CS301- Data Structures Fall 2010 Paper

FINALTERM  EXAMINATION

Fall 2010

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