Homework 6
CS2110 Progamming for Informatics
Due Thursday, March 25, 2021, by 10:00pm
6 points

1. Create a Box class, representing rectangular 3D boxes. The boxes can be any size and can be located anywhere in 3D space, but in this simple version their orientations are fixed so that their edges are always aligned with/parallel to coordinate system axes. You class must implement all the methods below:

__init__(self, centerX = 0.0, centerY = 0.0, centerZ = 0.0, width = 1.0, height = 1.0, depth = 1.0)
setCenter(self, x, y, z)
setWidth(self, width)
setHeight(self, height)
setDepth(self, depth)
volume(self)
surfaceArea(self)
overlaps(self, otherBox). box1.overlaps(box2) should return True if the two 3D boxes touch/intersect at all, even they just touch exactly at their edges or corners. (Think of boxes as filled/solid objects so that if a box fully contains another, they are also considered to be overlapping.)
isInside(self, otherBox). box1.isInside(box2) should return True if no point of box 1 is outside or even on the boundary of box2
__repr__(self)

Note that "width" is a box's extent along the x dimension, while "height" and "depth" are the y and z extents, respectively.
Note: think carefully about the overlaps and contains test. It is easy to get these wrong. I recommend (before you start coding) sketching some pictures to help you analyze the possibilities.

Use of the class in a Python shell might look like this:

   >>> box1 = Box(10.0, 5.0, 0.0, 2.0, 1.0, 1.0)
   >>> box1
   < 2-by-1-by-1 3D box with center at (10.0, 5.0, 0.0) >
   >>> box2 = Box(0, 0, 0, 3.5, 2.5, 1.0)
   >>> box1.volume()
   2.0
   >>> box2.surfaceArea()
   29.5
   >>> box1.overlaps(box2)
   False
   >>> box1.setCenter(2.75, 0.0, 0.0)
   >>> box1.overlaps(box2)
   True
   >>> box1.setCenter(2.76, 0.0, 0.0)
   >>> box1.overlaps(box2)
   False
   >>> box1.setCenter(2.75, 1.75, 1.0)
   >>> box1.overlaps(box2)
   True
   >>> box1.setCenter(0.0, 0.0, 0.0)
   >>> box1.overlaps(box2)
   True
   >>> box1.setWidth(50.0)
   >>> box1.overlaps(box2)
   True
   >>> box1.setDepth(50.0)
   >>> box2.overlaps(box1)
   True
   >>> box3 = Box(0, 0, 0)
   >>> box3.isInside(box3)
   False
   >>> box4 = Box(0.5, 0.0, 0.0, 2.0, 3.0, 4.0)
   >>> box3.isInside(box4)
   False
   >>> box4.setWidth(2.1)
   >>> box3.isInside(box4)
   True

2. Create a NimGame class that implements a two-player Nim-style game (see http://en.wikipedia.org/wiki/Nim for details of several variants). The game starts with one or more "heaps" of one or more items (we'll call them balls). Players take turns removing one or more balls from any heap. The player who removes the last item wins . You can play an interactive on-line version of the game here: here. Note that the on-line version is slightly different in that the player who removes the last item loses.

For this assignment, we'll keep things simple. Assume there's one human player playing against the computer and that the human always goes first.
To create the NimGame class, implement at least three methods:

an __init__ method, with one argument, a list specifying the number of balls in each heap initially
a __repr__ method that will print a nice human readable representation of the game state.
a remove method, with two arguments specifying how many balls the human player wishes to remove and the heap from which to remove them. This method should check that the specified number of balls and specified heap are valid. If the input is not valid, print an appropriate message but do not modify the game state. If the input is valid, remove the balls, and check whether or not the game is over/the player has won. If the game is not over, the method should then automatically select a (legal) number of balls for the computer to remove from some heap, either randomly or through a "smart" strategy, and it should update the game state accordingly (and check whether the game is over/computer has won). Note: you might want to add an additional internally-used method, gameOver, that returns True or False based on the current game state.

A sample use of the class might produce these results:

>>> game = NimGame([2,3,4])
Nim game initialized with 3 heaps.
>>> game
< Nim game with 3 heaps.
	Heap 0: 2 balls
	Heap 1: 3 balls
	Heap 2: 4 balls
>
>>> game.remove(2, 0)
You took 2 balls from heap 0.
Computer took 1 balls from heap 1
>>> game.remove(5,2)
You can't take that many balls from heap 2. Try again.
>>> game
< Nim game with 3 heaps.
	Heap 0: 0 balls
	Heap 1: 2 balls
	Heap 2: 4 balls
>
>>> game.remove(2,1)
You took 2 balls from heap 1.
Computer took 4 balls from heap 2
Computer wins!

3. Add one additional subclass of Animal, including at least one new method, to
the code from animals.py.  


Submit to ICON exactly one Python file.