import random
import statistics
from math import inf
from typing import Set, List, Tuple

from scipy.optimize import linprog

import util
from util import Side, Point, gen_point, display


def sidedness(slope: float, intersection: float, p3: Point, flipper: callable, eps=0.0000001) -> Side:
    # finds where a point is in regards to a line
    if flipper(p3.y) - eps <= flipper(slope * p3.x + intersection) <= flipper(p3.y) + eps:
        return Side.ON
    elif p3.y > slope * p3.x + intersection:
        return Side.ABOVE
    return Side.BELOW


def solve_1dlp(c: float, constraints: List[Tuple[float, float]]):
    """
    :param c: c1
    :param constraints: [(ai, bi), ...]
    :return: x1
    """
    try:
        if c > 0:
            return max(b/a for a, b in constraints if a < 0)
        return min(b/a for a, b in constraints if a > 0)
    except ValueError:  # unbounded
        return -inf if c > 0 else inf


assert solve_1dlp(1, [(-1, -2)]) == 2
assert solve_1dlp(1, [(-1, -2), (-1, -3)]) == 3
assert solve_1dlp(1, [(-1, -3), (-1, -2)]) == 3
assert solve_1dlp(-1, [(1, 3), (1, 2)]) == 2
assert solve_1dlp(1, [(-1, 3), (-1, 2)]) == -2


def solve_2dlp(c: Tuple[float, float], constraints: List[Tuple[Tuple[float, float], float]]):
    """
    :param c: (c1, c2)
    :param constraints: [(ai1, ai2, bi), ...]
    :return: x1, x2
    """
    c1, c2 = c
    x1, x2 = (-inf, -inf) if c1 > 0 else (inf, inf)
    #random.shuffle(constraints)

    for i, ((a1, a2), b) in enumerate(constraints[1:], start=0):
        if not a1*x1 + a2*x2 <= b:
            x1 = solve_1dlp(c1 - c2*a1/a2,
                            [(ai1 - ai2*a1 / a2, bi - ai2*b / a2) for (ai1, ai2), bi in constraints[:i]])
            x2 = (b - a1*x1) / a2

    return x1, x2


def mbc_ch(points: Set[Point], flipper: callable) -> Set[Point]:
    if len(points) <= 2:
        return points

    # Find the point with median x-coordinate, and partition the points on this point
    med_x = statistics.median(p.x for p in points)

    # Find left and right points in regards to median
    pl = {p for p in points if p.x < med_x}
    pr = {p for p in points if p.x >= med_x}

    # Find the bridge over the vertical line in pm
    slope, intercept = solve_2dlp((flipper(med_x), flipper(1)),
                                  [((flipper(-p.x), flipper(-1)), flipper(-p.y)) for p in points])

    # Find the two points which are on the line, should work
    on = {p for p in points if sidedness(slope, intercept, p, flipper) == Side.ON}
    left_point = min(on)
    right_point = max(on)

    # Prune the points between the two line points
    pl = {p for p in points if p.x <= left_point.x}
    pr = {p for p in points if p.x >= right_point.x}

    return set.union(mbc_ch(pl, flipper), {left_point, right_point}, mbc_ch(pr, flipper))


def mbc(points: Set[Point]) -> Set[Point]:
    return set.union(mbc_ch(points, lambda x: x), mbc_ch(points, lambda x: -x))


if __name__ == '__main__':
    points = {gen_point(1, 10) for _ in range(20)}

    upper_hull_points = mbc_ch(points, lambda x: x)
    lower_hull_points = mbc_ch(points, lambda x: -x)

    display(points, upper_hull_points.union(lower_hull_points))