1
1. CMPS 101 — Algorithms and Abstract Data Types
References:
1. Baase and Van Gelder: Computer Algorithms, 3rd Ed. Addison Wesley, 2000.
2. Cormen, Leiserson, Rivest: Introduction to Algorithms, 2nd Ed.. McGraw-Hill, 2001.
Scoring: Each question will have four choices for the answer,
(
a
)
–
(
d
)
. You will earn two (2) points for each correct
answer. A blank answer counts zero; a wrong answer counts –1. You will have one–two “grace” questions that you can
leave blank and still earn a perfect score.
The example problems here are indicative of the topics and format for the exam. The actual questions will be
variations with slightly different problem instances, numbers, and mathematical expressions. However, the concepts
that are tested by these questions will not change on the exam.
Problems:
1. [2] 6n2logn
+
2n
+
5isin:
(a) Θ
(
n2
)
.
(b) O
(
n2
)
.
(c) O
(
n3
)
.
(d) Ω
(
n3
)
.
2. [2] O
(
p
n
)
includes the functions:
(a) 1
2
p
nand 0
:
001n.
(b) 2
p
nlognand 2
p
n.
(c) 1
2
p
nlognand 1
2
p
n.
(d) 2
p
nand 10logn.
3. [2] If f
(
n
)
is in Θ
(
nE
)
, then:
(a) f
(
n
)
is in O
(
nE
)
but not in Ω
(
nE
)
.
(b) f
(
n
)
is in Ω
(
nE
)
but not in O
(
nE
)
.
(c) f
(
n
)
is in O
(
nE
)
andalsoinΩ
(
nE
)
.
(d) All of the above are possible, depending on fand E.
4. [2] If f
(
n
)
is in Θ
(
g
(
n
))
and lim
n
!
∞
f
(
n
)
g
(
n
)
exists, then some possible values for this limit are:
(a) 10 and 100.
(b) 0 and 100.
(c) 10 and ∞.
(d) 0, 1 and ∞.
5. [2] n
∑
k
=
1klog2
(
k
)
is in:
(a) Θ
(
nlog
(
n
))
.
(b) Θ
(
klog2
(
k
))
.
(c) Θ
(
n2log
(
n
))
.
(d) Θ
(
k2log2
(
k
))
.
