FINAL TERM EXAMINATION
Fall 2009
CS301- Data Structures
Time: 120 min
Marks: 75
Question
No: 1 ( Marks: 1 ) - Please choose one
__________
only removes items in reverse order as they were entered.
► Stack
► Queue
► Both of these
► None of these
Question
No: 2 ( Marks: 1 ) - Please choose
one
Here is
a small function definition:
void
f(int i, int &k)
{
i = 1;
k = 2;
}
Suppose
that a main program has two integer variables x and y, which are given the
value 0. Then the main program calls f(x,y); What are the values of x and y
after the function f finishes?
► Both x and y are still 0.
► x is now 1, but y is still 0.
► x is
still 0, but y is now 2.
► x is now 1, and y is now 2.
Question
No: 3 ( Marks: 1 ) - Please choose
one
Select
the one FALSE statement about binary trees:
► Every
binary tree has at least one node.
► Every non-empty tree has exactly one root node.
► Every node has at most two children.
► Every non-root node has exactly one parent.
Question
No: 4 ( Marks: 1 ) - Please choose
one
Every
AVL is _________________
► Binary Tree
► Complete Binary Tree
► None of these
►
Binary Search Tree
Question
No: 5 ( Marks: 1 ) - Please choose
one
Searching
an element in an AVL tree take maximum _______ time (where n is no. of nodes in
AVL tree),
► Log2(n+1)
► Log2(n+1) -1
► 1.44
Log2n
► 1.66 Log2n
Question
No: 6 ( Marks: 1 ) - Please choose
one
Suppose
that we have implemented a priority
queue by storing
the items in a heap. We are now executing a reheapification downward and the
out-of-place node has priority of 42. The node’s parent has a priority of 72,
the left child has priority 52 and the node’s right child has priority 62.
Which statement best describes the status of the reheapification.
► The reheapification is done.
► The next step will interchange the two children of
the out-of-place node.
► The next step will swap the out-of-place node with
its parent.
► The next step will swap the out-of-place node with
its left child.
Question
No: 7 ( Marks: 1 ) - Please choose one
Suppose
you implement a heap (with the largest element on top) in an array. Consider
the different arrays below, determine the one that cannot possibly be a heap:
► 7 6 5 4 3 2 1
► 7 3 6 2 1 4 5
► 7 6 4 3 5 2 1
► 7 3 6 4 2 5 1
Question
No: 8 ( Marks: 1 ) - Please choose
one
If
there are 23 external nodes in a binary tree then what will be the no. of
internal nodes in this binary tree?
► 23
► 24
► 21
► 22
Lesson
# 27(the number of internal nodes is N, the number of external nodes will be
N+1.)
Question No: 9 ( Marks: 1 ) - Please
choose one
If there
are N external nodes in a binary tree then what will be the no. of internal
nodes in this binary tree?
► N -1
► N+1
► N+2
► N
Question
No: 10 ( Marks: 1 ) - Please choose
one
Which
one of the following is NOT the property of equivalence relation:
► Reflexive
► Symmetric
► Transitive
► Associative
(lesson
no 34)
Question
No: 11 ( Marks: 1 ) - Please choose
one
The
definition of Transitivity property is
► For all element x member of S, x R x
► For all elements x and y, x R y if and only if y R
x
► For
all elements x, y and z, if x R y and y R z then x R z (lesson no 34)
► For all elements w, x, y and z, if x R y and w R z
then x R z
Question
No: 12 ( Marks: 1 ) - Please choose
one
Union is
a _______ time operation.
►
Constant (
lesson # 35 page 11)
► Polynomial
► Exponential
► None of the given option
Question
No: 13 ( Marks: 1 ) - Please choose
one
Which of
the following is NOT a correct statement about Table ADT.
► In a table, the type of
information in columns may be different. yes
► A table consists of several columns, known as
entities.
(Lesson # 38 page 1 )
► The row of a table is called a
record.
► A major use of table is in
databases where we build and use tables for keeping information.
Correct A table consists of several columns, known as
fields.
Question
No: 14 ( Marks: 1 ) - Please choose
one
In the
worst case of deletion in AVL tree requires
_________.
► Only one rotation
► Rotation at each non-leaf node
► Rotation at each leaf node
►
Rotations equal to log2 N (lesson # 23)
Question
No: 15 ( Marks: 1 ) - Please choose
on
Binary Search is
an algorithm of searching, used with the ______ data.
►
Sorted (lesson # 39)
► Unsorted
► Heterogeneous
► Random
Question
No: 16 ( Marks: 1 ) - Please choose
on
Which of
the following statement is correct?
