Find your group, and then get started on this worksheet on Berkeley time. It's best if everyone has a way to view this worksheet (on your phone/tablet is fine, but a laptop is better).

Now switch to Pensieve, a shared editing app that has this same worksheet in a format that makes it easy to collaborate with your group and ask questions of an AI tutor.

• Everyone: Go to pensieve.co, log in with your @berkeley.edu email, and enter your group number as the room number (which was in the email that assigned you to this lab). As long as you all enter the same number (any number), you'll all be using a shared document.

Once you're on Pensieve, you don't need to return to this page; Pensieve has all the same content (but more features). If for some reason Penseive doesn't work, return to this page and continue with the discussion.

Attendance

Fill out this discussion attendance form with the unique number you receive from your TA. As soon as you get your number, fill out the form, selecting arrival (not departure -- that's later).

Ice Breaker

Everyone say your name and some activity you enjoy doing outside. For each activity, ask if anyone else in your group likes to do that too. (Optional: after lab you could make plans to go do one of these activities together.)

Then, each person share an expression that people say when they really like something, such as "that's awesome" or "nice one" or "bruh." Each person should try to come up with a different expression. Feel free to ask your group for help if you're stuck. You can even use other languages than English. Then, during the discussion, if someone says or does something well, use your expression!

While and If

Learning to use if and while is an essential skill. During this discussion, focus on what we've studied in the first three lectures: if, while, assignment (=), comparison (<, >, ==, ...), and arithmetic. Please don't use features of Python that we haven't discussed in class yet, such as for, range, and lists. We'll have plenty of time for those later in the course, but now is the time to practice the use of if (textbook section 1.5.4) and while (textbook section 1.5.5).

Q1: Race

The race function below sometimes returns the wrong value and sometimes runs forever.

Find positive integers x and y (with y larger than x but not larger than 2 * x) for which either:

• race(x, y) returns the wrong value or
• race(x, y) runs forever

You just need to find one pair of numbers that satisfies either of these conditions to finish the question, but if you want to think of more you can.

Notes:

• x += 1 is the same as x = x + 1 when x is assigned to a number.
• 0 is a false value and all other numbers are true values.

If you want to discuss this problem with a TA, just ask.

Q2: Fizzbuzz

Implement the classic Fizz Buzz sequence. The fizzbuzz function takes a positive integer n and prints out a single line for each integer from 1 to n. For each i:

• If i is divisible by both 3 and 5, print fizzbuzz.
• If i is divisible by 3 (but not 5), print fizz.
• If i is divisible by 5 (but not 3), print buzz.
• Otherwise, print the number i.

Try to make your implementation of fizzbuzz concise.

Problem Solving

A useful approach to implementing a function is to:

1. Pick an example input and corresponding output.
2. Describe a process (in English) that computes the output from the input using simple steps.
3. Figure out what additional names you'll need to carry out this process.
4. Implement the process in code using those additional names.
5. Determine whether the implementation really works on your original example.
6. Determine whether the implementation really works on other examples. (If not, you might need to revise step 2.)

Importantly, this approach doesn't go straight from reading a question to writing code.

For example, in the is_prime problem below, you could:

1. Pick n is 9 as the input and False as the output.
2. Here's a process: Check that 9 (n) is not a multiple of any integers between 1 and 9 (n).
3. Introduce i to represent each number between 1 and 9 (n).
4. Implement is_prime (you get to do this part with your group).
5. Check that is_prime(9) will return False by thinking through the execution of the code.
6. Check that is_prime(3) will return True and is_prime(1) will return False.

Try this approach together on the next two problems.

Important: It's highly recommended that you don't check your work using a computer right away. Instead, talk to your group and think to try to figure out if an answer is correct. On exams, you won't be able to guess and check because you won't have a Python interpreter. Now is a great time to practice checking your work by thinking through examples. You could even draw an environment diagram!

If you're not sure about how something works or get stuck, ask for help from the course staff.

Q3: Is Prime?

Write a function that returns True if a positive integer n is a prime number and False otherwise.

A prime number n is a number that is not divisible by any numbers other than 1 and n itself. For example, 13 is prime, since it is only divisible by 1 and 13, but 14 is not, since it is divisible by 1, 2, 7, and 14.

Use the % operator: x % y returns the remainder of x when divided by y.

i = 2
while i < n:
    ...
    i = i + 1

Description Time: Come up with a one sentence description of the process you implemented to solve is_prime that you think someone could understand without looking at your code. Try not to just read your code, but instead describe the process it carries out.

Q4: Unique Digits

Write a function that returns the number of unique digits in a positive integer.

Hints: You can use // and % to separate a positive integer into its one's digit and the rest of its digits.

You may find it helpful to first define a function has_digit(n, k), which determines whether a number n has digit k.

Environment Diagrams

An environment diagram keeps track of names and their values in frames, which are drawn as boxes.

Q5: Bottles

Answer the following questions with your group. Step through the diagram to check your answers.

1) What determines how many different frames appear in an environment diagram?
a) The number of functions defined in the code
b) The number of call expressions in the code
c) The number of return statements in the code
d) The number of times user-defined functions are called when running the code

2) What happens to the return value of pass_it(bottles)?
a) It is used as the new value of remaining in the global frame
b) It is used as the new value of bottles in the global frame
c) It is used as the new value of pass_it in the global frame
d) None of the above

3) What effect does the line bottles = 98 have on the global frame?
a) It temporarily changes the value bound to bottles in the global frame.
b) It permanently changes the value bound to bottles in the global frame.
c) It has no effect on the global frame.

Q6: Double Trouble

Draw the environment diagram on paper or a whiteboard (without having the computer draw it for you)! Then, check your work by stepping through the diagram.

Document the occasion

Let your TA know you're done so that you can each get a departure number, and fill out the attendance form again (this time selecting departure instead of arrival). If your TA isn't in the room, go find them next door.

Optional: Exam Practice

If you all finish early, it's a great idea to get ready for Midterm 1 by trying out this slight variant of a Spring 2023 Midterm 1 question.

Q7: Repeating

Definition: A positive integer n is a repeating sequence of positive integer m if n is written by repeating the digits of m one or more times. For example, 616161 is a repeating sequence of 61, but 61616 is not.

Implement repeating which takes positive integers t and n. It returns whether n is a repeating sequence of some t-digit integer.