A Rectangle and a Square can be considered shapes. There are, of course, different kinds of shapes which are defined differently, but share with rectangles and squares that they have an area and circumference. Define an interface class Shape, of which Rectangle and Square are sub(sub)classes. Also define a class Circle that you derive from Shape.

Assignment

Below I give the Shape interface class from the previous exercise, together with the Rectangle and Square classes built on top of it (your submission is graded on its own, so it cannot import anything from another exercise). Shape defines the common interface every shape must support: a method area and a method circumference. Shape itself does not know how to compute either, so both simply return NotImplemented.

class Shape:
    def area( self ):
        return NotImplemented
    def circumference( self ):
        return NotImplemented

class Rectangle(Shape):
    def __init__( self, x, y, w, h ):
        self.x = x
        self.y = y
        self.w = w
        self.h = h
    def __repr__( self ):
        return "[({},{}),w={},h={}]".format( self.x, self.y, 
            self.w, self.h )
    def area( self ):
        return self.w * self.h
    def circumference( self ):
        return 2*(self.w + self.h)

class Square(Rectangle):
    def __init__( self, x, y, side ):
        Rectangle.__init__( self, x, y, side, side )

Now also create a class Circle that inherits directly from Shape (not from Rectangle or Square). A circle is created with the x and y coordinate of its center, and a radius r. If a circle is passed to the builtin functions repr or str, the string "[({},{}),r={}]".format(x, y, r) must be returned. Its area method must return \(\pi r^2\) and its circumference method must return \(2\pi r\) (use math.pi).

Example

>>> shape = Shape()
>>> shape.area()
NotImplemented
>>> shape.circumference()
NotImplemented

>>> r = Rectangle(1, 1, 8, 5)
>>> r
[(1,1),w=8,h=5]
>>> r.area()
40
>>> r.circumference()
26
>>> isinstance(r, Shape)
True

>>> s = Square(2, 3, 4)
>>> s
[(2,3),w=4,h=4]
>>> s.area()
16
>>> s.circumference()
16
>>> isinstance(s, Rectangle)
True
>>> isinstance(s, Shape)
True

>>> c = Circle(0, 0, 3)
>>> c
[(0,0),r=3]
>>> c.area()
28.274333882308138
>>> c.circumference()
18.84955592153876
>>> isinstance(c, Shape)
True
>>> isinstance(c, Rectangle)
False