Question

Inheritance - Polymorphism

One advantage of using subclasses is the ability to use polymorphism.

The idea behind polymorphism is that several different types of objects can have the same methods, and be treated in the same way.

For example, have a look at the code we’ve included for this problem. We’ve defined Shape as an abstract base class. It doesn’t provide any functionality by itself, but it does supply an interface (in the form of .area() and .vertices() methods) which are meaningful for any type of 2D Shape.

The total_area function makes use of this to calculate the area of any kind of Shape. We’ve provided an example of this with two Square instances.

We want you to write RightAngledTriangle and Rectangle classes which implement this interface.

The constructor for RightAngledTriangle accepts one argument, vertices, being a list of the points of the triangle relative to its origin. The first vertex will be at the right angle.

The constructor for Rectangle accepts width and height.

class Shape():
"""
A representation of a shape.

"""
def __init__(self, origin=(0, 0)):
"""Construct a shape object
  
Parameters:
origin(tuple<int, int>): origin of the shape
  
"""

self.origin = origin

def area(self):
"""
(int) Return the area of the shape.

"""
raise NotImplementedError()

def vertices(self):
"""
Return the vertices of the shape.

Return:
list<tuple<int, int>>: The vertices of the shape, as a list of tuples
representing two dimensional points.
This list may be returned in any order.
  
"""
raise NotImplementedError()

class Square(Shape):
"""A Square object"""
def __init__(self, side_length, origin=(0, 0)):
"""
Construct a square object
  
Parameters:
side_length (int): Length of the sides of the square
origin (tuple<int, int>): Coordinate of topleft corner of square
  
"""
super().__init__(origin=origin)

self.side_length = side_length

def area(self):
"""
(int) Return the area of the shape.
  
"""
return self.side_length * self.side_length

def vertices(self):
"""
Return the vertices of the shape.

Return:
list<tuple<int, int>>: The vertices of the shape, as a list of tuples
representing two dimensional points.
This list may be returned in any order.
  
"""
x, y = self.origin

return [
(x, y),
(x, y + self.side_length),
(x + self.side_length, y + self.side_length),
(x + self.side_length, y),
]

def total_area(shapes):
"""
Return the total area of the given list of shapes.

Parameters:
shapes (list<Shape>): The list of shapes to sum the area for.

Return:
int: The total area of the list of shapes, being the sum of the area of
each individual shape.

"""
area = 0.

for shape in shapes:
area += shape.area()

return area

def outer_bounds(shapes):
"""
Return the outer bounds of the given list of shapes.

Parameters:
shapes (list<Shape>): The list of shapes to return the outer bounds for.

Return:
tuple<tuple<int, int>, tuple<int, int>>:

The first element of the tuple is the top-left corner of a rectangle
which could enclose every shape in the given list.
The second element of the tuple is the bottom-right corner of that same
rectangle.

The top-left corner of the rectangle will be, at minimum, (0, 0).

"""
vertices = []

for shape in shapes:
for vertex in shape.vertices():
vertices.append(vertex)

top_left_x = 0
top_left_y = 0
bottom_right_x = 0
bottom_right_y = 0

for x, y in vertices:
if x < top_left_x:
top_left_x = x
elif x > bottom_right_x:
bottom_right_x = x

if y < top_left_y:
top_left_y = y
elif y > bottom_right_y:
bottom_right_y = y

return (top_left_x, top_left_y), (bottom_right_x, bottom_right_y)

# example usage
# note that total_area doesn't know nor care that we used instances of Square
shapes = [Square(2), Square(4, origin=(2, 2))]
area = total_area(shapes)

Answer 1

class Shape():
"""
A representation of a shape.

"""

def __init__(self, origin=(0, 0)):
"""Construct a shape object

Parameters:
origin(tuple<int, int>): origin of the shape

"""

self.origin = origin

def area(self):
"""
(int) Return the area of the shape.

"""

raise NotImplementedError()

def vertices(self):
"""
Return the vertices of the shape.

Return:
list<tuple<int, int>>: The vertices of the shape, as a list of tuples
representing two dimensional points.
This list may be returned in any order.

