Lab 1: Functions and Control
Due at 11:59pm on Friday, 06/22/2018.
Lab Checkin 1 questions here.
Starter Files
Download lab01.zip. Inside the archive, you will find starter files for the questions in this lab, along with a copy of the Ok autograder.
Submission
By the end of this lab, you should have submitted the lab with
python3 ok submit
. You may submit more than once before the
deadline; only the final submission will be graded.
Check that you have successfully submitted your code on
okpy.org.
 Questions 13 must be completed in order to receive credit for the lab.
 Questions 49 are optional. It is recommended that you complete these problems if you finish the required portion early or on your own time.
Quick Logistics Review
Using Python
When running a Python file, you can use options on the command line to inspect your code further. Here are a few that will come in handy. If you want to learn more about other Python commandline options, take a look at the documentation.
Using no commandline options will run the code in the file you provide and return you to the command line.
python3 lab01.py
i
: Thei
option runs your Python script, then opens an interactive session. In an interactive session, you run Python code line by line and get immediate feedback instead of running an entire file all at once. To exit, typeexit()
into the interpreter prompt. You can also use the keyboard shortcutCtrlD
on Linux/Mac machines orCtrlZ Enter
on Windows.If you edit the Python file while running it interactively, you will need to exit and restart the interpreter in order for those changes to take effect.
python3 i lab01.py
m doctest
: Runs doctests in a particular file. Doctests are surrounded by triple quotes ("""
) within functions. Each test consists of>>>
followed by some Python code and the expected output.python3 m doctest lab01.py
Using OK
In 61A, we use a program called Ok for autograding labs, homeworks, and projects. You should have Ok in the starter files downloaded at the start of this lab. For more information on using Ok commands, learn more here. To use Ok to run doctests for a specified function, run the following command:
python3 ok q <specified function>
By default, only tests that did not pass will show up. You can use the v
option to show all tests, including tests you have passed:
python3 ok v
Finally, when you have finished all the questions in
lab01.py, you must submit the assignment using the
submit
option:
python3 ok submit
Topics
Consult this section if you need a refresher on the material for this lab. It's okay to skip directly to the questions and refer back here should you get stuck.
Division
Let's compare the different divisionrelated operators in Python:
True Division: / (decimal division) 
Floor Division: // (integer division) 
Modulo: % (remainder) 




Notice that Python outputs ZeroDivisionError
for certain cases. We will go over this later in this lab under Error Messages.
One useful technique involving the %
operator is to check
whether a number x
is divisible by another number y
:
x % y == 0
For example, in order to check if x
is an even number:
x % 2 == 0
Functions
If we want to execute a series of statements over and over, we can abstract them away into a function to avoid repeating code.
For example, let's say we want to know the results of multiplying the numbers 13 by 3 and then adding 2 to it. Here's one way to do it:
>>> 1 * 3 + 2
5
>>> 2 * 3 + 2
8
>>> 3 * 3 + 2
11
If we wanted to do this with a larger set of numbers, that'd be a lot of repeated code! Let's write a function to capture this operation given any input number.
def foo(x):
return x * 3 + 2
This function, called foo
, takes in a single argument and will return the
result of multiplying that argument by 3 and adding 2.
Now we can call this function whenever we want this operation to be done:
>>> foo(1)
5
>>> foo(2)
8
>>> foo(1000)
3002
Applying a function to some arguments is done with a call expression.
Call expressions
A call expression applies a function, which may or may not accept arguments. The call expression evaluates to the function's return value.
The syntax of a function call:
add ( 2 , 3 )
  
operator operand operand
Every call expression requires a set of parentheses delimiting its commaseparated operands.
To evaluate a function call:
 Evaluate the operator, and then the operands (from left to right).
 Apply the operator to the operands (the values of the operands).
If an operand is a nested call expression, then these two steps are applied to that operand in order to evaluate it.
return
and print
Most functions that you define will contain a return
statement. The return
statement will give the result of some computation back to the caller of the
function and exit the function. For example, the function square
below takes
in a number x
and returns its square.
def square(x):
"""
>>> square(4)
16
"""
return x * x
When Python executes a return
statement, the function terminates immediately.
If Python reaches the end of the function body without executing a return
statement, it will automatically return None
.
In contrast, the print
function is used to display values in the Terminal.
This can lead to some confusion between print
and return
because calling a
function in the Python interpreter will print out the function's return value.
