IGNOU MMTE 2 SOLVED ASSIGNMENT

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MMTE 2 2025 - English

Assignment

Course Code: MMTE-002

Assignment Code: MMTE-002/TMA/2025

Maximum Marks: 100

1.

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

b) Explain the string matching problem with an example.

c) Explain the Longest Common Subsequence problem with an example.

2.

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

b) 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.

3. a) 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

b) 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.

4.

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

b) 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).

5. a) Construct the Huffman code tree for the set of frequencies in the table below: 

Character	Frequency
A	5
B	1
C	6
D	3
E	4

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

6. a) 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.

b) Find the Huffman code for the following set of characters: 

Character	a	b	c	d	e	f
Frequency	50	30	20	12	5	3

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

7. a) Find the minimum spanning tree for the following graph using Kruskal’s algorithm: 

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

8. a) 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 >

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

9. a) 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.

b) 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

10. a) 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 .

b) 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.

 

MMTE 2 2026 - English

Assignment (MMTE-002)

Course Code: MMTE-002

Assignment Code: MMTE-002/TMA/2026

Maximum Marks: 100

1. a) Write an algorithm to find the first two largest numbers in an in array of integers. For example, given the input ,2 ,3 ,7 − ,4 ,1,5 the algorithm should output ,7 .5 State precisely a loop invariant for you algorithm. Prove that your loop invariant holds and hence conclude that your algorithm works.

b) Analyse the algorithm to find the upper bound for run time of the above algorith.

Based on the image provided, here is the transcribed text of the exam questions:

2. a) With the help of an example, explain the following:
    i) Algorithm,
    ii) Input and output for an algorithm
    iii) Running time of an algorithm (5)

   b) Illustrate the operations of partition in quick sort on the array
    . 

3. a) Show step by step how you will construct a binary search tree by inserting keys in the order 12, 6, 4, 7, 8, 10, 7, 5, 13, 16, 11, starting from an empty binary tree. Explain step by step how you will delete the node with the key 13 from the binary tree. (5)

   b) Illustrate the operations of performing counter sort on the array . 

4. a) Show the results of inserting the keys
   

 C, R, A, U, J, S, F, T, O, P, M, L, N, W, Q

in order into an empty B-tree with minimum degree 2. Only draw the configurations of the tree just before some node must split, and also draw the final configuration. 

   b) Using bipartite checking algorithm find out whether the graph given below is bipartite or not. 

5. a) Show step by step how the merge procedure of merge sort will merge the arrays ,1 ,3 ,4 ,7 11,9 13, 14, and ,2 ,5 ,6 10,8 12, . 

b) For the following set of points, describe how the CLOSET-PAIR algorithm finds a closest pair of points:

(1,2),(2,−1),(3,−3),(3,2),(−3,4),(−1,2),(2,3),(1,1),(−5,−2).

c)   Find an optimal parenthesisation of a matrix chain product whose sequence of dimensions is (4,8,7,2,3).

6. a) Taking  v₁ as the root, find a spanning tree of the following graph using the breadth first search (BFS) algorithm.

    b)    Determine an LCS of (1, 1, 1, 1, 0, 1, 1, 0, 1, 0) and (1, 1, 1, 0, 0, 1, 1, 0, 1, 0).

7.  a)    Apply DFS algorithm to find a spanning tree of the following graph. Also find all the fundamental cycles of the spanning tree.



    b)    Use Kruskal's algorithm to find a minimal spanning tree in the graph given below


    c)    Use Dijkstra's algorithm to find the shortest paths in the graph given below with a as the source vertex.

8. a) Construct a MAXHEAP tree on the following list of numbers

15, 22, 7, 10, 43, 52 13, 16,

     b)  Construct a binary search tree with the following keys, inserting them in the given order:
          110, 8, 19, 6, 9, 12, 32.

9.  a)  Construct the Huffman code tree for the set of frequencies in the table below:

Character	Frequency
A	5
B	1
C	6
D	3
E	4

     b)  Show the minimum heap after each of the following operations
          i)    Create with values 13, 46, 68, 15, 87, 4, 33, 21, 1, 79.
          ii)   Insertion of value 9.
          iii)  Update of value 1 by 71.

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