Sort the following numbers using Quick sort algorithm :

32,5,25,10,31,42,26
Define B-trees along with conditions. Give an example of a B-tree.

2.(a) Sort the following numbers using Heap sort algorithm:

32,5,25,10,31,42,26 What is the time complexity of Build Max Heap? Sort the following numbers using Radix sort algorithm
329,457,657,839,436,720,213,582

What is the time complexity of Radix sort algorithm

3.(a) What is an optimal Huffman Code for the following set of frequencies?

Character a b c d e f
Frequency 45 13 12 16 9 5

How many total bits are required to encode the set of characters Write Kruskal's algorithm in pseudocode. Discuss its time complexity.

4.(a) Find an optimal parenthesisation of a matrix-chain product whose sequence of dimensions is 10, 12, How can you implement efficient FIND and UNION operations for disjoint sets?

5.(a) Illustrate all the steps of Rabin-Karp-Miller string matching algorithm for P 26, T =3141592653 and Q =11. For the following network flow, draw the residual network :

<img src='./qimages/14686-5b.jpg'>

Find an augmenting path p and use it to augment the flow along p. Draw the flow network of the augmented flow.

6.(a) Compute the DFT of the vector 4). Let 1^3 2^3 ... n^3 . Show that giving the constants.