What is an algorithm Briefly explain time complexity and space complexity of an algorithm.
Define notation n (Big Omega). If 2n^3 3n^2 1 and 2n^2 then show n Arrange the following growth rates in increasing order: O(log Draw all minimum spanning trees of the following weighted connected graph: <img src='./qimages/10757-1d.jpg'>
Write linear search algorithm and explain its best case, worst case and average case time complexity.

2.(a) Given the following list of 8 integers, sort them using insertion sort. Determine the number of comparisons required by the algorithm. Also find the total number of assignment operations in this process. <img src='./qimages/10757-2a.jpg'> Write any four characteristics of greedy algorithm.

3.(a) What is recurrence relation Draw a recursion tree for recurrence
2T 1.
Write adjacency list and adjacency matrix representation of the following graph <img src='./qimages/10757-3b.jpg'>

4.(a) Write binary search algorithm and search the value 28 in the following list, using binary search algorithm and show the steps:

1, 18, 27, 28, 30, 39
Write Prim's algorithm for finding minimum spanning tree. Find the complexity of this algorithm.

5.(a) Define the following terms
Connected graph
Cycle in an undirected graph
Consider the following fractional knapsack problem:

M=20;

Profits
P2, P3) 24, 15) w2, w3) 15, 10)

Show the running of the greedy algorithm for fractional knapsack.