University of Virginia
Department of Computer Science
Prospective Graduate Students Pre-Qualifying Exam
1 April 2005
There was an unfortunate misunderstanding when the Dean’s office informed the
Computer Science department that we could admit 25 new graduate students this year.
The CS admissions committee naturally interpreted the limit number as hexadecimal, and
admitted thirty-seven new graduate students. Apparently, the Dean’s office intended the
number to be interpreted as decimal, so we admitted 12 more students than permitted. As
a result, we are administering this exam to the admitted students to determine which
students should be unadmitted.
This exam has two questions in each of our three qualifying areas: theory, architecture
and systems. Please answer all questions to the best of your ability and submit your
answers before 11:59PM on Friday, April 1st 2005. If more than 25 students answer all
questions correctly, Pete Gillen has offered to conduct a basketball shoot-around
tomorrow morning to determine which of the remaining students should be unadmitted.
In the event that you are unadmitted, we are no longer able to pay your travel expenses
for the visit day. Please send a reimbursement check (or the equivalent in whisky) to
Louminary Sofa, Apartment of Commuter Science, University of East Virginia, 151
Reengineer’s Way, 204 Olsson Hall, Charlottansville, VA 22901.
Theory
1. Traveling Prospective Grad Student Problem. Ally Hacker has been admitted to
several computer science PhD programs and is planning a trip to visit all of the schools
she might want to attend. A map of the programs that have admitted Ally is below. The
lines on the edges indicate the mileage between each school. Determine the best possible
route for Ally to visit all worthwhile schools. Provide an algorithm for Ally can use do
determine which graduate school to attend that has worst case execution time O(n) where
n is the number of schools that have admitted Ally.
UVa
Georgia Tech
CMU Columbia
MIT
UCB
Stanford
UCSD
UW
UIUC Purdue
Rice
3500
100
1500
600
640
50
500 550
1400
3200
3400
900
350
180
380
230
1700
260
430
1750
1000
300
1400
