Day 17, Mat385

Last time

Next time

Announcements
- The Zooms continue
  A menu of our past zooms...
- I've approved 7 projects. If yours is still "ungraded", you need to revise. Visit Canvas and see what I had to say; then respond. Reach out if you want to discuss.
  I checked this afternoon, and haven't seen any revisions. That suggested that I should create a new assignment, only for those who need to revise. It's done, and I've made a new deadline of March 30th for that.
- I pushed a homework set back; so 6.1 is due Monday, and so on. I had to adjust our schedule a little, as well; but so far, nothing serious.
- Speaking of which, however, and looking a little down the road, I see that our second exam is coming in two weeks.
  It will cover everything from
  1. 2.2: Induction
  2. 3.1: Recursive Definitions
  3. 3.2: Recurrence Relations
  4. 3.3: Analysis of Algorithms
  5. 4.1: Sets
  6. 6.1: Graphs
  7. 6.2: Trees
  That should be enough for this exam. I'll hold off on 6.3, and following. The final will be in two parts: new stuff (6.3 and on), and the comprehensive part.
Last time:
- We finished off Section 6.1 (Graphs), and made no progress on 6.2.
Today:
- So today we'll cover Section 6.2 (Trees and their representations).
  I'm passing around a sheet with a couple of Decision Tree problems, which I mention in the 6.2 highlights. We'll talk about them a little more when we get to 6.3 (next time).
  In the meantime, I think that the second problem would make an interesting little project (with some research into the extent to which this strategy -- or one like it -- was used during the pandemic). If you'd like to take that one on, let me know.
Links:
- From the 6.2 highlights:
  - Handout: terminology and Fibonacci example
  - Tree problems
  - Josh Werrman's brute force solution to Will Short's puzzle.
  - Fibonacci numbers via a fractal tree
  - Example 24, p. 513
  - Sights and sounds of Tree traversal
  - Reverse Polish Notation
  - How many unique binary search trees?
- Graph Terminology Handout
- Tree Terminology Handout
- If you check out this code, you'll see where I compute the power set ("all-subsets") of a set, to cover all the bases. I think that the end result is pretty beautiful, too!
- Recursive in-order, post-order, pre-order in lisp
- Recursive computation of Fibonacci numbers (in lisp)
- Recursive computation of rows from Pascal's triangle (in lisp)
- "String exponention" (in lisp)
- Here is the recursive selection sort algorithm, in lisp:
- Here is a recursive binary search algorithm in lisp:
- Closed-form computation of Fibonacci numbers (in lisp)
- Some examples of the Euclidean algorithm:
  1. Simple and clean recursive Euclidean Algorithm in lisp:
  2. Written as a while loop, using the recurrence relation:
- Here is a recursive bubbleSort algorithm in lisp
  
  (coded up following our author's algorithm, in section 3.3, p. 214, as closely as possible).

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