However, unlike a return
statement, when Python evaluates a print
expression, the function does not terminate immediately.
def what_prints():
print('Hello World!')
return 'Exiting this function.'
print('61A is awesome!')
>>> what_prints()
Hello World!
'Exiting this function.'
Notice also that
return
will preserve the quotes.
Control
Boolean Operators
Python supports three boolean operators: and
, or
, and not
:
>>> a = 4
>>> a < 2 and a > 0
False
>>> a < 2 or a > 0
True
>>> not (a > 0)
False
and
evaluates toTrue
only if both operands evaluate toTrue
. If at least one operand isFalse
, thenand
evaluates toFalse
.or
evaluates toTrue
if at least one operand evaluates toTrue
. If both operands areFalse
, thenor
evaluates toFalse
.not
evaluates toTrue
if its operand evaluates toFalse
. It evaluates toFalse
if its operand evalutes toTrue
.
What do you think the following expression evaluates to? Try it out in the Python interpreter.
>>> True and not False or not True and False
It is difficult to read complex expressions, like the one above, and understand how a program will behave. Using parentheses can make your code easier to understand. Python interprets that expression in the following way:
>>> (True and (not False)) or ((not True) and False)
This is because boolean operators, like arithmetic operators, have an order of operation:
not
has the highest priorityand
or
has the lowest priority
It turns out and
and or
work on more than just booleans (True
,
False
). Python values such as 0
, None
, ''
(the empty string), and []
(the empty list) are considered false values. All other values are considered
true values.
Short Circuiting
What do you think will happen if we type the following into Python?
1 / 0
Try it out in Python! You should see a ZeroDivisionError
. But what about this expression?
True or 1 / 0
It evaluates to True
because Python's and
and or
operators shortcircuit. That is, they don't necessarily evaluate every operand.
Operator  Checks if:  Evaluates from left to right up to:  Example 

AND  All values are true  The first false value  False and 1 / 0 evaluates to False 
OR  At least one value is true  The first true value  True or 1 / 0 evaluates to True 
Shortcircuiting happens when the operator reaches an operand that allows them to make a conclusion about the expression. For example, and
will shortcircuit as soon as it reaches the first false value because it then knows that not all the values are true.
If and
and or
do not shortcircuit, they just return the last
value; another way to remember this is that and
and or
always return the last
thing they evaluate, whether they short circuit or not. Keep in mind that and
and or
don't always return booleans when using values other than True
and False
.
If Statements
You can review the syntax of if
statements in
Section 1.5.4
of Composing Programs.
Tip: We sometimes see code that looks like this:
if x > 3: return True else: return False
This can be written more concisely as
return x > 3
. If your code looks like the code above, see if you can rewrite it more clearly!
While Loops
You can review the syntax of while
loops in
Section 1.5.5
of Composing Programs.
Error Messages
By now, you've probably seen a couple of error messages. They might look intimidating, but error messages are very helpful for debugging code. The following are some common types of errors:
Error Types  Descriptions 

SyntaxError  Contained improper syntax (e.g. missing a colon after an if statement or forgetting to close parentheses/quotes) 
IndentationError  Contained improper indentation (e.g. inconsistent indentation of a function body) 
TypeError  Attempted operation on incompatible types (e.g. trying to add a function and a number) or called function with the wrong number of arguments 
ZeroDivisionError  Attempted division by zero 
Using these descriptions of error messages, you should be able to get a better idea of what went wrong with your code. If you run into error messages, try to identify the problem before asking for help. You can often Google unfamiliar error messages to see if others have made similar mistakes to help you debug.
For example:
>>> square(3, 3)
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
TypeError: square() takes 1 positional argument but 2 were given
Note:
 The last line of an error message tells us the type of the error. In the
example above, we have a
TypeError
.  The error message tells us what we did wrong  we gave
square
2 arguments when it can only take in 1 argument. In general, the last line is the most helpful.  The second to last line of the error message tells us on which line the
error occurred. This helps us track down the error. In the example above,
TypeError
occurred atline 1
.
Required Questions
What Would Python Display (Part 1)?
