CS8391 Data Structures Part B Questions Anna University

CS8391
DATA
STRUCTURES
ANNA UNIVERSITY QUESTION BANK
PART B QUESTIONS
FROM
REGULATION 2008 &2013 QUESTION PAPERS
COMPILED BY:
DR. P. SUBATHRA. M.E., Ph.D.,
PROFESSOR IN INFORMATION TECHNOLOGY
KAMARAJ COLLEGE OF ENGINEERING AND TECHNOLOGY
MADURAI DISTRICT, NEAR VIRUDHUNAGAR, TAMIL NADU, INDIA
UNIT I - LINEAR DATA STRUCTURES
1

ARRAYS
1. Consider an array A[1:n]. Given a position, write an algorithm to insert an element in the array. If
the position is empty, the element is inserted easily. If the postion is already occupied the element
should be inserted with the minimum number of shifts. (Note: The elements can shift to the left or
to the right to make the minimum number of moves)
2. Describe the data structures used to represent lists. (16)
SINGLY LINKED LIST
3. Describe the data structures used to represent lists. (16)
4. Write a C code for singly linked list with insert, delete, display operations using structure pointer.
(16)
5. Illustrate the algorithms to create the singly linked list and perform all the operations on the
created list. (16)
6. Write algorithms to insert and delete elements from a linked list. Consider all cases. (16)
7. What is a singly linked list? Write a C program that uses functions to perform the following
operations on singly list with suitable diagrammatic representations. Consider all cases: (16)
a. Insertion b. Deletion c. Traversal in both ways
8. Write a program to print the elements of a singly linked list. (8)
9. Explain with an example the creation of a linked list, insertion and deletion of nodes and
swapping of any two nodes.
10. Develop a C program to split the linked list into two sub lists containing odd and even ordered
elements in them respectively. (16)
11. Write a C Program to add two polynomials using linked list. (16)
12. Write a program to add two polynomials using linked list. (16)
13. Develop the program in C to delete a node with the minimum value from a singly linked list. (16)
14. Formulate an algorithm to perform an insertion in a singly linked list in an increasing order of
their INFO field. (10)
15. Explain the following: (8+8)
b. Application of lists
c. Polynomial manipulation
16. Given two sorted lists L1 and L2, write a procedure to compute (10)
2

d. L1 intersection L2
e. L1 union L2 using only the basic list operations
17. Given two sorted linear linked lists L1 and L2, how do you create a list L3, which consisits of the
uncommon elements of L1 and L2? Write a suitable ADT for the construction of doubly linked
list L3. (8)
DOUBLY LINKED LIST
18. Illustrate the algorithm to implement the doubly linked list and perform all the operations on the
created list. (16)
19. Illustrate the necessary algorithms to implement doubly linked list and perform all the operations
on the created list. (16)
20. Describe the creation of a doubly linked list and appending the list. Give relevant coding in C.
21. Write an algorithm to perform insertion and deletion on a doubly linked list. (8)
22. Write a C program that uses functions to perform the following opearations on doubly linked list
f. Creation b. Insertion c. Deletion d. Traversal in both ways
23. Develop an algorithm to implement a Doubly Linked List. Give relevant example and
diagrammatic illustrations.
24. Write a procedure to insert a node, delete a node, count and display nodes in doubly linked list.
(16)
25. Write a program to store the polynomial expression terms in random order, display the terms in
descending order of powers and count the number of terms in the expression using doubly linked
list. (16)
CIRCULAR LINKED LIST
26. Write the program in C to transform a circular list into a chain. (8)
UNIT II - LINEAR DATA STRUCTURES – STACKS, QUEUES
3

STACK
1. Develop an algorithm to implement a Stack ADT. Give relevant example and diagrammatic
illustrations. (16)
2. Develop an algorithm to implement Stack ADT. Give relevant examples with diagrammatic
representations. (16)
3. Write and explain the ADT operations for array implementation of a Stack. (8)
4. Discuss about Stack ADT in detail. Explain any one application of stack. (16)
5. Develop algorithm for inserting and deleting values from a stack. (8)
6. Define C functions to evaluate a postfix expression using stack operation. (8)
7. Write a C program to convert an infix expression into a prefix expression (8)
8. Write a program to conver an infix expression to a postfix expression and evaluate that postfix
expression. (16)
9. Explain the process of postfix expression evaluation with an example. (8)
10. Explain the process of conversion from infix expression to postfix expression using stack. (6)
11. Write an algorithm to convert infix to postfix notation and prefix notation using stack. (16)
12. Explain the process of conversion from infix expression to postfix expression using stack. (6)
13. Explain the process of postfix expression evaluation with an example. (8)
14. Write an algorithm to convert the infix expression to postfix expression using stack. (8)
15. Write an algorithm to convert the infix expression to postfix expression. (10)
16. Write algorithm to convert infix to postfix notation and prefix notation using stack. (16)
17. Show the simulation using stack for the following expression to convert infix to postfix:
p * q + ( r – s/ t). (6)
18. Show the simulation using stack for converting the expression p * q+ ( r- s / t) from infix to
prefix. (6)
19. Write an algorithm to convert an infix expression to a postfix expression. Trace the algorithm to
convert the infix expression “(a+b)”c/d+e/f” to a postfix expression. Explain the need for infix
and postfix expressions. (16)
20. Simulate using Stack to convert the infix expression to postfix expression. (6)
A*(B+D)/E-F*(G+H/K)
21. Show the simulation using stack for the following expression: (6)
12+3*14 – (5*16) + 7
4