► A Threaded Binary Tree is a
binary tree in which every node that does not have a left child has a THREAD
(in actual sense, a link) to its INORDER successor.
► A
Threaded Binary Tree is a binary tree in which every node that does not have a
right child has a THREAD (in actual sense, a link) to its PREOREDR successor.
► A Threaded Binary Tree is a binary tree in which
every node that does not have a right child has a THREAD (in actual sense, a
link) to its INORDER successor.
► A Threaded Binary Tree is a
binary tree in which every node that does not have a right child has a THREAD
(in actual sense, a link) to its POSTORDER successor.
Question
No: 17 ( Marks: 1 ) - Please choose
one
By using
__________we avoid the recursive method of traversing a Tree, which makes use
of stacks and consumes a lot of memory and time.
► Binary tree only
► Threaded binary
tree (lesson
# 27 page 3)
► Heap data structure
► Huffman encoding
Question
No: 18 ( Marks: 1 ) - Please choose
one
Which
of the following statement is NOT true about threaded binary tree?
► Right thread of the right-most node points to the dummy node.
► Left thread of the left-most node points to the dummy node.
► The left pointer of dummy node points to the root
node of the tree.
► Left
thread of the right-most node points to the dummy node.
Lecture
# 28 "The left pointer of this node is pointing to the root node of the
tree while the
right pointer is seen pointing itself i.e. to dummy node. There is no
problem in doing all these things. We have put the address of dummy node
in its right pointer and pointed the left thread of the left most node towards
the dummy node. Similarly the right thread of the right-most node is
pointing to the dummy node. Now we have some extra pointers whose help
will make the nextInorder routine function properly."
Question
No: 19 ( Marks: 1 ) - Please choose
one
Consider
a min heap, represented by the following array:
11,22,33,44,55
After
inserting a node with value 66.Which of the following is the updated min heap?
► 11,22,33,44,55,66
► 11,22,33,44,66,55
► 11,22,33,66,44,55
► 11,22,66,33,44,55
Question
No: 20 ( Marks: 1 ) - Please choose
one
Consider
a min heap, represented by the following array:
3,4,6,7,5
After
calling the function deleteMin().Which of the following is the updated min
heap?
► 4,6,7,5
► 6,7,5,4
► 4,5,6,7
► 4,6,5,7
Question
No: 21 ( Marks: 1 ) - Please choose
one
We can
build a heap in ________ time.
►
Linear (lecture # 30 page 8)
► Exponential
► Polynomial
► None of the given options
Question
No: 22 ( Marks: 1 ) - Please choose
one
Suppose
we are sorting an array of eight integers using quick sort, and we have just
finished the first partitioning with the array looking like this:
2 5 1 7 9 12 11 10
Which
statement is correct?
► The
pivot could be either the 7 or the 9.
► The pivot could be the 7, but it is
not the 9.
► The pivot is not the 7, but it could be the 9
► Neither the 7 nor the 9 is the pivot.
Question No: 23 ( Marks: 1 ) -
Please choose one
Which
formula is the best approximation for the depth of a heap with n nodes?
► log
(base 2) of n
► The number of digits in n (base 10), e.g., 145 has
three digits
► The square root of n
► n
Question
No: 24 ( Marks: 1 ) - Please choose
one
Suppose
you implement a Min heap (with the smallest element on top) in an array.
Consider the different arrays below; determine the one that cannot possibly be a heap:
► 16, 18, 20, 22, 24, 28, 30
► 16, 20, 18, 24, 22, 30, 28
► 16, 24, 18, 28, 30, 20, 22
►
16, 24, 20, 30, 28, 18, 22
Question
No: 25 ( Marks: 1 ) - Please choose
one
While
joining nodes in the building of Huffman encoding tree if there are more nodes
with same frequency, we choose the nodes _______.
► Randomly
► That occur
first in the text message
► That are lexically smaller among others.
► That are
lexically greater among others
Question No: 26 ( Marks: 1 ) -
Please choose one
Consider
the following paragraph with blanks.
A
…….…….. is a linear list where …………… and ………… take place at the
same end
. This end is called the …….……….
What
would be the correct filling the above blank positions?
► (i) queue (ii) insertion (iii) removals (iv) top
► (i) stack (ii) insertion (iii) removals (iv) bottom
► (i)
stack (ii) insertion (iii) removals (iv) top
► (i) tree (ii) insertion (iii) removals (iv) top
Question
No: 27 ( Marks: 1 ) - Please choose
one
A binary
tree with 33 internal nodes has _______ links to internal nodes.
