Why do we need asymptotic notation? Justify with an example. Solve the following recurrence relation using iteration method.
T(n) = 2T(n-1) + 1, T(0) = 1
How does greedy approach differ with dynamic approach? Find the maximum loot from following information using 0/1 Knapsack problem, where weight of knapsack (W) is 20.
| Items | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| Profit(P) | 4 | 2 | 2 | 1 | 2 | 3 | 50 |
| Weight(w) | 12 | 2 | 3 | 4 | 1 | 1 | 10 |
Find the LCS between "TELEMEDICINE" and "ELECTIFINE".
Attempt any Eight questions
[8x5=40]Using Quick sort, arrange the following data set in ascending order.
23, 6, 7, 89, 24, 9, 11, 56, 43, 22, 99, 3.
Select the maximum size set of mutually compatible activities, S : {1,2, 3, 4, 5, 6,7 , 8, 9, 10} with respective start and end time {(5,9), (1,2), (3,4), (2,6), (5,7), (8,9), (4,10), (9,7), (12,13), (15,20)}
Explain the detail worst case analysis of Randomized Quick Sort.
Define about left turn, right turn, ear, mouth and diagonal. Explain the Graham's scan algorithm to find convex hull.
What is an optimal Huffman code for the following set of frequencies, based on the first 8 Fibonacci numbers?
A:1, B:1,C:2, D:3, E:5, F:8, G:13,H:21
Define convex hull. How a given polygon can be triangulated? Justify your answer with example.
Why do we need concept of NP completeness? Discuss about Approximation algorithm for vertex cover problem.