CSI2114  Fall 2004  Midterm Exam
University of Ottawa
School of Information Technology and Engineering
Date: Sunday October 24, 2004
This is a closed books exam. No calculators allowed. You have 2 hours to ﬁnish.
Answer in the spaces provided.
There are 30 marks available in total.
Good Luck!
NAME:
STUDENT NUMBER:
SECTION:
Page
Marks of each page
PAGE 2
out of 7
PAGE 3
out of 8
PAGE 4
out of 6
PAGE 5
out of 6
PAGE 6
out of 3
BONUS
TOTAL
out of 30
1
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View Full DocumentSome summations you might need:
∑
n
i
=0
i
=
n
·
(
n
+1)
2
,
∑
n
i
=0
a
i
=
a
n
+1

1
a

1
,
∑
n
i
=1
log
n
=
O
(
n
log
n
),
∑
n
i
=1
i
·
2

i
<
2
Question 1
[1 point] What is the running time complexity of the following Algorithm (in
bigOh notation) ?
Algorithm
Hello(A).
Let
A
be an array of size
n
.
for
i
←
0
to
n

1
do
for
j
←
n

1
to
i
do
A
[
i
]
←
A
[
i
] +
A
[
j
]
a)
O
(log
n
)
b)
O
(
n
)
c)
O
(
n
log
n
)
?
d)
O
(
n
2
)
Why?
(Here not required for full marks) You can count the number of executions of the inner
loop for each step in the outer loop:
n
+(
n

1)+(
n

2)+
. . .
+1 =
∑
n
k
=1
k
=
n
+1
2
n
=
O
(
n
2
)
Or, you could turn the loops directly into sums:
∑
n

1
i
=0
∑
n

1
k
=
i
1 =
∑
n

1
i
=0
n

i
=
n
+1
2
n
=
O
(
n
2
Question 2
[3 points] Fill the blanks below: (for each question, give the best possible
bigOh).
•
3
n
2
+ 2
n
+ 5
n
3
is
O
(
n
3
)
•
3
n
2
+
n
log
n
+
1
n
3
is
O
(
n
2
)
•
30
n
2
+ 2
n
+
n
8
is
O
(2
n
)
Question 3
[1 point] Which of the following functions grows fastest?
?
a)
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 Fall '09
 mohammadomar
 Articles with example pseudocode, Tree traversal, Nested set model

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