Description
The goal of this assignment is to learn and practice (via programming) the concepts that we
have learned so far: numbers, algebraic expressions, boolean expressions, strings, operations
on strings, type conversion, variables, use of Python’s builtin functions including input and
output functions, designing your own functions, documenting your own functions via
docstrings, and testing your functions. Before you can start this assignment, you need to know
how to use a (IDLE’s) text editor to edit python modules (i.e. files) as well as how to use
python shell interactively to test your code. If you have no idea how to do these things
watching video of the 2nd and 3rd lecture, for example, will help. Submit your assignment by
the deadline via Brightspace (as instructed and practiced in the first lab.) You can make
multiple submissions, but only the last submission before the deadline will be graded. What
needs to be submitted is explained next.
IMPORTANT NOTE for this and future assignments:
Your grade will partially be determined by automatic (unit) tests that will test your functions.
All the specified requirements below are mandatory (including function names, and the
behaviour implied by examples in Section 2). Any requirement that is specified and not met
may/will result in deduction of points. Your 3 tests will be graded in similar way.
The assignment has 13 programming questions (in Section 1 below). Each question asks you to
design one function. Put all these functions (for all the questions below) in ONE file only,
called a1_xxxxxx.py (where xxxxxx is replaced with your student number). Within this file,
a1_xxxxxx.py, separate your answers (i.e. code) to each question with a comment that looks
like this:
###################################################################
# Question X
###################################################################
To have an idea on what this file a1_xxxxxx.py should look like, I included with this
assignment a solution to an nonexistent assignment. You can view this mockup solution by
opening the included file called a1_mockup_assignment_solution.py
In addition to a1_xxxxxx.py you must submit two more files called a1_xxxxxx.txt and
declaration-YOUR-FULL-NAME.txt What should be in those files is explained below. Put all
these three required documents into a folder called a1_xxxxxx where you changed xxxxxx to
your student number, zip that folder (do not use rar compression format) and submit it as
explained in Lab 1. Submit that compressed folder by the deadline via Brightspace.
About declaration-YOUR-FULL-NAME.txt file:
It needs to be a plane text file and it must contain references to any code you used that you
did not write yourself, including any code you got from a friend, internet, social media/
forums (including Stack Overflow and discord) or any other source or person. The only
exclusion from that rule is the code that we did in class or as part of the lab work and code
from official python.org documentation. So here is what needs to be written in that file. In
every question where you used code from somebody else, you must write:
1. question number
2. copy-pasted parts of the code that were written by somebody else. That includes the code
you found/were-given that you then slightly modified.
3. whose code it is: name of a person or place on internet/book where you found it.
While you may not get points for that part of the question, you will not be in position of
being accused of plagiarism.
You have an option not to include this file, however not including declaration-YOUR-FULLNAME.txt will be taken as you declaring that all the code in the assignment was written by
you. Any student caught in plagiarism will receive zero for the whole assignment and will be
reported to the dean. Finally showing/giving any part of your assignment code to a friend also
constitute plagiarism and the same penalties will apply.
Your program must run without syntax errors. In particular, when grading your assignment, TAs
will first open your file a1_xxxxxx.py with IDLE and press Run Module. If pressing Run Module
causes any syntax error, the grade for the whole assignment will be zero.
Furthermore, for each of the functions below, I have provided one or two tests to test your
functions with. For example, you should test question 1 by making function call f_to_k(90)
in the Python shell. To obtain a partial mark your function may not necessarily give the
correct answer on these tests. But if your function gives any kind of python error when run on
the tests provided below, that question will be marked with zero points.
After reading each of these questions once, go to the Section 2: “Testing your code” below
and see what the output of your function should give. In that section, you can find a couple of
function calls and the required results for each question. Studying these example function
calls will help you a lot to understand what each individual question requires, or rather what
its function should do.
To determine your grade, your functions will be tested both with examples provided in
Section 2: “Testing your code” and with some other examples. Thus you too should test your
functions with more example than what I provided in Section 2.
Each function must be documented with docstrings (as will be explained upcoming lectures).
In particular, each function has to have docstrings that specify:
– type contract
– description about what the function does (while mentioning parameter names)
– preconditions, if any
The purpose of this assignment is to practice concepts that you have seen in the first 2.5
weeks of class. Thus this assignment does not require use of loops, if and other branching
statements, lists … etc, (except Question 10 if you want to be creative). Thus you must solve
the questions below without loops, if and other branching statements, lists etc. Question that
break this rule will receive zero since they suggest that the required understanding of the
material covered in first 2.5 weeks is not attained.
