class Point:
    def __init__(self, x: float, y: float):
        self.x = x
        self.y = y


def interpolation_lagrange(points: list[Point], x: float) -> float:
    interpolation: float = 0.
    n = len(points)
    for i in range(n):
        term: float = 1. # 0.0 will always give 0, it's a product ! So lets put 1
        # Lagrange L(x)
        for k in range(n):
            if k != i:
                term *= ((x - points[k].x) / (points[i].x - points[k].x))
        # interpolation with a piece of Lagrange (y_i)
        interpolation += term * points[i].y

    return interpolation


def interpolation_newton(points: list[Point], x: float) -> float:
    interpolation = 0. # alpha sum
    n = len(points)
    for i in range(n):
        a_i = 1.
        for k in range(n-1):
            a_i *= (points[k+1].y - points[k].y) / (points[k+1].x - points[k].x)

    return interpolation


def ex1() -> None:
    p1 = Point(-1, 0)
    p2 = Point(0, -1)
    p3 = Point(1, 0)
    p4 = Point(3, 70)

    points = []
    points.append(p1)
    points.append(p2)
    points.append(p3)
    points.append(p4)

    """
    
    """

    racine_x_2 = interpolation_lagrange(points, 2.0)
    racine_x_3 = interpolation_lagrange(points, 3.0)
    print(f'racine X = 2 = {racine_x_2}, racine X = 3 = {racine_x_3}')


if __name__ == '__main__':
    ex1()