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VTU Computer Science (Semester 3)
Data Structures and Applications
December 2015
Total marks: --
Total time: --
INSTRUCTIONS
(1) Assume appropriate data and state your reasons
(2) Marks are given to the right of every question
(3) Draw neat diagrams wherever necessary

1 (a) Explain the functions supported by C to carry out dynamic memory allocation with example.
6 M
1 (b) What is recursion? What are the various types of recursion? Write a recursive function to implement binary search.
7 M
1 (c) Define the term 'Space and time complexity'. Determine the time complexity of an iterative and recursive functions that adds n elements of an array using tabular method.
7 M

2 (a) Write a note on dynamically allocated array's with example.
6 M
2 (b) How would you represent two spare polynomials using array of structures and also write a function to add two polynomials and give the analysis of the function.
10 M
2 (c) For the given sparse matrix A and its transpose. Give the triple representation 'A' is the given sparse matrix and 'B' will be its transpose. $\text {Sparse matrix A }= \begin{bmatrix} 25 &0 &0 &11 &0 &-10 \\0 &12 &3 &0 &0 &0 \\0 &0 &0 &6 &0 &0 \\0 &0 &0 &0 &0 &0 \\81 &0 &0 &0 &0 &0 \\0 &0 &-18 &0 &0 &0 \end{bmatrix}$
4 M

3 (a) Define stack. Implement push and pop functions for stacks using arrays.
5 M
3 (b) Write the postfix form of the following expressions using stack.
i) ASB*C-D+E/F/(G+H)
ii) A-B/(C*D$E) 6 M 3 (c) What is the advantages of circular queue over linear queue? Write insert and delete functions for circular implementation of queues. 5 M 3 (d) Evaluate the following postfix expression 623+382/+*2$3+using stack.
4 M

4 (a) Write C functions to implement the insert and delete operations on a queue using linked list.
8 M
4 (b) With the node structure show would you store the given polynomials a and b in linked list? Write a C function for adding 2 polynomials using linked lists.
8 M
4 (c) Write a note on doubly linked list. How is it different from single linked list?
4 M

5 (a) What is binary tree? State its properties. How it is represented using array and linked list? Give example.
8 M
5 (b) Show the binary tree with the arithmetic expression A/B*C*D+E. Give the algorithm for inorder, preorder, postorder traversals and show the result of these traversals.
8 M
5 (c) What is heap? Explain different types of heap.
4 M

6 (a) Define binary search tree. Draw the binary search tree for the following input 14, 15, 4, 9, 7, 18, 3, 5, 16, 4, 20, 17, 9, 14, 5
7 M
6 (b) Construct a binary tree having the following sequence:
i) Preorder seq ABCDEFGHI
ii) Inorder seq BCAEDGHFI
5 M
6 (c) Write a iterative search routine for a binary search tree.
5 M
6 (d) Define the following terms:
i) Forests
ii) Graphs
iii) Winner trees.
3 M

7 (a) Briefly explain the following with examples:
i) HBLT    : ii) WBTL
8 M
7 (b) Write short notes on:
i) Priority queues
ii) Binomial heaps
iii) Priority heaps
iv) Fibonacci heaps.
12 M

Write short notes on:
8 (a) AVL trees.
5 M
8 (b) Red-black trees
5 M
8 (c) Optimal binary search trees.
5 M
8 (d) Splay trees.
5 M

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