# How to Think Like a Computer Scientist: The PreTeXt Interactive Edition

## Exercises18.6Exercises

### 1.

We can represent a rectangle by knowing three things: the location of its lower left corner, its width, and its height. Create a class definition for a Rectangle class using this idea. To create a Rectangle object at location (4,5) with width 6 and height 5, we would do the following:
r = Rectangle(Point(4, 5), 6, 5)

Solution.
class Point:
""" Point class for representing and manipulating x,y coordinates. """

def __init__(self, initX, initY):

self.x = initX
self.y = initY

def getX(self):
return self.x

def getY(self):
return self.y

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

class Rectangle:
"""Rectangle class using Point, width and height"""

def __init__(self, initP, initW, initH):

self.location = initP
self.width = initW
self.height = initH

loc = Point(4, 5)
r = Rectangle(loc, 6, 5)
print(r)


### 2.

Add the following accessor methods to the Rectangle class: getWidth, getHeight, __str__.

### 3.

Add a method area to the Rectangle class that returns the area of any instance:
r = Rectangle(Point(0, 0), 10, 5)
test(r.area(), 50)

Solution.
class Point:
""" Point class for representing and manipulating x,y coordinates. """

def __init__(self, initX, initY):

self.x = initX
self.y = initY

def getX(self):
return self.x

def getY(self):
return self.y

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

class Rectangle:
"""Rectangle class using Point, width and height"""

def __init__(self, initP, initW, initH):

self.location = initP
self.width = initW
self.height = initH

def area(self):
return self.width * self.height


### 4.

Write a perimeter method in the Rectangle class so that we can find the perimeter of any rectangle instance:
r = Rectangle(Point(0, 0), 10, 5)
test(r.perimeter(), 30)


### 5.

Write a transpose method in the Rectangle class that swaps the width and the height of any rectangle instance:
r = Rectangle(Point(100, 50), 10, 5)
test(r.width, 10)
test(r.height, 5)
r.transpose()
test(r.width, 5)
test(r.height, 10)

Solution.
class Point:
""" Point class for representing and manipulating x,y coordinates. """

def __init__(self, initX, initY):

self.x = initX
self.y = initY

def getX(self):
return self.x

def getY(self):
return self.y

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

class Rectangle:
"""Rectangle class using Point, width and height"""

def __init__(self, initP, initW, initH):

self.location = initP
self.width = initW
self.height = initH

def transpose(self):
temp = self.width
self.width = self.height
self.height = temp


### 6.

Write a new method in the Rectangle class to test if a Point falls within the rectangle. For this exercise, assume that a rectangle at (0,0) with width 10 and height 5 has open upper bounds on the width and height, i.e. it stretches in the x direction from [0 to 10), where 0 is included but 10 is excluded, and from [0 to 5) in the y direction. So it does not contain the point (10, 2). These tests should pass:
r = Rectangle(Point(0, 0), 10, 5)
test(r.contains(Point(0, 0)), True)
test(r.contains(Point(3, 3)), True)
test(r.contains(Point(3, 7)), False)
test(r.contains(Point(3, 5)), False)
test(r.contains(Point(3, 4.99999)), True)
test(r.contains(Point(-3, -3)), False)


### 7.

Write a new method called diagonal that will return the length of the diagonal that runs from the lower left corner to the opposite corner.
Solution.
class Point:
""" Point class for representing and manipulating x,y coordinates. """

def __init__(self, initX, initY):

self.x = initX
self.y = initY

def getX(self):
return self.x

def getY(self):
return self.y

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

class Rectangle:
"""Rectangle class using Point, width and height"""

def __init__(self, initP, initW, initH):

self.location = initP
self.width = initW
self.height = initH

def diagonal(self):

d = (self.width**2 + self.height**2) ** 0.5
return d


### 8.

In games, we often put a rectangular “bounding box” around our sprites in the game. We can then do collision detection between, say, bombs and spaceships, by comparing whether their rectangles overlap anywhere.
Write a function to determine whether two rectangles collide. Hint: this might be quite a tough exercise! Think carefully about all the cases before you code.