Global variables are not allowed. If you do not know what that means, for now, interpret this
to mean that inside of your file a1_xxxxxx.py variables can only be created (ie. assigned
value) inside of the bodies of your functions.
To avoid confusion, unless otherwise specified in the questions here is what you can use in
this assignment:
– comparison operators: <,<=, ==, !=, >, >=
– Boolean operators: and, or, not
– arithmetic operators: +, -, *, /, **, %, //
– the following Python built in functions: print, input, round, len, int, float, str
– string operators: +, *
– any function from the math module (recall import math, dir(math), and then you can call
help on any function in math module. eg. help(math.sqrt) )
– anything from Turtle module
– keywords: def, return
Section 1: Assignment 1 questions
1. (2 points) Write a function mh2kh(s) that given the speed, s, expressed in miles/hour
returns the same speed expressed in kilometres/hour.
2. (2 points) Two numbers a and b are called pythagorean pair if both a and b are
integers and there exists an integer c such that a2 + b2 = c2. Write a
function pythagorean_pair(a,b) that takes two integers a and b as input and returns
True if a and b are pythagorean pair and False otherwise.
3. (2 points) Write a function in_out(xs,ys,side) that takes three numbers as input, where
side is non-negative. Here xs and ys represent the x and y coordinates of the bottom
left corner of a square; and side represents the length of the side of the square.
(Notice that xs, ys, and side completely define a square and its position in the plane).
Your function should first prompt the user to enter two numbers that represent the x
and y coordinates of some query point. Your function should print True if the given
query point is inside of the given square, otherwise it should print False. A point on the
boundary of a square is considered to be inside the square.
4. (2 points) Write a function safe(n) that takes a non-negative integer n as input where n
has at most 2 digits. The function determines if n is a safe number. A number is not
safe if it contains a 9 as a digit, or if it can be divided by 9. The function should test if
n is safe and return True if n is safe and False otherwise.
5. (2 points) Write a function quote_maker(quote, name, year) that returns a sentence,
i.e. a string of the following form: In year, a person called name said: “quote”
See the next Section 2 below for some examples of how your function must behave.
6. (2 points) Write a function quote_displayer() that prompts the user for a quote, name,
and year. The function should then print a sentence using the same format as
specified in the previous question. (To do that, your solution must make a call
to quote_maker function from the previous question to obtain a string that you then
print).
7. (2 points) In this question you will write a function that determines and prints the
result of a rock, paper, scissors game given choices of player 1 and player 2. In
particular, write a function rps_winner() that prompts the user for choice of player 1
and then choice of player 2, and then it displays the result for player 1 as indicated in
the examples given in Section 2. You may assume that the user will only enter words:
rock, paper or scissors in lower case. Recall that paper beats rock, that rock beats
scissors and that scissors beat paper. If both players make the same choice, we have a
draw.
8. (2 points) Write a function fun(x) that takes as input a positive number x and solves
the following equation for y and returns y. The equation is 104y=x+3.
9. (2 points) Write a function ascii_name_plaque(name) that takes as input a string
representing a person’s name and draws (using print function) a name plaque as shown
in the examples given in Section 2 below. Recall that you may not use loops nor if/
branching statements. (Question 10 is the only exceptions to that rule.)
10. (2 points) Write a function draw_train() that draws with Turtle graphics the train from
the image below. If you are imaginative, you may choose to draw something else fun
as long as it is of similar or higher complexity than the train below. In that case, call
the function my_fun_drawing(). Whatever you choose, it should not be simpler than
the train in this image. For example fill in colour of the train is not optional. The
following parts of the image can be skipped: smoke from the engine, green
background, and blue shade on the windows (the windows can be white). In this
questions you can use loops and/or if statements if you want to draw something more
complex.
11. (2 points) Write a function
alogical(n) , that takes as
input a number, n, where n
is bigger or equal to 1, and
returns the minimum
number of times that n
needs to be divided by 2 in
order to get a number
equal or smaller than 1. For
example 5.4/2=2.7. Since
2.7 is bigger than 1, dividing 5.4 once by 2 is not enough, so we continue. 2.7/2=1.35
thus dividing 5.4 twice by 2 is not enough since 1.35 is bigger than 1. So we continue.