"""

raise NotImplementedError()

class Square(Shape):
"""A Square object"""

def __init__(self, side_length, origin=(0, 0)):
"""
Construct a square object

Parameters:
side_length (int): Length of the sides of the square
origin (tuple<int, int>): Coordinate of topleft corner of square

"""

super().__init__(origin=origin)

self.side_length = side_length

def area(self):
"""
(int) Return the area of the shape.

"""

return self.side_length * self.side_length

def vertices(self):
"""
Return the vertices of the shape.

Return:
list<tuple<int, int>>: The vertices of the shape, as a list of tuples
representing two dimensional points.
This list may be returned in any order.

"""

x, y = self.origin

return [
(x, y),
(x, y + self.side_length),
(x + self.side_length, y + self.side_length),
(x + self.side_length, y),
]

class Rectangle(Shape):
"""A Rectangle object"""

def __init__(self, width, height, origin=(0, 0)):
"""
Construct a rectangle object

Parameters:
width (int): Width of the rectangle
height (int): Height of the rectangle
origin (tuple<int, int>): Coordinate of topleft corner of rectangle

"""

super().__init__(origin=origin)

self.width = width
self.height = height

def area(self):
"""
(int) Return the area of the shape.

"""

return self.width * self.height

def vertices(self):
"""
Return the vertices of the shape.

Return:
list<tuple<int, int>>: The vertices of the shape, as a list of tuples
representing two dimensional points.
This list may be returned in any order.

"""

x, y = self.origin

return [
(x, y),
(x, y + self.height),
(x + self.width, y + self.height),
(x + self.width, y),
]

class RightAngledTriangle(Shape):
"""A RightAngledTriangle object"""

def __init__(self, vertices, origin=(0, 0)):
"""
Construct a right angled triangle object

Parameters:
vertices list<tuple<int, int>>: Length of the sides of the square
origin (tuple<int, int>): Coordinate of topleft corner of square

"""

super().__init__(origin=origin)

self.vertices = vertices

def area(self):
"""
(int) Return the area of the shape.

"""

return (abs(self.vertices[0][0] + self.vertices[0][1] - self.vertices[1][0] - self.vertices[1][1]) *
abs(self.vertices[0][0] + self.vertices[0][1] - self.vertices[2][0] - self.vertices[2][1]))/2

def vertices(self):
"""
Return the vertices of the shape.

Return:
list<tuple<int, int>>: The vertices of the shape, as a list of tuples
representing two dimensional points.
This list may be returned in any order.

"""

return self.vertices

def total_area(shapes):
"""
Return the total area of the given list of shapes.

Parameters:
shapes (list<Shape>): The list of shapes to sum the area for.

Return:
int: The total area of the list of shapes, being the sum of the area of
each individual shape.

"""

area = 0.

for shape in shapes:
area += shape.area()

return area

def outer_bounds(shapes):
"""
Return the outer bounds of the given list of shapes.

Parameters:
shapes (list<Shape>): The list of shapes to return the outer bounds for.

Return:
tuple<tuple<int, int>, tuple<int, int>>:

The first element of the tuple is the top-left corner of a rectangle
which could enclose every shape in the given list.
The second element of the tuple is the bottom-right corner of that same
rectangle.

The top-left corner of the rectangle will be, at minimum, (0, 0).

"""

vertices = []

for shape in shapes:
for vertex in shape.vertices():
vertices.append(vertex)

top_left_x = 0
top_left_y = 0
bottom_right_x = 0
bottom_right_y = 0

for x, y in vertices:
if x < top_left_x:
top_left_x = x
elif x > bottom_right_x:
bottom_right_x = x

if y < top_left_y:
top_left_y = y
elif y > bottom_right_y:
bottom_right_y = y

return (top_left_x, top_left_y), (bottom_right_x, bottom_right_y)

# example usage
# note that total_area doesn't know nor care that we used instances of Square
shapes = [Square(2), Square(4, origin=(2, 2)), Rectangle(2, 3), Rectangle(4, 3, origin=(3, 3)),
RightAngledTriangle([(0, 0), (2, 0), (0, 2)])]
area = total_area(shapes)
print('Total area:', area)