Homework Assignment #5
CS 410/584 Algorithm Design & Analysis: Spring 2009
This assignment is due Wednesday, 3 June, at the beginning of class. You should work
alone on this assignment. However, you are free to discuss the problems on the class
mailing list. (Or you can send me email questions directly; please put “CS 584” at the
beginning of the subject line.) Please put “410” or “584” on your paper, depending on
which section you are registered in.
Reading: Chapters 33 and 34 all, 35.1
Note: On any homework exercise where you are asked to give (or modify) an algorithm,
you must also provide an English description of how it works and at least one example
execution.
Exercises: 30.2-2 (5 points; show the results of the recursive calls of FFT.), 33.1-5 (15
points), 33.2-3 (15 points), 33-3 (20 points. 584 only).
5A (15 points): This question concerns string matching. Suppose a text string has been
preprocessed to create a sorted list of positions of each character in the string. For
example
“this is a test text”
would have the lists
a: 9
e: 12, 17
h: 2
i: 3, 6
s: 4, 7, 13
t: 1, 11, 14, 16, 19
x: 18
blank: 5, 8, 10, 15
Give an efficient algorithm for finding all occurrences of a pattern in the text if such lists
exist for the text. Hint: Exploit the sorted order of the lists.
5B (10 points): Given four distinct points, give an algorithm to determine if they are the
corners of a square. Do not use division or square root.