Using bipartite checking algorithm find out whether the graph given below is bipartite or not.
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With the help of an example, explain the following:
i) Algorithm,
ii) Input and output for an algorithm
iii) Running time of an algorithm (5)
b) Illustrate the operations of partition in quick 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 |
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 .
Use Kruskal's algorithm to find a minimal spanning tree in the graph given below
Apply DFS algorithm to find a spanning tree of the following graph. Also find all the fundamental cycles of the spanning tree.
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.
Use Dijkstra's algorithm to find the shortest paths in the graph given below with a as the source vertex.