UMBC CMSC441, Design & Analysis of Algorithms, Fall 2002, Section 0101

Homework Assignments

Homework 1, Due Tuesday 09/17

1. Exercise A.2-1, page 1067.
2. Exercise 4.2-1, page 72.
3. Problem 4-1, parts a, b, e, g and h, page 85.

Homework 2, Due Tuesday 09/24

1. Exercise 6.4-4, page 136.
2. Exercise 6.5-7, page 142.
3. Problem 6-3, page 143.

Homework 3, Due Tuesday 10/01

1. Exercise 5.2-4, page 98.
2. Problem 7-4, page 162.
3. Exercise 8.1-3, page 168.

Homework 4, Due Tuesday 10/08

1. Problem 8-4, page 179.
2. Exercise 9.3-8, page 193.
3. Problem 15-2, page 364.

Homework 5, Due Tuesday 10/15

1. Exercise 15.3-5, page 350.
2. Problem 15-4, page 367.
3. [Tickets to Rides: Dynamic Programming] You arrive at Waldo's World Amusement Park with T minutes before the park closes. The park has n rides and your objective is to complete as many rides as possible before the park closes. (For this problem, taking the same ride twice counts as 2 rides.) You are given a table W such that W(i,t) gives you the waiting time for ride i at time t. For convenience, assume that t is to be given as minutes before the park closes. Ride i itself takes r_i minutes and all times are measured in integer minutes.
   1. Define a subproblem, MaxRides, that can be used to solve this dynamic programming problem. To do this, you must describe the input parameters to MaxRides and the "return value" using English sentences.
   2. Give a mathematical formula that shows how MaxRides can be computed recursively. Then, explain all the parts of the formula using English sentences.
   3. Describe how MaxRides can be computed bottom up using a dynamic programming table. Be sure to include a description of the dimensions of the table and the order that the entries of the table are to be filled. Which entry has the solution to the original problem?
   4. Analyze and justify the running time of your dynamic programming algorithm.

Homework 7, Due Thursday 11/7

1. Exercise 22.2-5, page 539. Hint: there's an example with <= 8 vertices.
2. Exercise 22.4-5, page 552.
3. Exercise 22.5-5, page 557.

Homework 8, Due Thursday 11/14

1. Problem 21-1, pages 518-519.
2. Exercise 23.2-5, page 574.
3. Problem 23-4, pages 577-578.

Homework 9, Due Thursday 11/21

1. Exercise 24.1-4, page 591.
2. Exercise 24.3-6, page 600.
3. Problem 24-3, pages 615.

Homework 10, Due Tuesday 12/10