-
- The Zooms continue
- A menu of our past zooms...
- All but 2 projects have been green-lighted. Time to get at those!
I'm going to be adding you all to the wiki at some point. I'll alert
you when I do, because your links to establish your accounts
(automagically generated) will almost certainly go to spam....:(
- 6.2 Homework graded: 2, 36, 56
- #36: shoot for some sort of optimization, if possible:
- #56: how many non-isomorphic rooted trees with $n$ nodes?
- Find some way to organize your efforts (many missed
1; some even 2 or more...:):
- Another organizational scheme is by the number of
children $r$ has (as you can see, there are four of one
child, three of two children; one of three and one of
four.
- Another strategy (and the best strategy!) is recursive:
How do we build trees of five nodes? Out of trees of fewer nodes!
- one (rooted) tree with one node
- one tree with two nodes
- two trees with three nodes
- four trees with four nodes
- nine trees with five nodes
How many non-isomorphic trees are there with six nodes?
- Find some way to organize your efforts (many missed
1; some even 2 or more...:):
- #36: shoot for some sort of optimization, if possible:
- Our second exam is next week, Thursday 4/7. On Tuesday we'll
review. I've promised some review problems by Monday --
hopefully sooner.
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
Here is an overview of the sections above.
- We nearly finished Section 6.3 (Decision Trees), but we have a few more bits to do.
- Today we'll finish Section 6.3 (Decision Trees).
- Then we'll get going on Euler Paths and Hamiltonian Circuits.
- Rooted Trees
- Kaliningrad, Russia (formerly Konigsberg)
- From the 7.2 highlights:
- EulerPath:
- 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:
- 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).
