CSC 151 2019S, Class 35: An introduction to sorting

Overview

• Preliminaries
  • Notes and news
  • Upcoming work
  • Extra credit
  • Questions
• The problem of sorting
• Writing sorting algorithms
• Some examples
• Formalizing the problem

Preliminaries

News / Etc.

• I brought food-like substances.
• Mentor sessions Thursday 7-8 p.m., Thursday 8-9 p.m.
• Today is a “talk day” rather than a lab day.
• Congrats to your classmate who tied for second in the Kinetic Sculpture Competition!
• Welcome to any prospective students. Good luck on your decisions!

Upcoming work

• Project due Tuesday!
  • Rubric available for your perusal.
  • Send me code, instructions for running, and report.
  • The parts of the report are specified in the rubric. I’d expect an introdution that describes the problem, a description of the key algorithms you wrote, a description of what you did with the results of those algorithms, and some conclusions about what you might have learned. Four sections, 1-2 pargraphs each.
• Reading for Wednesday: Algorithms for sorting lists and vectors
• No lab writeup
• Friday’s quiz: Searching and sorting
• Flash cards Wednesday: Searching and sorting
  • Our last flash cards!
• Exam 3 due next Tuesday.
  • It is not “officially” released until this Wednesday; I still have time to correct typos and infelicities.
  • Prologue due Friday night.

Extra Credit

I would certainly appreciate suggestions of other extra credit activities (preferably via email).

Extra credit (Academic/Artistic)

• Tomorrow: CS Table, Tuesday, Facebook Data, Noon, Middle PDR
• Three talks by Prof. Dr. Yvonne Foerster (https://yvonnefoerster.com/)
  • Wednesday: May 1, 4:30-6pm, HSSC S3325: Beyond the Anthropocene: Technology, Innovation, and the (Post-)Human Condition
  • Thursday, May 2, Noon-12:50pm, HSSC N3110 Degrees of Freedom: Embodiment, Neuroplasticity, and the Need for a Critical Neuroscience (Lunch and beverages provided)
  • Friday, May 3, Noon-12:50pm, Bucksbaum 152: Designing Future Bodies: Fashion and Technology (Lunch and beverages provided)

Extra credit (Peer)

• New: Sunday, 2pm, Herrick: Singers vs. Orchestra

Extra credit (Wellness)

Extra credit (Wellness, Regular)

• Today: 30 Minutes of Mindfulness at SHAW every Monday 4:15-4:45
• Any organized exercise.
• 60 minutes of some solitary self-care activities that are unrelated to academics or work. Your email reflection must explain how the activity contributed to your wellness.
• 60 minutes of some shared self-care activity with friends. Your email reflection must explain how the activity contributed to your wellness.

Extra credit (Misc)

Other good things

• The Grinnellian: Student concert, next Saturday.

Questions

The problem of sorting

• We like to sort; it is useful to have things in order.
  • It makes binary search easier.
  • It makes our remove-duplicates algorithm much faster (or at least easier).
  • A really inefficient way to do max or min. (Nicer if you need like the first three or last three or ….)
  • Can help with hash tables.
• Writing sorting algorithms is therefore an important task for computer scientists.
• That will be our task for the next few days.

Writing sorting algorithms

• Look at similar algorithms we’ve written in the past and adapt.
• Do things by hand and then try to generalize.

Some examples

Insertion sort

• Split our world into sorted and unsorted.
• Initially, the first element is sorted and everything else is unsorted.
• Repeatedly take the first element of unsorted and put it in the correct place in sorted.

Radix

• Put all the A’s together
• Put all the B’s together
• Put all the C’s together
• Put all the D’s together
• In each group, do the same thing with the second letter
• And so on and so forth
• Can improve with knowledge of the distribution

Radix plus insertion

• Divide into three groups, smaller, middle, larger. Then run insertion.

Selection

• Conceptually we have two lists: sorted and unsorted
• Repeatedly find the smallest thing in unsorted and add it to the end of sorted.

Timsort will come on Friday

Clownsort / Permutation sort

• Randomly permute the list
• See if it’s sorted
• If so, you’re done
• If not, start over

Parallel bubble sort

• Compare to the person next to you (people in odd positions to people in even positions) and swap if out of order.

Machine learning sort

• Give the problem to a machine learning algorithm
• Use what it comes up with

Analysis

Insertion sort

• Putting the first thing in the new list costs us about 1.
• Putting the second thing the new list costs us about 2 (in the worst case)
• Putting the third thing the new list costs us about 3 (in the worst case)
• Worst case 1+2+3+4+…+n. = n*(n+1)/2. An “n squared” algorithm
• Idea: Instead of comparing to neighboring elements, use binary search to find the location.
  • For binary search to work, things must be sorted.
  • For binary search to work, they must be in an array.
• Once we find where it goes, we have to shift things over.

Note: With searching, we found that it was useful to think about limiting the form of the values (sortted) and using a “divide and conquer” algorithm.

Improving sorting algorithms

We’ve seen that divide-and-conquer was a succesful strategy for searching; can we use it for sorting?

• Divide the list in half (how?)
• Do something with each half (what?)
• Put them back together (how?)

Mergesort

• Divide the list into two halves, positionally
• Sort each half (using recursion)
• Merge the two together, by repeatedly grabbing the smaller of the first remaining element in each half.

Median sort

• Divide the list into those less than the median and greater than the median
• Sort the two halves
• Append together

Quicksort

• Median sort, using a randomly chosen median
• Base case: 1 element

Formalizing the problem