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 sparse polynomials using array of structures and also write a function to add two polynomial and give the analysis of the function.

10 M

2(c)
For the given sparse matrix A and its transpose, give the triplet 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 expression using stack:

i)ASB*C-D+E/F/(G+H)

A-B/(C*D$E)

i)ASB*C-D+E/F/(G+H)

A-B/(C*D$E)

6 M

3(c)
What is the advantage 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 6 2 3 + - 3 8 2 / + * 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 how 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

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

i) Forests

ii) Graphs

iii) Winner trees

3 M

7(a)
Briefly explain the following with examples:

i) HBLT ii) WBLT

i) HBLT ii) WBLT

8 M

Write short notes on:

7(b)(i)
Priority queues

3 M

7(b)(ii)
Binomial heaps

3 M

7(b)(iii)
Priority heaps

3 M

7(b)(iv)
Fibonacci heaps

3 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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