► 31
► 32 (n-1 links to internal nodes)
► 33
► 66 (2n
links)
A
binary tree with N internal nodes has N+1 external nodes.
Property:
A binary
tree with N internal nodes has 2N links:
N-1 links to internal nodes and N+1 links to
external nodes.
Question
No: 28 ( Marks: 1 ) - Please choose
on
Which
traversal gives a decreasing order of elements in a heap where the max element
is stored at the top?
► post-order
► level-order
► inorder
► None of the
given options
Question
No: 29 ( Marks: 1 ) - Please choose
one
What
requirement is placed on an array, so that binary search may be used to locate an entry
► The array elements must form a
heap.
► The array must have at least 2 entries.
► The array must
be sorted. (lecture # 38)
► The array’s size must be a power of two.
Question
No: 30 ( Marks: 1 ) - Please choose
one
Which of
the following is a non linear data structure?
► Linked List
► Stack
► Queue
►
Tree (lecture # 11 page 4)
question No: 31 ( Marks: 1 )
If
a Binary Tree has N internal nodes what are the no. of external nodes in it.
.
Lesson # 27(the number of internal nodes is N, the number of external nodes
will be N+1.)
Question
No: 32 ( Marks: 1 )
What
is meant by Symmetry in equivalence relations?
Sol.=
Symmetry in equivalence relations mean for all elements x and y, x R y if and
only if y R x
Question
No: 33 ( Marks: 2 )
How
heap sort works to sort a set of data.
Question
No: 34 ( Marks: 2 )
How we
can apply Find operation on elements combined through Union operation.
Question
No: 35 ( Marks: 3 )
How
we can use concept of equivalence relations to generate a Maze.
Question
No: 36 ( Marks: 3 )
Suppose
we are sorting an array of eight integers using a some quadratic sorting
algorithm. After four iterations of the algorithm’s main loop, the array
elements are ordered as shown here:
2
4 5 7
8 1 3 6
Which
statement is correct? (Note: Our selectionsort picks largest items first.)
A. The
algorithm might be either selectionsort or insertionsort.
B. The
algorithm might be selectionsort, but it is not insertionsort.
C. The algorithm is not selectionsort, but it might
be insertionsort. (Correct)
D. The
algorithm is neither selectionsort nor insertionsort.
E. None
of these.
Question
No: 37 ( Marks: 3 )
How many
leaf and non-leaf nodes are present in a complete binary tree if its depth is 7
?
Solution:
Leaf
nodes = 2^7=128
Non-leaf
nodes =127
Question
No: 38 ( Marks: 5 )
If we
insert a new element into an AVL tree of height 4, is one rotation sufficient
to re-establish balance? Justify your answer.
Question
No: 39 ( Marks: 5 )
Write
down the C++ code from Selection Sort Algorithm.
Question
No: 40 ( Marks: 10 )
Consider
the following data:
the
cat in the hat
a) Build frequency table for the
above data.
b) Create a Huffman tree to determine
the binary codes for each character.
c) What will be the code of each
letter?
a)
|
Character
|
Frequency
|
|
c
|
1
|
|
i
|
1
|
|
n
|
1
|
|
e
|
2
|
|
a
|
2
|
|
h
|
3
|
|
t
|
4
|
|
sp
|
4
|
|
Character
|
Code
|
|
c
|
0000
|
|
i
|
0001
|
|
n
|
0010
|
|
e
|
0011
|
|
a
|
010
|
|
h
|
011
|
|
t
|
10
|
|
sp
|
11
|
c)
Question
No: 41 ( Marks: 10 )
Suppose
we have build a Skip list .Now we want to add and remove items from the list
.Give Algorithms for insert
(item) and delete (item) methods of the Skip List.
Solution:
When we are going to insert (add) an item (x,0)
into a skip list, we use a randomized algorithm. We send the item in a pair.
insert
To
insert an item (x, o) into a skip list, we use a
randomized algorithm:
•
We
repeatedly toss a coin until we get tails, and we denote with i the number of times the coin came
up heads
•
If
i ³
h, we add to
the skip list new lists Sh+1, … , Si +1, each containing only the two
special keys
•
We
search for x in the skip list and find the
positions p0, p1 , …, pi of the items with largest key
less than x in each list S0, S1, … , Si
•
For
j ¬ 0, …, i, we insert item (x, o) into list Sj after position pj
delete
To
remove an item with key x from a skip list, we proceed as
follows:
•
We
search for x in the skip list and find the
positions p0, p1 , …, pi of the items with key x, where position pj is in list Sj
•
We
remove positions p0, p1 , …, pi from the lists S0, S1, … , Si
•
We
remove all but one list containing only the two special key
