COP 4531: Lecture 13

Learning objectives

After this class, you should be able to:

1. Given a problem, identify if dynamic programming is likely to be effective in solving it.
2. Given a problem, determine if it satisfies the optimal substructure property.
3. Given a recursive solution to a problem, derive its time complexity.
4. Given a recursive solution (with repeated subproblems) to a problem, give an improved algorithm that uses memoization to reduce the time taken.
5. Prove optimal substructure properties for the Longest Common Subsequence (LCS) problem, and for other similar problems.
6. Give a recursive solution for the Longest Common Subsequence (LCS) problem, and for other similar problems.
7. Give a dynamic programming solution for the Longest Common Subsequence (LCS) problem, and for other similar problems.

Reading assignment

1. Lectures 11-13 slides.
2. CLR: Sections 15.3-1, 15.4.
3. CLR: Chapter 16, page 415.

Exercises and review questions

• Questions on current lecture's material
  1. Exercise 15.4-1.
  2. Exercise 15.4-4.
  3. (Optional - extra credit for homework) You can find a database of mitochondrial DNA sequences -- human and ape -- at www.genpat.uu.se/mtDB. You can try to compare the sequences and see which ones are close.

• Questions on next lecture's material
  1. (Post your answer on the discussion board) Give an example of an activity-selection problem instance with at least five activities, and give a solution (not-necessarily optimal, but having at least two activities) to it.