Using bipartite checking algorithm find out whether the graph given below is bipartite or not.
Answer: The graph is *not bipartite*. ### Reasoning using the bipartite checking (2-coloring) algorithm A graph is bipartite iff ___ __________ ________ ________ ________ ____.
_________ _______ ___ _______ _______ ___ __________ _________ ________ _______.
____ ________ ________ _________ ____ _____.
_______ ________ ______ __________ _____ _________ ________.
_______ __________ ________ ______ ________ _________ _______ _______ _______ __________ ______ ___.
___ ________ ________ ________ _______ ____ ______.
______ ________ _________ ________ _______ ______.
______ _________ _________ ______ ____ ______ ____ ____ _____ ______.
________ ______ ______ ____ ______ ______ ___ ________ ______ _______ __________.
_______ _______ __________ _________ _________.
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Use Kruskal's algorithm to find a minimal spanning tree in the graph given below
Show the minimum heap after each of the following operations
i) Create with values 13, 46, 68, 15, 87, 4, 33, 21, 1, 79.
ii) Insertion of value 9.
iii) Update of value 1 by 71.
Construct a binary search tree with the following keys, inserting them in the given order:
110, 8, 19, 6, 9, 12, 32.
Find an optimal parenthesisation of a matrix chain product whose sequence of dimensions is (4,8,7,2,3).
Show step by step how you will construct a binary search tree by inserting keys in the order 12, 6, 4, 7, 8, 10, 7, 5, 13, 16, 11, starting from an empty binary tree. Explain step by step how you will delete the node with the key 13 from the binary tree. (5)
b) Illustrate the operations of performing counter sort on the array .
Construct the Huffman code tree for the set of frequencies in the table below:
| Character | Frequency |
| A | 5 |
| B | 1 |
| C | 6 |
| D | 3 |
| E | 4 |
Construct a MAXHEAP tree on the following list of numbers
15, 22, 7, 10, 43, 52 13, 16,