22. Simulate the conversion of infix to postfix expression using stack for the following expression: 3
– (4 / 2) + ( 1* 5 ) + 6. (8)
23. Trace the stack for the conversion of ((((A/B)-C)+(D+E))-(A*C)) from infix to postfix. (4)
QUEUE
1. Define Queue ADT. How is circular queue implemented? Give example.
2. Develop an algorithm to implement Queue ADT. Give relevant examples and diagrammatic
representations. (12)
3. Write and explain the ADT operations for array implementation of a Queue. (8)
4. Formulate an ADT to implement Queue using linked list. (8)
5. Explain about Queue ADT in detail. Explain any one application of queue with suitable example.
(16)
6. List the applications of Queues. (6)
7. Write an ADT for Enqueue and Dequeue. (6)
8. Develop algorithm for inserting and deleting values from a queue. (8)
CIRCULAR QUEUE
9. Write a C program to implement the circular queue using arrays. (8)
10. Write ADTs for insert and deleted operations in a Circular Queue using singly linked list. (8)
11. Describe circular queue implementation in detail giving all the relevant features. (16)
12. Differentiate between double ended queue and Circular queue. (4)
13. Write an algorithm to implement circular queue using arrays. (10)
14. Write an algorithm to perform the four operations in a double ended queue that is implemented as
an array. (16)
15. Write an algorithm to convert the infix expression to postfix expression. (10)
16. Write an algorithm to implement the circular queue using arrays. (10)
17. A circular queue has a size of 5 and has elements 10, 20 and 40 where F=2 and R=4. After
inserting 50 and 60, what is the value of F and R. Trying to insert 30 at this stage what happens?
Delete 2 elements from the queue and insert 70, 80 & 90. Show the sequence of steps with
necessary diagrams with the value of F and R. (6)
DEQUE (DOUBLE ENDED QUEUE)
18. Differentiate between double ended queue and Circular queue. (4)
5

19. Write a code to create generic data structure called dequeue which consists of a list of items. The
following operations are performed in deque: (12)
a. Push(x): insert item x on the front of the deque.
b. Pop(): Remove the front item from the deque and return it.
c. Inject(x): insert item s on the rear end of the deque
d. Eject(x): remove the rear item from the deque and return it.
Unit III
NON LINEAR DATA STRUCTURES – TREES
TREES
1. Define Tree. Explain the tree traversals with algorithms and examples. (16)
2. With suitable syntax, explain the tree traversals. (8)
6

3. Explain the tree traversals. Give all the essential aspects. (16)
4. Write an iterative algorithm to traverse a tree in preorder. (6)
BINARY TREES
5. Explain the array representation of a binary tree with suitable example. (8)
6. Construct a binary tree to satisfy the following orders:
Inorder : 2, 3, 4, 5, 6 7, 8, 9, 11, 12, 15, 19, 20
Postorder : 3, 2, 5, 6, 4, 8, 11, 9, 15, 20, 19, 12, 7
7. Write short notes on the applications of trees. (4)
8. Write a C program to delete all the leaf nodes of a binary tree. (8)
9. List the different types of Tree Traversal. Develop an algorithm for traversing a Binary Tree.
Validate the algorithm with a suitable example. (16)
10. Write in detail the various methods in which a binary tree can be represented. Discuss the
advantage and disadvantage of each method. (10)
11. Explain by an algorithm to create and delete a particular node from a binary tree. (8)
BINARY SEARCH TREES
12. Give the analysis of insertion and deletion operations of nodes in binary search tree. (16)
13. Explain binary search tree ADT in detail. (16)
14. Formulate an algorithm for performing insertion and deletion in a binary search tree. (10)
15. Write suitable ADTs to perform insertion and deletion operations in Binary Search Tree. (8)
16. Write a program to insert a node in a binary search tree. (8)
17. Make a BST for the following sequence of numbers. 45, 36, 76, 23, 89, 115, 98, 39, 41, 56, 69,
48. Traverse the tree in preorder, inorder and postorder. (6)
18. Simulate the result of inserting: 61, 32, 36, 14, 6, 75, 82, 3, 19, 87, 94 one at a time, into an
initially empty binary search tree. (4)
19. Simulate the deletion of the elements 36, 87, 61, 75 one by one from the above binary search tree.
(4)
20. Explain the operations of insertion of nodes into and deletion of nodes from a binary search tree
with code. (10)
21. Construct binary search tree to insert the following key elements. (10)
22, 44, 18, 35, 20, 12, 52, 19, 39 and delete 44 from it.
7

