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- The Zooms continue
- A menu of our past zooms...
- Remember that your project revisions are due tomorrow at midnight. Let's try to get those nailed down.
I mention one old project today, that might serve as a model for you.
- 6.1 Homework graded: 15, 20, 55
- #15: You need two maps for this one, because it's not simple. Check out the symmetries -- symmetries, too, have to be preserved!
So there is redundancy in how one chooses to map the parallel edges, in particular.
- #20: You only need a map between nodes, since this graph
is simple. Once you map the nodes, the arc map is determined!
(Upshot -- don't waste your time! It's precious....)
Do you see the cube? Another way of thinking/working is to give a name to a graph (showing that they're both isomorphic to a familiar graph). They're both (distorted) cubes.
Here's what Griffin saw (and I liked):
- #55 (references the graph of #39). John also created the
adjacency matrix, for comparison purposes:
- #15: You need two maps for this one, because it's not simple. Check out the symmetries -- symmetries, too, have to be preserved!
- Our second exam is next week, Thursday 4/7. Next Tuesday we'll review.
The exam will cover everything from
- 2.2: Induction
- 3.1: Recursive Definitions
- 3.2: Recurrence Relations
- 3.3: Analysis of Algorithms
- 4.1: Sets
- 6.1: Graphs
- 6.2: Trees
- We finished off Section 6.2 (Trees).
- Today we'll cover Section 6.3 (Decision Trees).
- Next time we move into Chapter 7, with section 7.2.
- 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
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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:
- Simple and clean recursive Euclidean Algorithm in lisp:
- 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).
