CSC 344
Homework 4

Assigned 30 March, due 20 April

Problems from the textbook

There are a lot of them, but most of them are either short or straightforward (e.g. apply an algorithm given in the book to a specific input). There is one programming assignment.

• 6.1.6 (see p. 126 for the number of comparisons made by merge-sort): when do you save work by pre-sorting?
• 6.1.9: are there two numbers in the list that add up to a given number?
• 6.1.10: find all sets of anagrams in a list of words (program)
• 6.2.7: doing Gaussian elimination by hand on your own examples
• 6.3.4: build AVL tree for given examples
• 6.3.7: build 2-3 tree for a specific example, and analyze it
• 6.4.1: build heap for a specific example
• 6.5.6 and 6.5.7: example of fast exponentiation. Use power 19 instead of 17, so it's easier to see the difference between left-to-right and right-to-left algorithms. Note: I originally dropped this problem because people had already done fast exponentiation on homework 3 (problem 4.1.3)... but almost all of you completely missed the point and wrote linear-time algorithms! So let's try again with these problems.
• 6.5.10: representation of polynomials
• 6.6.7: reducing a problem to 0-1 linear programming.
• 6.6.9: reducing edge-coloring to vertex-coloring
• XC: 6.6.10: jealous husbands
• XC: 7.1.7: checking ancestry in a tree. Note: The best solution I've come up with assumes that the number of nodes can be stored in a single machine word (on which you can do constant-time arithmetic operations). If you drop that assumption, I don't think it's possible.
• 7.2.1, 7.2.2, 7.2.3: Horspool string matching
• 7.3.1, 7.3.2: examples of open and closed hashing
• 7.4.6: build 2-3-4 tree for given example