IGNOU MMTE 2 SOLVED ASSIGNMENT 2025

Ques 1.

Define and explain the Big-O, Big - 2 and Big - notations with examples.

Ques 2.

Explain the string matching problem with an example.

Ques 3.

Explain the Longest Common Subsequence problem with an example.

Ques 4.

Sort the following numbers using the QuickSort algorithm: 2, 9, 7, 6, 4, 3, 8, 5

Ques 5.

Construct a Binary Search Tree for the following sequence of numbers: 15, 50, 70, 60, 20, 90, 10, 40, 100, 35 with 40 as the value of the key for the root node.

Ques 6.

Show the results of inserting the keys below in order into an empty B-tree of minimum degree 2:

2, 5, 4, 3, 6, 9, 8, 7, 1, 2

Ques 7.

Determine the LCS of (1, 1, 1, 1, 1, 0, 0, 1, 1, 1) and (1, 0, 1, 0, 0, 1, 1, 0, 1, 0) using dynamic programming approach, showing all the steps.

Ques 8.

Find an optimal parenthesisation of a matrix chain whose sequence of dimensions is (5, 10, 3, 12, 15).

Ques 9.

Let me NO {0} and n∈ N. Let the god of x, y ∈ Z be denoted by (x, y). Prove that (m, n) = (m (mod n), n).

Ques 10.

Construct the Huffman code tree for the set of frequencies in the table below: 

Ques 11.

Find an optimal parenthesisation of the matrix chain product whose sequence of dimensions is 10, 25, 10, 5, 17.

Ques 12.

Find a minimal spanning tree for the following graph using the Prim’s algorithm, showing all the steps. Take v1 as the root.

What is the weight of the minimal spanning tree you get? Give reasons for your answer.

Ques 13.

Find the Huffman code for the following set of characters: 

Show all the steps of the algorithm. Also compute the number of bits require to encode the data.

Ques 14.

Find the minimum spanning tree for the following graph using Kruskal’s algorithm: 

Ques 15.

Let α = 352 b, = 671. Find s and t such that as + bt = gcd ).b,a( Show the steps of the algorithm

Ques 16.

Illustrate the working of the function PARTITION of the quicksort algorithm using the array and using the last element as PIVOT:

< 35, 22, 11, 45, 26, 71, 82, 37 >

Ques 17.

Write the steps to search the numbers 18 and 45 in the binary search tree:

Ques 18.

Explain the breadth first search algorithm using the graph given below with v1 as the source vertex:

For each stage of the algorithm give:

i) ),v(d π )v( for each vertex, where )v(d is the distance from the source to the vertex v and is the predecessor of v.

ii) White and gray vertices

iii) Vertices in the queue

Also, give the breadth search tree.

Ques 19.

Check whether the following array represents a max-heap. If not run an algorithm to convert it into a max-heap:

6, 20, 18, 15, 17, 11, 12, 13

Ques 20.

Illustrate, giving all the steps, the operation of the counting sort algorithm on the array

A = 3,4,2,7,5,4,2,1,3,1,7 .

Ques 21.

Consider the following undirected graph G with vertices labeled from 1 to 5:

Determine if there exists a clique of size 3 in the graph G. If yes, provide the vertices forming the clique.

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