Overview

• Preliminaries.
  • Admin.
  • Questions.
• More efficient sorting techniques.
• Divide and conquer, revisited.
• Merge sort.
• Analyzing merge sort.
• Lab

Preliminaries

Admin

• Exam 3 is ready.
• For people who attended class today and worked on the lab in class, there is no writeup.
• People who did not show up to today's class are expected to do lab writeup 29: Problems 6 and extra 1.
  • TB, WBC, RC, MH, TJ, RJ, YK, AL, ELB, JOP, AOP, WR, AS, AS, JY
• Upcoming extra credit opportunities:
  • Any self-care week activity
  • One Grinnell rally on December 4 at 4pm.
    • And yes, I have contacted Dean Arora about the timing.
  • Home game for Basketball, December 4 at 5:30pm
  • Pie on ear swim meet Dec 6-8

More efficient sorting techniques

Thinking about insertion sort ... * For a list of length n, we call insert n times * Insert into the empty list * Insert into a list of length 1 * Insert into a list of length 2 * Insert into a list of length 3 * And so and so forth * If we're lucky, insert happens at the front, that's one step Approximately n total calls to cons (or whatever) * If we're unlucky, insert happens at the end * Inserting into a sublist of length k takes about k recursive calls * Overall running time * 0 + 1 + 2 + ... n-1 is approximately (n^2)/2 * If I double the input size and I'm unlucky ... * E.g., if it's 1 minute to sort 100 things, it will take 4 minutes to sort 200 things (2n)^2/2 = 4(n^2)/2 * When we have an inefficient algorithm ... can we do better?

Divide and conquer, revisited

• Divide in half
• Sort each side
• Merge 'em back together

Analyzing merge sort

• See white board. ALex took a photo.