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 Merge procedure of the Merge Sort algorithm. Demonstrate the use of recursive Merge sort algorithm for sorting the following data of size 8: [19, 18, 16, 12, 11, 10, 9, 8]. Compute the complexity of Merge Sort algorithm.
Explain the term Decision problem with the help of an example. Define the following problems and identify if they are decision problem or optimisation problem? Give reasons in support of your answer.
(i) Travelling Salesman Problem
(ii) Graph Colouring Problem
(iii) 0-1 Knapsack Problem
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.
What are P and NP class of Problems? Explain each class with the help of at least two examples.
Explain the Topological sorting with the help of an example. Also, explain the algorithm of finding strongly connected components in a directed Graph.
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.
Subset Sum Problem