CS303: Algorithms and Data Structures Fall 2007
Assignment 2 (written) Due Date: September 19, 2007 (during lab hours)
1. (15 pts) For what values of N is ?
2
2lg10 NNN >
2. (20 pts) Suppose and
() ()()
NFONT =
1
(
)
(
)
(
)
NFONT
=
2. Can you conclude that
() () ()
1
21 ONTNT =? Justify your answer.
3. (15 pts) From the textbook, exercise 4.6. In the sequence H E L L * O *, a letter means push and an
asterisk means pop. Give a way to insert asterisks in the sequence E A S Y so that the sequence
values returned by the pop operations is (i) E A S Y ; (ii) Y S A E ; (iii) A S Y E ; (iv) A Y E S ; or,
in each instance, prove that no such sequence exists.
4. (30 pts) Show how to implement a queue using two stacks. Analyze the running time of the queue
operations.
5. (20 pts)The human genome is a sequence of roughly 3.5 billion nucleotides, each of which is one of
four types, A, C, G, or T. Representing each of A, C, G, or T as a string of 2 bits, the entire genome
string would take up roughly 0.875 gigabytes of storage, thus would fit comfortably on a laptop hard
disk.
a. (10 pts) Suppose your computer can perform 109 operations per second. Say you wanted to
analyze the genome running a naïve string matching algorithm known to take n2 operations on
inputs of length n. Comment on the feasibility of this.
b. (10 pts) Suppose that by using a more appropriate data structure, your algorithm could perform
the same task using only n lg n operations on inputs of length n. What then?
Note: Answers without any proof or workings won’t count! This question is easier than it looks. Don’t be intimidated by
the amount of text.