Merge Sort
Jed Rembold
April 24, 2026
Happy Friday!
- Scan the QR code or go to https://tools.jedrembold.prof/daily
- Fun group question: True or False: guessing today’s entrance code is an NP problem?
Quick Announcements
- Infinite Adventure due on Monday
- Midterm 2 corrections due a week from today
- Luau tomorrow!
- No videos to watch before class next week.
- I’m just going to present on some fun/useful libraries/tools and we’ll have time for a few activities
Daily LO’s
- How does merge sort work?
- How does merge sort scale?
- What are P vs NP type problems?
Group Problems
Problem 1: Sort It Again!
- I am distributing small stacks of playing cards to each of your groups
- Designate:
- The splitter: the one responsible for cutting the array in half repeatedly
- The pointers: the ones responsible for pointing at the leftmost unused card when merging
- The merger: the one responsible for comparing cards and merging the smallest into the next available space. Count how many merges happen!
- Shuffle the cards and deal out 5 in a row
- Sort them according to merge sort, following your roles
- How many total merges happened? Does this look like \(5\log_2(5) = 11.6\)?
- Shuffle all the cards back together and deal them all out.
- Sort again. How many merges this time? Does it look like \(12\log_2(12) = 42\)?
Problem 2: Classification Court
- We are going to again cycle through some real-world scenarios
- For each, you’ll have 2 minutes to discuss within your group about if the problem should be classified as a P on NP type problem.
Problem 2a: The Grocery List
- You have prices for different items on a grocery list and need to determine the total cost
Problem 2b: The Delivery Route
- You have 20 houses to deliver packages to. Find a route that will visit all the houses and return you home at the end having driven less than 10 miles.
Problem 2c: Exam Grading
- A student turned in a multiple-choice test. Use an answer key to see if they got a 100%.
Problem 2d: Password Cracking
- I forgot my password and need to figure it out to access my email.
Problem 2e: Section Scheduling
- I have 30 students with different availability. Can I schedule 3 sections that will work for all students?
Problem 2f: Registration
- Given prerequisites and planned offerings, is it possible to graduate with this major in the next two years?
Problem 2g: Beyond Checkers
- Given a current chessboard layout, can you choose a move that guarantees you the win, assuming your opponent plays perfectly?
Problem 2h: Shopping Spree!
- Find a combination of items in your favorite grocery store that total to exactly $100.
Problem 3: Dining Plans
- Say you have $15 flex-dollars left and pay a visit to Blitz Market.
- A P type problem might be: What is the single most expensive item you can afford?
- But how could you “upgrade” this problem?
- What else could you ask or what constraints could you add that would transform this into an NP type problem?
- Remember, NP problems are still easy to verify
- But to solve them you usually would have to check all branching possibilities