Question

(c) Simulate breadth first search on the graph shown in Fig HW2Q1c. You can assume that the starting vertex is 1, and the neighbors of a vertex are examined in increasing numerical order (i.e. if there is a choice between two or more neighbors, we pick the smaller one). You have to show: both the order in which the vertices are visited and the breadth first search tree. No explanations necessary.

(d) On the same graph, i.e. the graph in Fig HW2Q1c, simulate depth first search . You can assume that the starting vertex is 1, and the neighbors of a vertex are examined in increasing numerical order (i.e. if there is a choice between two or more neighbors, we pick the smaller one). You have to show: both the order in which the vertices are visited and the depth first search tree. No explanations necessary.

(e) What is the topological order (no explanations necessary) on the graph shown in Fig HW2Q1e, if we use the method discussed in class and in section 9.4.1 of Brassard and Bratley (i.e. the algorithm which adds a print statement at the end of the DFS procedure and then reverses a list at the end) assuming that the starting vertex is 1, and the neighbors of a vertex are examined in increasing numerical order. Please note that I am asking specifically what will be the topological order produced by this algorithm i.e. it is not enough just to show another topological order.

(f) Trace the execution of Kruskal’s algorithm on the graph shown in Fig HW2Q1f. Show the connected components each time a new edge is added.

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Answer 1

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