1.35/2=0.675. Since 0.675 is less than 1, the answer is 3. In particular, these
calculations determine that 5.4 needs to be divided by 2 three times minimum in order
to get a number that is less than or equal to 1. See Section 2 for more examples.
Recall that you may not use loops nor if/branching statements. (Question 10 are the
only exceptions to that rule.)
12. (2 points) Write a function cad_cashier(price,payment) that takes two real nonnegative numbers with two decimal places as input, where payment>=price and where
the second decimal in payment is 0 or 5. They represent a price and payment in
Canadian dollars. The function should return a real number with 2 decimal places
representing the change the customer should get in Canadian dollars. Recall that in
Canada, while the prices are expressed in pennies, the change is based on rounding to
the closest 5 cents. See the examples in Section 2 for clarification and examples on
how your function must behave.
13. (5 points) Suppose that a cashier in Canada owes a customer some change and that the
cashier only has coins ie. toonies, loonies, quarters, dimes, and nickels. Write a
function that determines the minimum number of coins that the cashier can return. In
particular, write a function min_CAD_coins(price,payment) that returns five numbers
(t,l,q,d,n) that represent the smallest number of coins (toonies, loonies, quarters,
dimes, and nickels) that add up to the amount owed to the customer (here price and
payment are defined as in the previous question). You program must first call
cad_cashier function, from question 13, to determine the amount of change that
needs to be returned. Then before doing anything else, you may want to convert this
amount entirely to cents (that should be of type int). Once you have the total number
of cents here are some hints on how to find the minimum number of coins.
Hints for your solution (algorithm) for question 14:
To find the minimum number of coins the, so called, greedy strategy (i.e. greedy algorithm)
works for this problem. The greedy strategy tries the maximum possible number of the
biggest-valued coins first, and then the 2nd biggest and so on. For example, if price is $14.22
and payment $20, the customer is owed $5.80 (after rounding to closest 5 cents), thus 580
cents, the greedy strategy will first figure the maximum number of toonies it can give to the
customer. In this case, it would be 2 toonies. It cannot be 3 toonies as that equals $6 and the
cashier would return too much money. Once the cashier returns 2 toonies, he/she still needs
to return 180 cents. The next biggest coin after toonie is a loonie. So the greedy strategy
would try loonies next. Only 1 loonie can fit in 180 cents, so the cashier should next return 1
loonie. Then there is 80 cents left. The next biggest coin to consider is a quarter … and so on
… ending with nickels. (For this example the function should return (2,1,3,0,1) ). Thus for this
question, you are asked to implement this strategy to find the optimal solution. See section 2
for more examples.
Side note: in the Canada (and most other) coin systems, the greedy algorithm of picking the
largest denomination of coin which is not greater than the remaining amount to be made will
always produce the optimal result (i.e. give the smallest number of coins). This is not
automatically the case, though: if the coin denominations were 1, 3 and 4 cents then to make
6 cents, the greedy algorithm would choose three coins: one 4-cent coin and two 1-cent coins
whereas the optimal solution is two 3-cent coins.
Section 2: Testing your code
We would like to see evidence that you have tested your functions in python shell, like we did
in class. Do this by opening your assignment solution, i.e. opening a1_xxxxxx.py, with IDLE
and then test each of your functions individually. Then copy and paste the python shell
output into a text file called a1_xxxxxx.txt The contents of a1_xxxxxx.txt must have
something like this in it:
>>> # testing Question 1
>>>
>>> mh2kh(5)
8.0467
>>>
>>> mh2kh(110.4)
177.67113600000002
>>>
>>>
>>> # testing Question 2
>>>
>>> pythagorean_pair(2,2)
False
>>> pythagorean_pair(6,2)
False
>>> pythagorean_pair(6,8)
True
>>> pythagorean_pair(300,-400)
True
>>>
>>>
>>> # testing Question 3
>>>
>>> in_out(0,0,2.5)
Enter a number for the x coordinate of a query point: 0
Enter a number for the y coordinate of a query point: 1.2
True
>>> in_out(2.5,1,1)
Enter a number for the x coordinate of a query point: -1
Enter a number for the y coordinate of a query point: 1.5
False
>>> in_out(-2.5,1,2.1)
Enter a number for the x coordinate of a query point: -1
Enter a number for the y coordinate of a query point: 1.5
True
>>>
>>>
>>> # testing Question 4
>>>
>>> safe(93)
False
>>> safe(82)
True
>>> safe(29)
False
>>> safe(36)
False
>>> safe(9)
False
>>> safe(7)
True
>>>
>>>
>>> # testing Question 5
>>>
>>> quote_maker(“Everything should be made as simple as possible but not simpler.”, “Albert Einstein”, 1933)
‘In 1933, a person called Albert Einstein said: “Everything should be made as simple as possible but not simpler.”‘
>>>
>>> quote_maker(“I would never die for my beliefs because I might be wrong.”, “Bertrand Russell”, 1951)
‘In 1951, a person called Bertrand Russell said: “I would never die for my beliefs because I might be wrong.”
