Apply DFS algorithm to find a spanning tree of the following graph. Also find all the fundamental cycles of the spanning tree.
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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 .
Taking v1 as the root, find a spanning tree of the following graph using the breadth first search (BFS) algorithm.
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.
Analyse the algorithm to find the upper bound for run time of the above algorith.
Show step by step how the merge procedure of merge sort will merge the arrays ,1 ,3 ,4 ,7 11,9 13, 14, and ,2 ,5 ,6 10,8 12, .
Using bipartite checking algorithm find out whether the graph given below is bipartite or not.
