Lab 1: Functions and Control

Due at 11:59pm on Friday, 06/22/2018.

Lab Check-in 1 questions here.

Starter Files

Download Inside the archive, you will find starter files for the questions in this lab, along with a copy of the Ok autograder.


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

  • Questions 1-3 must be completed in order to receive credit for the lab.
  • Questions 4-9 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 command-line options, take a look at the documentation.

  • Using no command-line options will run the code in the file you provide and return you to the command line.

  • -i: The -i 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, type exit() into the interpreter prompt. You can also use the keyboard shortcut Ctrl-D on Linux/Mac machines or Ctrl-Z 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
  • -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

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, you must submit the assignment using the --submit option:

python3 ok --submit


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.


Let's compare the different division-related operators in Python:

True Division: /
(decimal division)
Floor Division: //
(integer division)
Modulo: %
>>> 1 / 5

>>> 25 / 4

>>> 4 / 2

>>> 5 / 0
>>> 1 // 5

>>> 25 // 4

>>> 4 // 2

>>> 5 // 0
>>> 1 % 5

>>> 25 % 4

>>> 4 % 2

>>> 5 % 0

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


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 1-3 by 3 and then adding 2 to it. Here's one way to do it:

>>> 1 * 3 + 2
>>> 2 * 3 + 2
>>> 3 * 3 + 2

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)
>>> foo(2)
>>> foo(1000)

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 comma-separated operands.

To evaluate a function call:

  1. Evaluate the operator, and then the operands (from left to right).
  2. 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)
    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 print will display text without the quotes, but return will preserve the quotes.


Boolean Operators

Python supports three boolean operators: and, or, and not:

>>> a = 4
>>> a < 2 and a > 0
>>> a < 2 or a > 0
>>> not (a > 0)
  • and evaluates to True only if both operands evaluate to True. If at least one operand is False, then and evaluates to False.
  • or evaluates to True if at least one operand evaluates to True. If both operands are False, then or evaluates to False.
  • not evaluates to True if its operand evaluates to False. It evaluates to False if its operand evalutes to True.

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 priority
  • and
  • 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 short-circuit. 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

Short-circuiting happens when the operator reaches an operand that allows them to make a conclusion about the expression. For example, and will short-circuit 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 short-circuit, 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
    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


  • 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 at line 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)
>>> xk(10, 6)
>>> xk(4, 6)
>>> xk(0, 0)
>>> 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)
>>> how_big(12)
>>> how_big(1)
>>> how_big(-1)
>>> 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! Typing Ctrl-C 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
>>> False or 0
>>> not 10
>>> not None
>>> True and 1 / 0 and False
Error (ZeroDivisionError)
>>> True or 1 / 0 or False
>>> True and 0
>>> False or 1
>>> 1 and 3 and 6 and 10 and 15
>>> 0 or False or 2 or 1 / 0
>>> not 0
>>> (1 + 1) and 1
>>> 1/0 or True
>>> (True or False) and 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
    >>> sum_digits(4224) # 4 + 2 + 2 + 4 = 12
    >>> sum_digits(1234567890)
"*** 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: print (unlike 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)
    >>> both_positive(1, 1)
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:

  1. x
  2. 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
    >>> falling(4, 0)
    >>> falling(4, 3)  # 4 * 3 * 2
    >>> falling(4, 1)  # 4
"*** YOUR CODE HERE ***"
total, stop = 1, n-k while n > stop: total, n = total*n, n-1 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)
    >>> double_eights(88)
    >>> double_eights(2882)
    >>> double_eights(880088)
    >>> double_eights(12345)
    >>> double_eights(80808080)
"*** 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 In your terminal, start an interactive session with Python:

python3 -i

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 Ctrl-C 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 return True if the user confirms that the guess matches the correct number. Feel free to reference the implementation of guess_random as you implement guess_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 return True if the guess is greater than the correct number.

>>> result = is_too_high(5)
Is 5 too high? [y/n] y
>>> result

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 guess_linear
python3 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!