Using the definition of show that 6n^2 20n Q

Given a list of n distinct integers. Write an algorithm to determine the position of an integer in the list using a linear search and count the number of comparison operations required.

By applying induction method, show that for all positive integers n

1^2 2^2 .... n^2 n(n (2n 6 .

Illustrate the representation of the following graph through adjacency list and adjacency matrix:

<img src='./qimages/13115-1d.jpg'>

Find the optimal solution to the knapsack (fractional) problem n 5 and m 10, where n is the number of objects and m is the capacity of knapsack.

Profit and weight of each object are given below:

P2, P3, P4, P5) 35, 20, 40)
W2, W3, W4, W5) 1).

Write Prim's algorithm to find the minimum cost spanning tree.

Apply QuickSort to sort the following array. Show all the steps.

15 5 10 8 7 2 20 30

What are the worst case and best case in QuickSort algorithm?

4. Define the following terms

Optimization

Dynamic programming

Recurrence relation

Asymptotic bounds

Unconnected graph

5. For the given graph, apply DFS traversal scheme and write DFS sequence. Also write the time complexity of DFS and BFS algorithms.

<img src='./qimages/13115-5.jpg'>