CMPSCI 311: Theory of Algorithms

David Mix Barrington

Fall, 2003

Homework Assignment #4

Due Friday 17 October 2003 in class

(or earlier to hand-in box in CMPSCI main office)

All twelve questions are from [L]. Point values are as indicated. There are 100 total points.

• Question 4.5.7, page 147 (10): This will require you to read 4.5, which we didn't cover in class, but you can handle it.

• Question 4.6.9, page 152 (5): Remember that you must show that an n-point example exists for any number n, though you don't need to be too formal about it.

• Question 5.1.1, page 161 (10): Levitin's hint suggests solving the n=1 version first. If you can do n=1, you can probably figure out the solution for general n.

• Question 5.1.2, page 161 (10):

• Question 5.1.7, page 162 (5):

• Question 5.2.1, page 168 (5):

• Question 5.2.3, page 169 (10): Prove your answers.

• Question 5.2.5, page 169 (5):

• Question 5.2.8, page 169 (10):

• Question 5.3.1, page 173 (10):

• Question 5.3.6, page 174 (10):

• Question 5.3.10, page 175 (10): There are several ways to solve this, only some of them using DFS. You must both present and analyze the running time of some correct method that returns the entire correct n by n array, as long as its time is bounded above by some polynomial in n.

Last modified 10 October 2003