If your group has fewer than 3 people, feel free to merge with another group in the room.

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).

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.

Ice Breaker

Say your name and a city (or place) that you like, which is not Berkeley and is not where you have lived. Feel free to share why you like it.

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: 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.

def fizzbuzz(n):
    """
    >>> result = fizzbuzz(16)
    1
    2
    fizz
    4
    buzz
    fizz
    7
    8
    fizz
    buzz
    11
    fizz
    13
    14
    fizzbuzz
    16
    >>> print(result)
    None
    """
    i = 1
    while i <= n:
        if i % 3 == 0 and i % 5 == 0:
            print('fizzbuzz')
        elif i % 3 == 0:
            print('fizz')
        elif i % 5 == 0:
            print('buzz')
        else:
            print(i)
        i += 1

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.

Q2: 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

def is_prime(n):
    """
    >>> is_prime(10)
    False
    >>> is_prime(7)
    True
    >>> is_prime(1) # one is not a prime number!!
    False
    """
    if n == 1:
        return False
    k = 2
    while k < n:
        if n % k == 0:
            return False
        k += 1
    return True

Q3: 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.

def unique_digits(n):
    """Return the number of unique digits in positive integer n.

    >>> unique_digits(8675309) # All are unique
    7
    >>> unique_digits(13173131) # 1, 3, and 7
    3
    >>> unique_digits(101) # 0 and 1
    2
    """
    unique = 0
    while n > 0:
        last = n % 10
        n = n // 10
        if not has_digit(n, last):
            unique += 1
    return unique

# Alternate solution
def unique_digits_alt(n):
    unique = 0
    i = 0
    while i < 10:
        if has_digit(n, i):
            unique += 1
        i += 1
    return unique

def has_digit(n, k):
    """Returns whether k is a digit in n.

    >>> has_digit(10, 1)
    True
    >>> has_digit(12, 7)
    False
    """
    assert k >= 0 and k < 10
    while n > 0:
        last = n % 10
        n = n // 10
        if last == k:
            return True
    return False

Document the occasion

Please all fill out the attendance form (one submission per person per week).