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Module 3: Graph and Tree Algorithms
20247m
Write the Pseudo-code for the Dijkstra's Algorithm. Further, find the single source (A) shortest path on the following graph:
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PreviousA graph with five nodes is represented using the adjacency list as follows: | | | | | | |---|---|---|---|---| | A | -> | B (10) | C (3) | | | B | -> | C (1) | D (5) | | | C | -> | B (4) | D (8) | E (2) | | D | -> | E (7) | | | | E | -> | D (9) | | | Answer the following: (i) Draw the graph for the above adjacency list. (ii) Write the algorithm for the Breadth-First Traversal (BFS). (iii) Show the BFS traversal of the graph with the starting node as A.NextAnswer the following: (i) Explain the concept of a Minimum Spanning Tree (MST) in a connected, weighted, undirected graph. (ii) Compare and contrast Prim's and Kruskal's algorithms for finding the MST. (iii) Analyze the time complexity of both algorithms and discuss their advantages and scenarios where one is preferred over the other.