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# Assignment 5: The Game of Nim

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Objectives
● Practice breaking a larger problem down into smaller “mental chunks”using functions
● Gain practice using loops and modulus (%)
Introduction to Top-Down Design
A good way to design large programming problems is to use functions to break them down into
a series of smaller sub-problems, which can be solved somewhat independently and then
combined to arrive at a complete solution. You can essentially focus your attention on solving
each piece of the program, and not get confused with the overall challenge of the whole
program. After checking that each function works correctly (i.e., for a set of inputs, it produces
the expected output), you can then start to stitch the pieces together, now factoring in how they
interlock. Such a process is methodical and reduces the chances of unexpected errors
appearing, because something you expected for one function had unintended consequences
when working with another function. This is known as coupling , and is best to have a program
with minimum coupling between functions.
This technique of breaking a program down into manageable mental chunks is called top-down
design . The programmer typically breaks the algorithm down into smaller and smaller
sub-algorithms. A solution derived from such a planned-out design will tend to be composed of
small, manageable code segments which:
● tackle a specific smaller task,
● are self-contained, and only the inputs and outputs matter,
● will likely be easier to write, and
● will be easier to test and debug, so will save you time in the long run!
One way of testing these small, manageable code segments is known as black-box testing . In
black-box testing of a function, the tester only knows the desired behavior of the function,
namely what the inputs and anticipated expected outcome should be, but not how the function
computes the output. You’ve already seen black-box testing in T4, when you created test cases
for the i_steal_pennies() function:
testit(i_steal_pennies(0.88)==[3, 1, 0, 3])
Pseudocode is an outline of the logic of a program in regular English. It uses the structural
conventions of a programming language but is intended for a human, not a machine, to read. In
the process of creating the pseudocode, the comments describing each function will be easier
for others to understand and later modify the code as necessary (a vital skill in the programming
industry!). Writing the pseudocode for a program is a good practice before writing code,
because it’s easy to ignore syntax problems and focus on creating a good design to the
program. Here is an example pseudocode for the is_even.py code:
function is_even(y):
if y is divisible by 2:
return True
else:
return False
function main():
year = a random integer between 0 and 2015
if is_even(year):
print “Year is even”
else:
print “Year is odd”
main()
Notice the syntax is not Python, but it reads like code. Pseudocode is intended to be readable
by a human, but also convertible to code by a programmer.
The Game of Nim
Nim is a game of logic and strategy. The goal of Nim is to be the player who removes the last of
some group of items (e.g., balls) from a pile. A player must remove some number during their
turn. The player who removes the last one wins. You can try a version of the game at:
http://education.jlab.org/nim/index.html against the computer. In this version, there are 9 or 10
protons in a pile, and you and the computer are each allowed to take either 1 or 2 protons each
time. The player who takes the last proton wins!
The instructions
A key idea in this teamwork is to use fruitful functions for returning values. Note that when a
function returns a value, it is typical to put the value into a variable or use it directly.
The following examples illustrate these ideas and also demonstrate the use of modulus:
● peel_digits.py
● is_even.py
Your task is to create the game of Nim that works as follows (which is slightly different than the
pepper example done in class):
● The human player will give the program the number of balls to start.
● The starting number of balls must be 15 or higher.
● The player will then play against the computer, with the human player going first.
● The player and the computer will then take turns choosing between 1 to 4 balls to
remove from the pile.
● During the human player’s turn, your program will need to ask the human player to input
the number of balls to remove.
● During the computer’s turn, your program will remove a number of balls. More on how
your algorithm determines this number below… for now, assume it’s between 1 and 4
balls.
● The player who takes the last ball wins! Inform the user who wins at the end of the
program.
Hints and Requirements
● Use functions to break code into smaller logical groupings for easier debugging.
● After asking the human player for the number of balls to start, test it to make sure it is 15
or larger. Use a loop to allow the player re-enter the number until it is 15 or larger.
● You will also need to use a loop in order to have play continue until the last ball is
picked.
● In the loop, you will need to alternate between the human player and the computer, but
you may assume the human always plays first.
● When it is the human player’s turn, your program will ask him/her to input the number of
balls they wish to remove. Test this input to make sure it is between 1 and 4, using a
loop to continually ask for the number of balls until it is valid (i.e. between 1 and 4).
