Analyse why there is a need for eco-cities in India.

Describe the concept of Economic Base Theory and discuss its limitation.

Discuss the significance of urban forests in achieving the UNSDGs.

Explain the concept of Urban Ecology. Write the major challenges of Managing life support resources in urban environment.

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.

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 .

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

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.

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

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 >

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

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

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.

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.

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

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

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).

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

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.

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