[:-1][0][0])
    val = num / denom
    values.append(val)
    return val, values


l = [(0, 1), (1, 0), (2, 2)]
print(fd(*l))
l = [(1, 0), (2, 2), (3, 3)]
print(fd(*l))