Apply DFS algorithm to find a spanning tree of the following graph. Also find all the fundamental cycles of the spanning tree.
We first interpret the graph (vertices are labeled ( {1,2,3,4,6,7,8,9} ); there is no vertex 5). Edges present in the graph (from the figure): Left part [ (1,2), (1,3), (2,3), (2,4), (3,4) ] Middle–right part [ (4,6), (6,7), (7,9), (6,9), (6,8), (8,9), (4,8) ] --- ## 1. DFS Spanning Tree Assume: * Start vertex = 1 * Adjacency explored in increasing numerical order ### DFS traversal [ 1 \rightarrow 2 \rightarrow _____ ______ _________ __________ ____ ___ __________ ___ ___ ________ _________.
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Construct a binary search tree with the following keys, inserting them in the given order:
110, 8, 19, 6, 9, 12, 32.
Taking v1 as the root, find a spanning tree of the following graph using the breadth first search (BFS) algorithm.
Use Dijkstra's algorithm to find the shortest paths in the graph given below with a as the source vertex.
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.
Apply DFS algorithm to find a spanning tree of the following graph. Also find all the fundamental cycles of the spanning tree.
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, .