22. What is binary search tree? Write a C program to perform the following operations in a binary
search tree. i). Insert ii). Delete iii). Find Min iv). Find Max (16)
23. Write an algorithm to search for key elements from Binary Search Tree. (6)
24. Write generic code to insert into binary search tree (8)
25. Write an algorithm for binary search tree. Give example. (16)
26. Write generic code to insert into a binary search tree. (8)
27. Write the routine for the post order traversal. Give the preorder, postorder and inorder traversal
for the following tree. (8)
28. Write an ADT for Inorder, Preorder and Postorder traversals. Traverse the given tree using
Inorder, Preorder and Postorder Traversals. (12)
29. Write the function to perform insertion in a binary search tree. Show the result of inserting 4, 3, 8,
1, 9, 7, 10, 2, 5 into an empty binary search tree. (8)
EXPRESSION TREES
30. Explain expression tree with an example. (8)
31. Construct an expression tree for the expression (a+b*c) +((d*e+1)*g). give the output when you
apply preorder, inorder and postorder traversals. (6)
AVL TREES
32. Write the four AVL rotation functions only. (6)
8

33. Define AVL Trees. Explain its rotation operations with example.(16)
34. Define AVL tree and starting with an empty AVL search tree, insert the following elements in the
given order: 35, 45, 65, 75, 15, 25. (8)
35. Explain the AVL rotation with a suitable example. (8)
36. Explain the following routines in AVL tree with example. (16)
a. Insertion b. Deletion c. Single rotation d. Double rotation
37. Explain the AVL rotations with suitable example. (8)
38. Discuss how to insert an element in an AVL tree. (8)
39. Construct an AVL tree with the values 11, 5, 35, 8, 4, 2, 3, 77, 1 into an initially empty tree.
Write the code for inserting into an AVL tree. (10)
40. Assume the following keys form the Binary Search Tree (50, 30, 60, 40, 35, 80, 90). Analyze the
time complexity involved in searching the keys 90 and then 80, when the given BST is converted
into AVL or Splay tree. Identify the suitable tree data structure for representing this data and
justify your answer with valid reasons. (15)
41. Explain the possible AVL rotations with algorithm and example. (13)
42. Show the results of inserting 4, 1, 2, 5, 6, 7, 3 into an initially empty AVL tree. (8)
43. Define AVL tree and starting with an empty AVL search tree, insert the following elements in the
given order: 2, 1, 4, 5, 9, 3, 6, 7. (8)
44. Assume the following keys from the Binary Search Tree (50, 30, 60, 40, 35, 80, 90). Analyze the
time complexity involved in searching the keys 90 and 80, when the given BST is converted into
AVL or Splay tree. Identify the suitable tree data structure for representing this data and justify
your answer with valid reasons. (15)
45. Construct AVL tree for the following after rotation. (4+8+4)
9

THREADED BINARY TREES
46. Explain the Threaded Binary Tree with example. (8)
47. Explain about threaded binary tree in detail. (8)
48. Develop an algorithm to implement a Threaded Binary Tree. Validate the algorithm with a
suitable example. (16)
B TREES
49. Explain the operations which are done in B Tree with examples. (16)
50. Discuss in detail the B-tree. What are its advantages? (16)
51. Construct a B Tree with order m=3 for the key values 2, 3, 7, 9, 5, 6, 4, 8, 1 and delete the values
4 and 6. Show the tree in performing all operations. (6)
52. Draw B tree of order m=5 for the keys { K, O, S, V, M, F, B, G, T, U, W}. (6)
a. Delete the keys K and G in order. (4)
b. Justify the number of splits needed for insert/ delete with proper reasons. (3)
53. Insert into a B- Tree of order 5 with the following data: 8, 96, 116, 2, 7, 104, 110, 37, 86, 55, 46,
137, 145, 4, 5, 58, 6. (10)
54. Consider a B-Tree of order m=200. Calculate the number of keys searched in 4 passes. (6)
HEAPS
55. Compare min heaps and leftist trees. (4)
56. Explain binary heap that has a max-value at the root. (6)
10