Q1: WWPD: Control
Use Ok to test your knowledge with the following "What Would Python Display?" questions:
python3 ok q control u
>>> def xk(c, d):
... if c == 4:
... return 6
... elif d >= 4:
... return 6 + 7 + c
... else:
... return 25
>>> xk(10, 10)
______23
>>> xk(10, 6)
______23
>>> xk(4, 6)
______6
>>> xk(0, 0)
______25
>>> def how_big(x):
... if x > 10:
... print('huge')
... elif x > 5:
... return 'big'
... elif x > 0:
... print('small')
... else:
... print("nothin'")
>>> how_big(7)
______'big'
>>> how_big(12)
______huge
>>> how_big(1)
______small
>>> how_big(1)
______nothin'
>>> n = 3
>>> while n >= 0:
... n = 1
... print(n)
______2
1
0
1
Hint: Make sure your
while
loop conditions eventually evaluate to a false value, or they'll never stop! TypingCtrlC
will stop infinite loops in the interpreter.
>>> positive = 28
>>> while positive:
... print("positive?")
... positive = 3
______Infinite Loop
>>> positive = 9
>>> negative = 12
>>> while negative:
... if positive:
... print(negative)
... positive += 3
... negative += 3
______12
9
6
Q2: WWPD: Veritasiness
Use Ok to test your knowledge with the following "What Would Python Display?" questions:
python3 ok q short_circuiting u
>>> True and 13
______13
>>> False or 0
______0
>>> not 10
______False
>>> not None
______True
>>> True and 1 / 0 and False
______Error (ZeroDivisionError)
>>> True or 1 / 0 or False
______True
>>> True and 0
______0
>>> False or 1
______1
>>> 1 and 3 and 6 and 10 and 15
______15
>>> 0 or False or 2 or 1 / 0
______2
>>> not 0
______True
>>> (1 + 1) and 1
______1
>>> 1/0 or True
______Error
>>> (True or False) and False
______False
Coding Practice
Q3: Sum Digits
Write a function that takes in a nonnegative integer and sums its digits. (Using floor division and modulo might be helpful here!)
def sum_digits(n):
"""Sum all the digits of n.
>>> sum_digits(10) # 1 + 0 = 1
1
>>> sum_digits(4224) # 4 + 2 + 2 + 4 = 12
12
>>> sum_digits(1234567890)
45
"""
"*** YOUR CODE HERE ***"
total = 0
while n > 0:
total, n = total + n % 10, n // 10
return total
Use Ok to test your code:
python3 ok q sum_digits
Optional Questions
What Would Python Display (Part 2)?
Q4: WWPD: What If?
Use Ok to test your knowledge with the following "What Would Python Display?" questions:
python3 ok q what_if u
Hint:
return
) does not cause the function to exit!
>>> def ab(c, d):
... if c > 5:
... print(c)
... elif c > 7:
... print(d)
... print('foo')
>>> ab(10, 20)
______10
foo
>>> def bake(cake, make):
... if cake == 0:
... cake = cake + 1
... print(cake)
... if cake == 1:
... print(make)
... else:
... return cake
... return make
>>> bake(0, 29)
______1
29
29
>>> bake(1, "mashed potatoes")
______mashed potatoes
'mashed potatoes'
More Coding Practice
Q5: Fix the Bug
The following snippet of code doesn't work! Figure out what is wrong and fix the bugs.
def both_positive(x, y):
"""Returns True if both x and y are positive.
>>> both_positive(1, 1)
False
>>> both_positive(1, 1)
True
"""
return x and y > 0 # You can replace this line!
return x > 0 and y > 0
The original line (return x and y > 0
) will check that two things are
true:
x
y > 0
When will x
be considered True? In Python, any number that is not 0
is considered True. Thus, the first doctest will fail: x = 1
and 1 != 0
, and y = 1 > 0
, so both clauses are True.
Use Ok to test your code:
python3 ok q both_positive
Q6: Falling Factorial
Let's write a function falling
, which is a "falling" factorial
that takes two arguments, n
and k
, and returns the product of k
consecutive numbers, starting from n
and working downwards.
def falling(n, k):
"""Compute the falling factorial of n to depth k.
>>> falling(6, 3) # 6 * 5 * 4
120
>>> falling(4, 0)
1
>>> falling(4, 3) # 4 * 3 * 2
24
>>> falling(4, 1) # 4
4
"""
"*** YOUR CODE HERE ***"
total, stop = 1, nk
while n > stop:
total, n = total*n, n1
return total
Use Ok to test your code:
python3 ok q falling
Q7: Double Eights
Write a function that takes in a number and determines if the digits contain two adjacent 8s.
def double_eights(n):
"""Return true if n has two eights in a row.
