Solve any one question from Q.1(a,b,c) &Q.2(a,b,c)

1(a)
Show that f(x) = 0 (x

^{3}) if function f(x) is defined as \[f(x) = 5x^{3}+6x^{2}+1\]
3 M

1(b)
Differentiate between linear and non-linear data structure with example.

3 M

1(c)
Explain divide and conquer strategy with example. Also comment on the time analysis.

6 M

2(a)
Explain fast Transpose of sparse matrix with suitable example. Discuss time complexity of fast transpose.

6 M

2(b)
Explain polynomial representation using arrays with suitable example.

3 M

2(c)
Derive recurrence relation to represent set of natural numbers giving remainder one when divided by three.

3 M

Solve any one question from Q.3(a,b,c) & Q.4(a,b,c)

3(a)
Represent the following polynomial by using-generalized linked list:

(a, b, (c, d (e, g,), h) (f))

(a, b, (c, d (e, g,), h) (f))

3 M

3(b)
Write an algorithm for postfix evaluation with suitable example.

6 M

3(c)
Write a pseudo C code to reverse singly linked list.

3 M

4(a)
Convert the following prefix expression into postfix * + a - bc / - de + -fgh

3 M

4(b)
Write an algortihm to convert infix expression to postfix expression.

6 M

4(c)
Write an algorithm to delete intermediate node from Doubly linked list.

3 M

Solve any one question from Q.5(a,b) & Q.6(a,b)

5(a)
What is circular queue? Explain the advantages of circular queue over linear queue.

6 M

5(b)
Write pseudo C/C++ code to represent queue as an ADT.

7 M

6(a)
Explain array implementation of priority queue with all basic operations.

6 M

6(b)
Write pseudo C/C++ code to implement circular queue using linked list.

7 M

Solve any one question from Q.7(a,b) &Q.8(a,b)

7(a)
Explain quick sort and sort the given list using quick sort:

39, 09, 81, 45, 90, 27, 72, 18

39, 09, 81, 45, 90, 27, 72, 18

6 M

7(b)
Write an algorithm for binary search. Derive recurrence relation and find out time complesity of the search.

7 M

8(a)
Explain heap sort and sort the given list using heap sort:

08, 03, 02, 11, 05, 14, 00, 02, 09, 04, 20.

08, 03, 02, 11, 05, 14, 00, 02, 09, 04, 20.

6 M

8(b)
Write a short note an stability of sorting. Compare bubble sort, insertion sort and selesction sort with one example and discuss time complexity.

7 M

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