57. Develop an algorithm to implement a Binary Heap. Validate the algorithm with a suitable
example. (16)
58. Explain binary heaps in detail. Give its merits. (16)
59. What is heap order property? Explain the operations which can be done in heap with examples.
(16)
60. Write the HeapSort algorithm. (8)
61. Show how heapsort processes the input 142, 543, 123, 65, 453, 879, 579, 434, 111, 242, 811, 102
(8)
62. Write a program that performs the following operations in a binary heap. (8)
a. Insert b. DeleteMin c. BuildHeap d. FindMin
63. Explain heap structures. How are binary heaps implemented? Give its algorithm with example.
(16)
64. Illustrate the construction of Binomial Heaps and its operations with a suitable example. (16)
65. Merge the given Binomial heaps. Write procedure for merge operation.
c. Delete three elements from the merged Binomial Queue. (5)
66. Explain insertion and deletion operations on Fibonacci heaps. Construct Fibonacci heaps for the
following set of elements 10, 11, 5, 35, 8, 4, 2, 3, 77, 1, 45. (13)
67. On an empty binomial heap, carry out the following sequence of operations: insert (27) insert(17)
insert(19) insert(20) insert(24) insert(12) insert(10) insert(14) insert(18), deletemin. After each
operation draw the resulting structure of the heap. (6)
68. Implement the Fibonacci heaps and compare their performance with binary heaps when used in
Dijkstra’s algorithm. (16)
UNIT IV
NON LINEAR DATA STRUCTURES – GRAPHS
GRAPH REPRESENTATION
11

24. Write the representation for the graph shown in Figure 1 as: (8)
a. Adjacency matrix b. Adjacency Lists c. Adjacency multilists
GRAPH TRAVERSAL
25. Write algorithm to compute the depth first search and apply the same to Figure 1. List the vertices
in the order they would be visited. (8)
26. Present the pseudocode of the different graph traversal methods and demonstrate with an
example. (13)
27. Given the BFS and DFS of the following Graph. (8)
28. Write the routines for post-order traversal. Give the preorder, postorder and inorder traversals for
the following tree. (8)
29. Write and trace the following algorithms with suitable example. (10)
a. Breadth-First Traversal
b. Depth-First Traversal
30. Apply depth first and breadth first search to the complete graph on four vertices. List the vertices
in the order they would be visited. (16)
31. Discuss any two applications of depth-first search. (8)
SPANNING TREE
12

32. Develop an algorithm to find the minimal spanning tree using Prim’s algorithm. Validate the
algorithm with a suitable example. (16)
33. Describe the Prim’s algorithm for minimum spanning tree. Give an example. (16)
34. Write a pseudo code for Prim’s algorithm. Also give an example to construct a minimum
spanning tree. (6)
35. Consider the following graph shown below and obtain the minimum spanning tree using prim’s
algorithm. (10)
36. Compute the minimum spanning tree for the following graph. (8)
37. Explain the Kruskal’s algorithm with an example. (10)
38. Consider the following graph. Obtain minimum spanning tree by Kruskal’s algorithm (10)
13

39. Determine the minimum spanning tree of a given Graph using Kruskal’s algorithm. Write
Kruskal’s MST algorithm. (10+3)
40. Find the minimum spanning tree for the given graph using both Prim’s and kruskal’s algorithm
and write the algorithms. (8 +8)
41. Explain about Prim’s and Kruskal’s algorithm in detail. (16)
42. Construct minimum spanning tree for the following graph using Prim’s and Kruskal’s algorithm.
(16)
43. Explain Prim’s and Kruskal’s algorithm. Find the minimum spanning tree for the following graph
using any one of the algorithms. (16)
14

TOPOLOGICAL SORT
44. Explain Topological sort with an example (6)
45. Write procedure to perform topological sort and explain. (16)
BICONNECTIVITY- CUT VERTEX
46. Define network flow problem. Explain the maximum flow algorithm for the graph given below.
(16)
EULER’S CIRCUIT
47. Explain Euler’s circuit with an example. (6)
48. Write a program to find an Euler circuit in a graph. Trace the algorithm with example. (6)
49. Give a short note on Euler circuits. (6).
50. Explain Euler Circuit with an example (6)
GRAPH SHORTEST PATH
51. Explain the Dijkstra’s algorithm for finding the shortest path with a sample graph. (16)
52. Consider the following graph. Determine the shortest distance to all other nodes using Dijkstra’s
algorithm. Write Procedure. (10+3)
53. Using Dijkstra’s algorithm find the shortest path from the source node A. (15)
15