● Create a fruitful function which determine how many balls the computer will pick up using
the following strategy (NOTE: The following reveals how to maximize the computer’s
wins. Try to solve it first on your own, based on what you learned in class. The answer is
provided here if you can’t come up with a solution, because I am more interested in your
implementation than your ability to solve this puzzle):
○ An optimal strategy for this version of Nim is to try to make sure that it will be
the opponent’s turn to play when the number of balls in the pile becomes 5. Thus,
the computer will play so that a multiple of 5 balls is always left in the pile after
their turn, then the computer will win. How can you implement this? The
computer should take sufficiently many balls from the pile each time to leave the
opponent with a multiple of 5 balls. (Hint: use the modulus % function here!)
○ If it is not possible to leave the opponent with a pile of balls that is a multiple of 5,
then the computer is going to lose unless the human player makes a mistake. In
this case, have the computer take a randomly chosen number of balls from the
pile, since any strategy is as good as another.
○ Return the number of balls the computer will take from your fruitful function.
● Be sure to announce who has won!
● Be sure to include our standard header at the top of your program with name, username,
assignment number, purpose and acknowledgements. Be sure to give credit where
● Be sure to include good coding practices as we’ve discussed in class, including following
coding standards (see Chapter 7 on Iteration) and the use of a main() function.
● (Optional) You may optionally use graphics, but please make the logic work first because
debugging with graphics is harder. Please be sure to include comments for the sections
in your code which does graphics.
Design Write-up
This assignment requires more planning and design than previous assignments. As such, I’d
like for you to have a process of documenting your thought process throughout this assignment.
Use the space below to document your process. You’ll fill out parts of this table at different
points in the process of thinking about your design and creating code.
INITIAL DESIGN PLAN : Design a pseudocode
plan which meets the computational
requirements to solve the problem. Your
pseudocode does not need to be syntactically
correct. It needs to capture the flow of logic in a
1. First use a loop to ask the player
they pick a number that is 15 or
higher.
2. Have a loop so that the game will
keep playing until the ball count is 0.
3. Have the player take a number of
balls 1-4 and have the computer
take a number of balls that will allow
it to win. If it cannot win based off of
the player’s previous move, take a
random number of balls.
IMPLEMENTATIONS : A list in bullet form of
specifically what was accomplished, including
any challenges overcome and innovations that
were not specifically required by the
assignment.
1. I made it to where the game will
play based on any starting number
higher than 15.
2. I made it to where any chance the
computer has to win, it will.
3. I made the program restrict what
you could input when you got down
to less than 4 balls left, to ensure
you didn’t go into negative numbers.
4. Had the end result print if you won
or lost.
TESTING : A list in bullet form of all input values
used for testing. Here you should be careful to
select representative input cases, including
For starting balls I had 4 different values.
● 15
● 16
both representative typical cases as well as
extreme cases.
● 150
● 151
This was to test both the always winning
side of the computer and the random
integer side of the computer at both the
minimum side, as well as an extreme side.
Before I implemented the computer, I
needed to test to make sure my limitations
on the values that could be inputed when
you reached less than 4 worked.
To do this I once I reached 3, 2, and 1, I
used the values 4, 3, and 2 respectively.
So,
● 4 when it is 3
● 3 when it is 2
● 2 when it is 1
ERRORS : A list in bullet form of all known
errors and deficiencies in your implementation.
● If you put anything other than an
integer when prompted, you will
SUMMARY: A brief summary description of the
design and implementation, including how
much your initial design plan evolved, the final
result you achieved, and the amount of time
you spent as a programmer in accomplishing
these results. This should be no more than two
paragraphs. Consider this like a report of what
you did.
My initial design was just really broad. I
implemented everything in my plan, but
that I did not account for, such as limiting
input values when you reached less than 4
so you did not go below 0. The final result
was a fairly good working nim game. If you
make a mistake the computer will always
win, but if you know what you are doing,
you can always win. I spent about 2 hours
making this program.
comments on and reactions to this assignment.
Consider this like a reflection.
I didn’t think this assignment was too bad. I
am just not sure how specific I need to be
when doing the pseudo code. As previously
mentioned, I was able to implement
everything I said prior to coding, however,
there were some extra things that I needed
to add on later to make everything function
properly.

Assignment 5: The Game of Nim
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