Assuming that data to be transmitted consists of only characters ‘a’ to ‘g’, design the Huffman code for the following frequencies of character data. Show all the steps of building a huffman tree. Also, show how a coded sequence using Huffman code can be decoded
To design a Huffman code for the characters _______ ____ __________ ________ _______.
__________ ____ _____ _____ __________ __________ ___ ____ _______ ______ ____ __________.
__________ __________ _____ ___ ____ _____ _____ ________ ______ ______ ______ ___.
_____ _________ ____ ________ ____ ________ ___ __________ _____.
__________ _____ _________ ___ ____ ____ ______.
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Explain the Topological sorting with the help of an example. Also, explain the algorithm of finding strongly connected components in a directed Graph.
Differentiate between Cubic-time and Factorial-time algorithms. Give example of one algorithm each for these two running times.
What is an Optimisation Problem? Explain with the help of an example. When would you use a Greedy Approach to solve optimisation problem? Formulate the Task Scheduling Problem as an optimisation problem and write a greedy algorithm to solve this problem. Also, solve the following fractional Knapsack problem using greedy approach. Show all the steps.
Suppose there is a knapsack of capacity 20 Kg and the following 6 items are to packed in it. The weight and profit of the items are as under:
Select a subset of the items that maximises the profit while keeping the total weight below or equal to the given capacity.
Explain the algorithm to find the optimal Binary Search Tree. Demonstrate this algorithm to find the Optimal Binary Search Tree for the following probability data (where pi represents the probability that the search will be for the key node ki, whereas qi represents that the search is for dummy node di. Make suitable assumptions, if any)
| i | 0 | 1 | 2 | 3 | 4 |
| pi | 0.10 | 0.15 | 0.20 | 0.10 | |
| qi | 0.05 | 0.10 | 0.10 | 0.10 | 0.10 |
Explain the Rabin Karp algorithm for string matching with the help of an example. Find the time complexity of this algorithm.
Define the NP-Hard and NP-Complete problem. How are they different from each other. Explain the use of polynomial time reduction with the help of an example
Write the Prim’s algorithm to find the minimum cost spanning tree of a graph. Also, find the time complexity of Prim’s algorithm. Demonstrate the use of Kruskal’s algorithm and Prim’s algorithm to find the minimum cost spanning tree for the Graph given in Figure 1. Show all the steps.