54. For the given graph, find the shortest path from vertex 1 to all other vertices. (8)
55. Illustrate the Dijkstra’s algorithm for finding the shortest path with the following graph. (12)
56. Write the pseudo code for Dijkstra’s shortest path algorithm. Trace the algorithm for the
following graph. (8)
57. Find the shortest path from V1 to V7 using Dijkstra’s algorithm in the graph given below. (16)
16

58. Write the Pseudo code for Dijkstra’s shortest path algorithm. Give suitable example to trace the
algorithm. (10)
59. Develop an algorithm to compute the shortest path using Dijkstra’s algorithm. Validate the
algorithm with a suitable example. (16)
60. Explain greedy algorithm by solving the problem of single source shortest path of a digraph using
Dijkstra’s algorithm. (10)
61. Explain any one of the shortest path algorithms with suitable example.
62. Find the shortest path from ‘a’ to ‘d’ using Dijkstra’s algorithm in the graph in Figure 2. Given in
question (10)
UNIT V
SEARCHING, SORTING AND HASHING TECHNIQUES
SEARCHING
1. Write a C program to search a number with the given set of numbers using binary search. (8)
2. Explain the following:
17

a. Binary Searching (8)
b. Rehashing (8)
3. Write an algorithm to search a number in a given set of numbers using binary search. (8)
SORTING
4. Sort the given integers and show the intermediate results using selection sort. 45, 25, 10, 2, 9, 85,
102, 1 (8)
5. Write a C code to sort an integer array using selection sort (8)
6. Write the algorithm for Shell sort. (6)
7. Show how Heap sort processes the input 15, 75, 10, 80, 21, 35, 23, 8, 12, 7. (6)
8. Explain Heap sorting of data with suitable example. (10)
9. Explain shell sort algorithm with an example. (6)
10. Illustrate with an example the insertion sort algorithm to sort a list of elements in ascending order.
(6)
HASHING TECHNIQUES
11. Explain separate chaining and extendible hashing. (16)
12. With a procedure and a relevant example discuss separate chaining in hashing. (16)
13. Explain the open addressing and chaining methods of collision resolution techniques in hashing.
(16)
14. What is hashing? Explain open addressing and separate chaining methods of collision resolution
techniques with examples. (16)
15. Explain open addressing with its probing in detail.
16. Briefly explain the three common collision resolution strategies in open addressing hashing. (16)
17. Explain the collision resolving schemes in hashing with proper illustrations. (16)
18. What is collision in terms of hashing? Explain any thre collision resolution methods with
example. (8)
19. Illustrate with example the open addressing and chain method of collision resolution techniques
in hashing. (16)
20. Write short notes on hashing and the various collision resolution techniques. (8)
18

21. Illustrate collision resolution methods in hashing. (8)
22. Explain about different types of hash functions. (8)
23. Given Input (4371, 1323, 6173, 4111, 4299, 9669, 1989) and a hash function h(X) = X (mod 10)
show the result of: (16)
a. Separate chaining hash table.
b. Open addressing hash table using linear Probing
c. Open addressing hash table using Quadratic Probing
d. Open addressing hash table with second hash function h2(X)=7-(Xmod 7)
24. Explain the following:
a. Binary Searching (8)
b. Rehashing (8)
25. Write functions to insert/ retrieve an item into/from a hash table of size 31 using open addressing
and linear probing. Devise your own hash function and obtain the hash addresses for the keys 78,
101, 155, 289, 2345, 4000. Assume the following for the item. (16)
typedef struct item
{
Int key;
Double info;
}ITEM;
26. Show the extendable hash structure for the file if the hash function is h(x)=xmod 8 and bucket
can hold three records.
27. Formulate an algorithm to implement open addressing hash table with operations,
InitializeTable(), Insert(), Delete() and Find(). (10)
28. Consider inserting the key 10, 22, 31, 4, 15, 28, 17, 88, 59 into a hash table of length m=11 using
open addressing with the primary hash function h’(k)=k mod m. illustrate the result of inserting
these keys using linear probing, using quadratic and using double hashing with h2(k)=1+(k
mod(m-1)). (6)
29. Write a program to implement extendible hashing. If the table is small enough to fit in main
memory, how does its performance compare with open and closed hashing? (16)
30. Create extendible hash structure to insert the following key elements 2, 3, 5, 7, 11, 17, 19, 23,
29,31 (16)
19

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