CS 170, Spring 2000
Midterm #1
Professor M. Clancy
This is an open-book test. You have approximately eighty minutes to complete it. You may consult any
books, notes or other paper-based inanimate objects available to you. To avoid confusion, read the problems
carefully. If you find it hard to understand a problem, ask us to explain it. If you have a question during the
test, please come to the front or the side of the room to ask it.
This exam comprises 15% of the points on which your final grade will be based. Partial credit may be given
for wrong answers. Your exam should contain six problems (numbered 0 through 5) on eight pages, with two
more blank pages at the back of the exam. Please write your answers in the spaces provided in the test; in
particular, we will not grade anything on the back of an exam page unless we are clearly told on the front of
the page to look there.
Relax -- this exam is not worth having a heart failure about.
Problem #0 - 1 point, 1 minute
Put your name on each page. Also make sure you have provided the information requested on the first page.
Problem #1 - 4 points, 10 minutes
Suppose that the following statements initialize the union/find structure descibed in CLR section 22.3.
for (k=0; k
On the next page show the data structures, including ranks of representative elements, that result for each of the following statements. Assume that the statements are executed in sequence. Also assume, as in CLR, that the path compression and union-by-rank optimizations are used, and that the representative element of the second argument becomes the parent when the two arguments have equal rank.
Union (0,1);
Union (2,3);
Union (0,2);
Union (4,5);
Union (0,4);
Results of Union calls
|
call | resulting data structure, including rank(s)
------------+-----------------------------------------------------------
Union(0,1); |
|
CS 170, Midterm #1, Spring 2000
CS 170, Spring 2000 Midterm #1 Professor M. Clancy 1
