Algorithms (Sec: 102) Homework 4: Graph Algorithms: Part I

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In this homework, we will focus our attention to searching on graphs and finding minimum span-ning trees.

Problem 1: Graph Traversal 50 points

1. Demonstrate both breadth-first search (BFS) and depth-first search (DFS) algorithms (with v1 as the start node) on the unweighted, undirected graph shown in Figure 1. Clearly show how each node-attribute (including frontier) changes in each iteration in both the algorithms. (20 points)

2. Implement both BFS and DFS algorithms in Python using a graph class based on adjacency list representation, and demonstrate it on the example graph shown in Figure 1. (30 points)

Figure 1: Example Graph for Search Algorithms

Topic 4: Graph Algorithms: Part I 2

Problem 2: Minimum Spanning Trees 50 points

1. Demonstrate Prim’s algorithm (with vertex v10 as the start node) for the Petersen graph shown in Figure 2. (20 points)

2. Implement Prim’s algorithm in Python as a method within the graph class built using adja-cency matrix representation, and demonstrate it on the Petersen graph shown in Figure 2. (15 points)