>>>
>>>
>>> # testing Question 6
>>>
>>> quote_displayer()
Give me a quote: The best lack all conviction while the worst are full of passionate intensity.
Who said that? Bertrand Russell
What year did she/he say that? 1960
In 1960, a person called Bertrand Russell said: “The best lack all conviction while the worst are full of passionate intensity.”
>>>
>>>
>>> # testing Question 7
>>>
>>> rps_winner()
What choice did player 1 make?
Type one of the following options: rock, paper, scissors: rock
What choice did player 2 make?
Type one of the following options: rock, paper, scissors: paper
Player 1 wins. That is False
It is a tie. That is not True
>>> rps_winner()
What choice did player 1 make?
Type one of the following options: rock, paper, scissors: paper
What choice did player 2 make?
Type one of the following options: rock, paper, scissors: rock
Player 1 wins. That is True
It is a tie. That is not True
>>> rps_winner()
What choice did player 1 make?
Type one of the following options: rock, paper, scissors: scissors
What choice did player 2 make?
Type one of the following options: rock, paper, scissors: paper
Player 1 wins. That is True
It is a tie. That is not True
>>> rps_winner()
What choice did player 1 make?
Type one of the following options: rock, paper, scissors: paper
What choice did player 2 make?
Type one of the following options: rock, paper, scissors: paper
Player 1 wins. That is False
It is a tie. That is not False
>>>
>>>
>>> # testing Question 8
>>>
>>> fun(7)
0.25
>> fun(20)
0.3404319590043982
>>> fun(999999997)
2.25
>>> fun(0.1)
0.12284042345856817
>>>
>>>
>>> # testing Question 9
>>>
>>> ascii_name_plaque(“vida”)
**************
* *
* __vida__ *
* *
**************
>>> ascii_name_plaque(“Captain Kara ‘Starbuck’ Thrace”)
****************************************
* *
* __Captain Kara ‘Starbuck’ Thrace__ *
* *
****************************************
>>> ascii_name_plaque(“Seven of Nine”)
***********************
* *
* __Seven of Nine__ *
* *
***********************
>>>
>>>
>>> # testing Question 10
>>>
>>> draw_train()
>>>
>>>
>>> # testing Question 11
>>>
>>> alogical(5.4)
3
>>> alogical(4)
2
>>> alogical(1000)
10
>>> alogical(4200231)
23
>>>
>>>
>>>
>>> # testing Question 12
>>>
>>> cad_cashier(10.58,11)
0.4
>>> cad_cashier(98.87,100)
1.15
>>> cad_cashier(10.58,15)
4.4
>>> cad_cashier(10.55,15)
4.45
>>> cad_cashier(10.54,15)
4.45
>>> cad_cashier(10.52,15)
4.5
>>> cad_cashier(10.50,15)
4.5
>>>
>>> # testing Question 13
>>>
>>> min_CAD_coins(10.58,11)
(0, 0, 1, 1, 1)
>>> min_CAD_coins(98.87,100)
(0, 1, 0, 1, 1)
>>> min_CAD_coins(10.58,15)
(2, 0, 1, 1, 1)
>>> min_CAD_coins(10.55,15)
(2, 0, 1, 2, 0)
>>> min_CAD_coins(10.54,15)
(2, 0, 1, 2, 0)
>>> min_CAD_coins(10.52,15)
(2, 0, 2, 0, 0)
>>> min_CAD_coins(10.50,15)
(2, 0, 2, 0, 0)
>>> min_CAD_coins(3, 20)
(8, 1, 0, 0, 0)
