untitled

The final exam is worth 22% of your overall grade.
The exam will cover material since Exam 2 and also have a comprehensive section of questions on topics from Exams 1 and 2.
The questions on new material will be worth 50% of the Exam 3 score.
The comprehensive section (worth 50% of Exam 3) will not focus on low-level detail (say, exactly how a partition algorithm works) but on higher-level important topics (example: what partition leads to quicksort's worst case.). But they might include questions on order-classes for algorithms' complexity. (So the paritition algorithms we saw are Theta(n).)
The time allowed for the exam will be 2 hours.
If you need to take the exam at an alternative time, please email me by Tuesday 2pm, May 4, and explain.
If you are an LNEC student needing extra time, contact me and let me know if you want to do it all in one go on the exam day, or if you need to split it into two parts.
Note: the previous info here about additional questions wasn't right.

Topics list for "new" material since Exam 2.

Dynamic Programming:

General principles of dynamic programming
- Optimal substructure property
Memoization
Fibonacci numbers
LCS
- You might be asked to complete the table for given inputs
- You won't be asked to reproduce the code. But know the complexity.
0/1 Knapsack -- see handout
- Why greedy doesn't work
- Understand how cells in the table get updated

P, NP and NP-C:

Text: Read Chap 10 but use the slides to guide your understanding. Material or sections that are in the book but not in the slides won't be on the exam. Email me if you have questions. Topics listed below.
Decsion problems vs. optimal values vs. optimal solutions
Definitions of class P, NP, NP-hard, and NP-c
NP-c problems: SAT, CNF-SAT, 3-CNF-SAT, k-COL, VertexCover, k-Clique, SubsetSum, 0/1-Knapsack, HamPath, HamCycle, TSP
Definition of an non-deterministic algorithm and definition of class NP
- How to prove that a problem is in NP
Size of input
What is a polynomial reduction? What's it mean if problem A reduces to problem B?
The Cook-LevinTheorem: what it is, what it means, why it's significant
The relationship between P, NP and NP-complete
- The big question: does P = NP?
Reductions: You won't be asked to come up with a "new" reduction on your own. You need to know what a reduction is, and how it's described. You might be asked questions about these example reductions:
- 3-Col to CNF-SAT (handout)
- Directed ham. cycle reduces to undirected ham. cycle (same handout as above and slides)
- Hamiltonian cycle to the TSP (slides)
- 3-CNF to k-Clique (slides)
- SubsetSub to 0/1 knapsack (HW6)
Coping with complexity. What's an approximation algorithm? If you don't remember, go back and think about the greedy approaches to TSP problem on Exam 2, and the greedy question on HW4 on graph coloring and vertex cover -- see posted solutions

Personalities:

There will be two straightforward questions (worth 4% total) on the famous figures from algorithms "Wall of Fame" on the class Web page. Be sure to memorize their names.

Exam 1: (Click here for previous review-guide for Exam 1.)

Basics
Order classes, worst-case, average-case, lower-bounds, optimal algorithms, etc.
Divide and conquer
- recurrence relations (No Main or Master theorem!)
- Examples: mergesort, quicksort, trominos, max and min, etc.
Sorting
- insertion sort, quicksort, mergesort
- lower bound for sorting using key-comparisons
- linear sorting

Exam 2: (Click here for previous review-guide for Exam 2.)