Due at 11:59pm on 09/03/2015.

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.


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.

  • Questions 1, 2, 4, and 5 (What Would Python Print?) are designed to help introduce concepts and test your understanding.
  • For the purpose of tracking participation, please complete at least questions 3 and 6 in lab01.py. Submit using OK.
  • Questions 7, 8, and 9 are completely optional coding practice. Question 7 is in lab01.py and Questions 8 and 9 are in lab01_extra.py. It is recommended that you complete these problems on your own time.

Using Your Class Account

You should have received your class account info (with a username of the form cs61a-xxx) by email. These accounts allow you to use instructional machines in the CS department and are useful if you do not have regular access to a computer. They are not required for CS 61A. See the section Using your class account for details.

This guide explains the basics of using the lab computers and how to use the terminal.

Using Python

When running a Python file, you can use flags 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 flags, take a look at the documentation.

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

    python3 lab01.py
  • -i: The -i option runs your Python script, then opens an interactive session. 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 lab01.py
  • -m doctest: Runs doctests in a particular file. Doctests are marked by triple quotes (""") and are usually located within functions.

    python3 -m doctest lab01.py

Using OK

In 61A, we use a program called OK for autograding labs, homeworks, and projects. You should have downloaded ok at the start of this lab in the zip file. You can use ok to run doctests for a specified function. For example,

python3 ok -q factors

By default, only errors will show up. You can use the -v option to show all tests, including successful ones:

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


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

True Division
(decimal division)
The / Operator
Floor Division
(integer division)
The // Operator
(similar to a remainder)
The % Operator
>>> 1 / 5

>>> 25 / 4

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

>>> 25 // 4

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

>>> 25 % 4

>>> 5 % 0

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

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 all operands are False, then or evaluates to False.

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. Just so you know, 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). Other Python values can be considered "false-y," including 0, None, and '' (the empty string). All other values are considered "truth-y."

Question 1: WWPP: Truthiness

Use OK to test your knowledge with the following "What Would Python Print?" questions:

python3 ok -q truthiness -u
>>> 0 or True
>>> not '' or not 0 and False
>>> 13 and False

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 Evaluates from left to right until: Example
AND The first "false-y" value False and 1 / 0 evaluates to False
OR The first "truth-y" value True or 1 / 0 evaluates to True

If and and or do not short-circuit, they just return the last value. This means that and and or don't always return booleans when using truth-y and false-y values.

Question 2: WWPP: Veritasiness

Use OK to test your knowledge with the following "What Would Python Print?" questions:

python3 ok -q short_circuiting -u

Hint: If an error occurs, write Error.

>>> 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

Question 3: 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

If Statements

You can review the syntax of if statements in Section 1.5.4 of Composing Programs.

Hint: 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!

Question 4: WWPP: What If?

Use OK to test your knowledge with the following "What Would Python Print?" questions:

python3 ok -q what_if -u

The functions below are already defined in lab01.py. If you get stuck, try python3 -i lab01.py and experiment.

>>> 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)
>>> def so_big(x):
...     if x > 10:
...         print('huge')
...     if x > 5:
...         return 'big'
...     if x > 0:
...         print('small')
...     print("nothin'")
>>> so_big(7)
>>> so_big(12)
huge 'big'
>>> so_big(1)
small nothin'

Hint: print (unlike return) does not cause the function to exit!

While Loops

You can review the syntax of while loops in Section 1.5.5 of Composing Programs.

Question 5: WWPP: Loops

Use OK to test your knowledge with the following "What Would Python Print?" questions:

python3 ok -q loops -u
>>> n = 3
>>> while n >= 0:
...     n -= 1
...     print(n)
2 1 0 -1

Hint: Make sure your while loop conditions eventually become false-y, or they'll never stop! Typing Ctrl-C will stop infinite loops in the interpreter.

>>> n = 4
>>> while n > 0:
...     n += 1
...     print(n)
5 6 7 # continues forever
>>> def go(n):
...     if n % 2 != 0:
...         print(n / 2)
...         return
...     while n > 0:
...         print(n)
...         n = n // 2
>>> go(4)
4 2 1
>>> go(5)

Here's some food for thought: is it possible for a program to detect if there is an infinite loop in any program? Put another way, can you create a program that determines if another program will halt?

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 he error. In the example above, TypeError occurred at line 1.

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.py. In your terminal, start an interactive session with Python:

$ python3 -i lab01.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 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.

Question 6: 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 return True if 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!

Question 7: 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 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!

Before you dive into the extra questions, be sure to run python3 ok --submit!

Coding Practice

The code for this section can be found in lab01_extra.py.

It's ok if you don't finish these questions during lab. However, we strongly encourage you to try them out on your own time for extra practice.

Question 8: Factor This!

Implement a function factors which takes in a number n and prints out (in descending order) all of the numbers that divide n evenly. For example, the factors of 20 are 20, 10, 5, 4, 2, 1.

def factors(n):
    """Prints out all of the numbers that divide `n` evenly.

    >>> factors(20)
"*** YOUR CODE HERE ***"
x = n while x > 0: if n % x == 0: print(x) x -= 1

Use OK to test your code:

python3 ok -q factors

Question 9: 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

Appendix: Using your class account

If you plan to use your own laptop for this class, you can ignore this appendix.

Logging into your class account

From your laptop

At the start of your first lab section, you should have received a class account form. At the top left of the form should be your username and your temporary password:

Login: cs61a-aaa
Password: ...

Most of the work in this class can be done without logging into your account. However, there may be times when you'll find working from an instructional account to be easier.

Let's login in now. Open up your terminal and type in the following command:

ssh cs61a-?@cory.eecs.berkeley.edu

where ? is replaced with the rest of your username.

If you're interested, here's an explanation of what the command does:

  1. ssh is a secure shell (i.e. terminal) that connects to other computers over a network.
  2. cs61a-? is the username on the remote computer.
  3. cory.eecs.berkeley.edu is the domain name of the remote computer. For our purposes it can be any of the servers that belong to Berkeley's CS department.

You can also watch this video for help.

The first time you attempt to ssh to a new server, the following message will appear:

The authenticity of host 'cory.eecs.berkeley.edu' can't be established.
RSA key fingerprint is ...
Are you sure you want to continue connecting (yes/no)?

Say yes. Your computer will remember the remote server, and won't ask you again.

Once you confirm, you will be prompted for your password. If you haven't changed your password yet, use the temporary password printed on your class account form.

When you type your password, nothing will show up! This is a security feature, not a bug. Continue typing and press enter to login.

From an instructional machine

Most of our instructional computers use Ubuntu, a version of the Linux operating system. To login, just find lab computer and enter your username and password.

Once you login, you'll want to open a terminal. On Ubuntu, you can open a terminal with Ctrl-Alt-T.

Changing your password

The temporary password is not the easiest thing to remember. While still logged in, you should change with the command:

ssh update

Registering your account

The first time you login to your class account, your terminal will ask you some registration questions about the following:

  • Last name
  • First name
  • Student ID
  • Email (please use your berkeley.edu email!)
  • Code name (we don't use this information, you can enter anything you want)

If your terminal doesn't prompt you for this information the first time you login, you can type register to begin the process. You don't need to do this again if you've already registered before.

If you find errors (e.g. you typed your last name as "ssh update"), fix them immediately by running the command:


Logging out

Once you've registered your account and changed your password, you can log out by pressing Ctrl-D, or with the command exit.