from math import sqrt
from multipledispatch import dispatch

class PointXY():
    def distance_from_zero(point):
        return sqrt( point.x ** 2 + point.y ** 2 )

    def distance_to(self, point):
        return sqrt( (point.x - self.x) ** 2 + (point.y - self.y) ** 2)

    def if_inside(self, r):
        return (r.a.x <= self.x <= r.b.x) and (r.a.y <= self.y <= r.b.y)

    def __str__(self):
        return 'x = ' + str(self.x) + ' y = ' + str(self.y)

    def __eq__(self, point):
        return self.distance_to(point) == 0

    def __ne__(self, point):
        return self.distance_to(point) != 0

    def __add__(self, point):
        return PointXY(self.x + point.x, self.y + point.y)

    def __mul__(self, multiplier):
        return PointXY(self.x * multiplier, self.y * multiplier)

    def __neg__(self):
        return PointXY(-self.x, -self.y)

    def __invert__(self):
        return PointXY(-self.x, -self.y)

    def __abs__(self):
        return sqrt(pow(self.x, 2) + pow(self.y, 2))

    def __init__(self, x:int, y:int):
        self.x = x
        self.y = y

class Rect():
    def area(self):
        return self.lenght * self.width

    def perimeter(self):
        return (self.lenght + self.width) * 2

    def scale(self, coef):
        self.lenght *= coef
        self.width *= coef

    def rotate(self):
        self.lenght, self.width = self.width, self.lenght

    def has_inside(self, p: PointXY):
        if (self.a.x <= p.x <= self.b.x) and (self.a.y <= p.y <= self.b.y):
            return 'точка внутри прямоуголника'
        else:
            return 'точка вне прямоугольника'

    @dispatch(int, int)
    def __init__(self, x: int, y: int):
        self.lenght = x
        self.width = y

    @dispatch(PointXY, PointXY)
    def __init__(self, a: PointXY, b: PointXY):
        self.a = a
        self.b = b
        self.lenght = sqrt((a.x - a.x) ** 2 + (b.x - a.y) ** 2)
        self.width = sqrt((b.x - a.x) ** 2 + (b.y - b.x) ** 2)

    def __str__(self):
        if str(hasattr(self, 'a')) == 'False':
            return 'x = ' + str(self.lenght) + ' y = ' + str(self.width)
        else:
            return 'x = ' + str(self.lenght) + ' y = ' + str(self.width) + ' a(' + str(self.a.x) + ':' + str(self.a.y) + ')' + ' b(' + str(self.b.x) + ':' + str(self.b.y) + ')'

class Display(Rect):
    def __init__(self, diagonal, height: int, width: int):
        super().__init__(height, width)
        self.diagonal = diagonal
        self.dpi = round((sqrt(pow(self.height, 2) + pow(self.width, 2))) / self.diagonal, 2)

    def get_dpi(self):
        return self.dpi

    def get_pixel_num(self):
        return super().area()

    def area(self):
        return round((self.height / self.get_dpi()) * (self.width / self.get_dpi()), 1)

    def get_resolution_px(self):
        return self.height, self.width