Discussion 3


Antonio Kam
anto [at] berkeley [dot] edu


  • Exams have been released πŸ“œ
    • There is a video walkthrough for all questions, please watch them if you want to better understand a question πŸ“Ή
  • HW 03 released today πŸ–ŠοΈ
  • New CSM sections will open soon πŸ‘€
    • Not sure when, probably next week? πŸ₯Ί
  • Midterm clobber policy
    • I believe it was mentioned in lecture, but exact logistics for this have yet to be figured out
Slides by Antonio Kam (anto@)

Temperature Check 🌑️

  • Environment Diagrams
  • Higher-order Functions
  • Recursion
Slides by Antonio Kam (anto@)

Results from last section

Slides by Antonio Kam (anto@)

Results from SU22

Slides by Antonio Kam (anto@)

Questions and Comments from last section

  • Making mistakes then trying to find where they are is confusing!
    • Honestly very interesting - this video might be interesting to watch; while it's not perfectly sound educational research, results have found that students tended to improve more with this method, but also found it more confusing πŸ€”
    • I was only planning on doing that for environment diagrams, because it's pretty difficult to make it work with other topics, but if you're interested, watch the video! I found this comment super interesting, so thank you to whoever left this πŸ₯³
  • HOF Double Inputs:
    • (lambda x: lambda y: x + y)(3)(4)
Slides by Antonio Kam (anto@)

Questions and Comments from last section

  • Nested while loops
    • Think of which block gets executed on the repeat; which indent is handling what situation
    • Reminder bullet point for me to write up an example
  • Environment Diagram review
    • Would highly recommend trying out FA19's pumbaa question and really understanding it - it's a truly good question for learning the rules behind environment diagrams
  • "My friend loves Hollow Knight and he has introduced me to the game’s music; the soundtracks are truly amazing :D"
    • I tend to listen to soundtracks to decide which games to play (which is quite backwards, whoops)
Slides by Antonio Kam (anto@)


  • Important to mention that the midterm is worth 30 points out of the total 300 (which goes to around 310 including extra credit)
  • Exams are not the only component of your grade in this class - you have discussion/lab attendance, and homeworks/projects where you're given unlimited attempts, and there are also no hidden tests
    • This means that quite a large portion of the points in this course are not based on exam performance.
  • Many people struggle on exams; it's completely normal to not feel too good about your own performance (in fact, quite a lot of exams in higher education will have averages lower than what you may have been used to in HS)
  • Please feel free to reach out to me if you have any questions.
  • Other resources: Advising OH, Instructor OH, etc.
Slides by Antonio Kam (anto@)

All slides can be found on

Slides by Antonio Kam (anto@)

What is recursion?

  • A recursive function is one where a function is defined in terms of itself.
  • Similar to higher-order functions except it returns a call to a function rather than the function itself
  • Will be hearing me talk about this a lot: recursive leap of faith
Slides by Antonio Kam (anto@)


  • Imagine you're in a line waiting for boba, but you don't know how many people there are in front of you (and you want to count how many people there are in front of you)
  • In this case, you can ask the person in front of you about how many people they have in front of them, and then they repeat this same process until...
  • The person at the front now tells the person behind them that there's nobody in front of them
  • Then everyone just needs to add 1 to their answer, and bring it backwards from there.
Slides by Antonio Kam (anto@)

3 Steps of Recursion

  1. Base Case
    • What is the smallest version of the problem we know the answer to?
    • I tend to think of this as the simplest input
  2. Recursive Case (recursive call on a smaller version of the problem)
    • What can I do to reduce my input to something simpler?
    • Similar to while loops
  3. Connecting it all together
    • Assuming your recursive call is correct (recursive leap of faith!), how do you solve the real problem
Slides by Antonio Kam (anto@)

Example with analogy

  1. Base Case
    • I'm at the front of the line
  2. Recursive Case (recursive call on a smaller version of the problem)
    • I ask the person in front of me to tell me how many people they have in front of them (assume that the answer that they give is correct)
  3. Connecting it all together
    • Add 1 to their answer
Slides by Antonio Kam (anto@)


def factorial(n):
    if n == 0 or n == 1: # Base Case
        return 1
    else: # Recursive Case
        return n * factorial(n - 1)
Slides by Antonio Kam (anto@)


  • To calculate a factorial of an integer, what you do is multiply the integer itself with the factorial of one less than itself
    • factorial(5) = 5 * factorial(4)
  • Notice the recursive pattern - factorial(4) will call factorial(3), and so on and so forth, until our base case is reached.
  • We know the result of factorial(1), so calling factorial(1) will just return 1 (base case)
Slides by Antonio Kam (anto@)

Example (Another Perspective)

  • What's the smallest input? What's the simplest problem I know the answer to?
    • 0 is the smallest input - factorial(0) also returns 1.
  • How can I reduce my problem?
    • If you have factorial(n), you can reduce your problem down by calling factorial(n - 1).
    • In this step, you also assume your reduced problem gives you the correct answer (so factorial(n - 1) gives you the correct result - which is the recursive leap of faith)
  • How do I use that result to solve my problem?
    • Multiply by n
    • n * factorial(n - 1)
Slides by Antonio Kam (anto@)

Recursion vs Iteration

Recursion Iteration
Base case is needed for a recursive problem A condition for a while loop is needed
Need to reduce down to the base case Need to reduce down to the while condition
Can't use variables to keep track of values because they reset (need a helper function for that) Can have variables to keep track of values.
Needs lots of frames - takes up memory Loops happen in 1 frame
Slides by Antonio Kam (anto@)

Recursion vs Iteration

# Recursion
def factorial(n):
    if n == 0 or n == 1:
        return 1
        return n * factorial(n - 1)

# Iteration
def factorial(n):
    result = 1
    while n > 0:
        result = result * n
        n -= 1
    return result
Slides by Antonio Kam (anto@)

Question 1 (Walkthrough)

Write a function that takes two numbers m and n and returns their product. Assume m and n are positive integers. Use recursion!

Hint: 5 * 3 = 5 + (5 * 2) = 5 + 5 + (5 * 1).

def multiply(m, n):
    """ Takes two positive integers and returns their product using recursion.
    >>> multiply(5, 3)
    "*** YOUR CODE HERE ***"
Slides by Antonio Kam (anto@)


Slides by Antonio Kam (anto@)


Slides by Antonio Kam (anto@)

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Slides by Antonio Kam (anto@)

Anonymous Feedback Form

Thanks for coming! πŸ₯³

Please give me feedback on what to improve!

Slides by Antonio Kam (anto@)

Draw recursive call diagram (not the environment diagram version)