import matplotlib.pyplot as plt
import collections
from enum import Enum, auto
from random import randint

Point = collections.namedtuple("Point", "x y")

class Side(Enum):
    ON = auto()
    ABOVE = auto()
    BELOW = auto()


def sidedness(slope, intersection, p3, eps=0.0000001):
    print(slope * p3[0] + intersection )
    """ finds where a point is in regards to a line """
    if p3[1] - eps <= slope * p3[0] + intersection <= p3[1] + eps or p3[0] - eps <= (p3[1] - intersection)/slope <= p3[0] + eps:
        return Side.ON
    elif p3[1] > slope * p3[0] + intersection:
        return Side.ABOVE
    return Side.BELOW

def diplay_prune_points(points, p1, p2):
    xs = [p[0] for p in points]
    ys = [p[1] for p in points]

    plt.plot(xs, ys, 'ro')
    plt.plot([p1[0], p2[0]], [p1[1], p2[1]])
    plt.show()


def solve1D(points, xm, iteration_num):
    #print("iter:", iteration_num)
    point = points[iteration_num]

    if iteration_num == 0:
        return -float('Inf'), -float('Inf')

    # lad point[1] = point[0] * a + b <=> y = x * a + b
    # isolere b og sæt ind i constraints
    a = None
    b = point[1] - point[0] # * a

    # minimere xm*a + b, hvor b har ny værdi
    # Vi regner kun med koefficienterne
    # obj_fun = (xm - point[0]) + points[1] = (xm*a - xi*a) + y

    # max eller min
    #print("XM og point[0]:", xm, point[0])
    a = xm - point[0]
    #print("a lige her:", a)

    a_constraint_list = []
    # looping over the i constraints
    for p in points[:iteration_num]:
        # we can't make a straigt vertical line
        if p[0] == point[0]:
            if p[1] > point[1]:
                p[0] = p[0] + 0.0001
            else:
                point[0] = point[0] + 0.0001

        print(p, point)
        # Spring over den i'te constraint
        if p != point:
            # y_j - yi
            c = p[1] - point[1]
            # x_j * a - xi * a
            a_diff = p[0] - point[0]

            print(c, a_diff, c/a_diff)
            # det her er forkert og skal fikses
            if a >= 0 and a_diff < 0:
                a_constraint_list.append(-float('Inf'))
            else:
                a_constraint_list.append(c/a_diff)

    # hvis a > 0 så min
    # hvis a < 0 så max.
    if a >= 0:
        v1 = max(a_constraint_list)
        v2 = point[1] - point[0] * v1
        v = (v1, v2)
    elif a < 0:
        v1 = min(a_constraint_list)
        v2 = point[1] - point[0] * v1
        v = (v1, v2)

    return v



def findBridge(points, xm):
    if xm > 0:
        v = (-float('Inf'), -float('Inf'))
    elif xm < 0:
        4 # noget
    else:
        # TODO: xm == 0
        4
    # looping over constraints
    for point in points:
        # checking for violation
        if not point[1] <= point[0] * v[0] + v[1]:
            v = solve1D(points, xm, points.index(point))
            #print("HER OVER: ", v)

    slope = v[0]
    intercept = v[1]

    line_points = [p for p in points if sidedness(slope, intercept, p) == Side.ON]

    if len(line_points) > 3:
        print("Halli HAllo")
        print(line_points)

    return line_points[0], line_points[1]


def find_median(points):
    if len(points) % 2 == 0:
        first_med_idx = int(len(points) / 2 - 1)
        second_med_idx = int(len(points) / 2)
        return (points[first_med_idx][0] + points[second_med_idx][0]) / 2
    else:
        idx = int((len(points)-1) / 2)
        return points[idx][0]


def upperHull(points, all_points):
    print("Punkter:", points)
    if len(points) < 2:
        return []
    xm = find_median(points)

    # end-points of bridge
    (xi, yi), (xj, yj) = findBridge(points, xm)

    #print(xm)
    print((xi, yi), (xj, yj))
    prune_points = [p for p in points if p[0] < xi or xj < p[0]] + [(xi, yi), (xj, yj)]

    # Neden for er mest for visualisering
    prune_all_points = [p for p in all_points if p[0] < xi or xj < p[0]] + [(xi, yi), (xj, yj)]
    diplay_prune_points(prune_all_points, (xi, yi), (xj, yj))

    Pl = [p for p in prune_points if p[0] < xm]
    Pr = [p for p in prune_points if p[0] >= xm]
    #print("Pl:", Pl, "Pr", Pr)

    print("\n")
    # recurse results and return
    ret = [(xi, yi), (xj, yj)]
    ret = ret + [p for p in upperHull(Pl, prune_all_points) if p not in ret]
    ret = ret + [p for p in upperHull(Pr, prune_all_points) if p not in ret]
    return ret



p1 = (2, 1)
p2 = (3, 4)
p3 = (5, 2)
p4 = (6, 5)

list_of_points = []

list_of_points.append(p1)
list_of_points.append(p2)
list_of_points.append(p3)
list_of_points.append(p4)




xs = [p[0] for p in list_of_points]
ys = [p[1] for p in list_of_points]

plt.plot(xs, ys, 'ro')
plt.show()

result = list(sorted(upperHull(list_of_points, list_of_points)))

result
res_xs = [p[0] for p in result]
res_ys = [p[1] for p in result]


#print("result", result)
plt.plot(res_xs, res_ys)
plt.plot(xs, ys, 'ro')
plt.show()