>>> double_eights(8)
False
>>> double_eights(88)
True
>>> double_eights(2882)
True
>>> double_eights(880088)
True
>>> double_eights(12345)
False
>>> double_eights(80808080)
False
"""
"*** YOUR CODE HERE ***"
prev_eight = False
while n > 0:
last_digit = n % 10
if last_digit == 8 and prev_eight:
return True
elif last_digit == 8:
prev_eight = True
else:
prev_eight = False
n = n // 10
return False
Use Ok to test your code:
python3 ok q double_eights
I Want to Play a Game
Now that you have learned about call expressions and control structures, you can code an algorithm! An algorithm is a set of steps to accomplish a task. You use algorithms every day  from adding numbers by hand to getting to your next lecture.
Let's play a number guessing game with Python! Pick a number and Python will guess randomly until it guesses correctly.
All the code for this guessing game will be in lab01_extra.py
. In your terminal,
start an interactive session with Python:
python3 i lab01_extra.py
The guess_random
function will prompt you for a number, ask if its guess is
correct (many times) and return the number of guesses Python had to make. To
tell Python if its guess is correct, just enter y
at the [y/n]
prompt. If
it's wrong, enter n
. Python isn't very good at guessing yet, so if it's
taking too long, you can type CtrlC
to make it stop.
>>> guess_random()
Pick an integer between 1 and 10 (inclusive) for me to guess: 7
Is 1 your number? [y/n] n
Is 5 your number? [y/n] n
...
Randomly guessing works, but you can create an even better guessing strategy.
Q8: Guess Linear
One weakness in the guess_random
strategy is that it can repeat (incorrect)
guesses. Rather than guessing wildly, let's guess numbers in increasing order.
Note:
is_correct
is a function that will ask the user if the guess is correct and returnTrue
if the user confirms that the guess matches the correct number. Feel free to reference the implementation ofguess_random
as you implementguess_linear
.
def guess_linear():
"""Guess in increasing order and return the number of guesses."""
prompt_for_number(LOWER, UPPER)
num_guesses = 1
guess = LOWER
"*** YOUR CODE HERE ***"
while not is_correct(guess):
guess += 1
num_guesses += 1 return num_guesses
The best way to test this function is by playing with it interactively. See if your algorithm does what you expect!
Q9: Guess Binary
Challenge question. The guess_linear
function can take a long time if
your number is large. However, a strategy called binary search can find the
correct number faster. The idea is to start in the middle of the range and
after each incorrect guess ask if the guess is_too_high
or too low. Either
way, you can eliminate half the remaining possible guesses.
Hint: Try using the
is_too_high
function to implement a faster strategy.is_too_high
will returnTrue
if the guess is greater than the correct number.>>> result = is_too_high(5) Is 5 too high? [y/n] y >>> result True
Hint: You may want to update other variables besides
guess
.
def guess_binary():
"""Return the number of attempted guesses. Implement a faster search
algorithm that asks the user whether a guess is less than or greater than
the correct number.
Hint: If you know the guess is greater than the correct number, then your
algorithm doesn't need to try numbers that are greater than guess.
"""
prompt_for_number(LOWER, UPPER)
num_guesses = 1
lower, upper = LOWER, UPPER
guess = (lower + upper) // 2
"*** YOUR CODE HERE ***"
while not is_correct(guess):
if is_too_high(guess):
upper = guess  1
else:
lower = guess + 1
guess = (lower + upper) // 2
num_guesses += 1 return num_guesses
If you choose a number between 1 and 10, this approach should need no more than 4 guesses to find your number.
The best way to test this function is by playing it interactively. Try to think
of edge cases  numbers that might cause your algorithm to do the wrong
thing. If you edit the Python file while running it interactively, you will
need to exit()
and restart the interpreter in order for those changes to take
effect.
So far, your algorithms have only had to find a number between 1 and 10. What if we expanded the possible range of numbers to be between 1 and 100? How many guesses would each algorithm make if you picked 100 to be your number?
A Second Look
Let's try to visualize the two algorithms you've just written! We've provided code that will run each algorithm 1000 times and plot the number of guesses the algorithms had to make. The numbers are randomly chosen from between 1 and 100.
python3 guessing_game_graph.py guess_linear
python3 guessing_game_graph.py guess_binary
Each bar represents the number of guesses the algorithm took to find the
correct number. The height of each bar represents the frequency of each number
of guesses. Look carefully at the axes when comparing the two graphs! You
should see that guess_linear
sometimes took up to 100 guesses; what was the
highest number of guesses that guess_binary
took?
You can see our plots for guess_linear and guess_binary. If your plots only have one bar, make sure your functions are returning the correct number of guesses!