Homework 5 Solution

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Figure 1: A directed weighted graph.

Question 1 (20 points)

Starting from G, trace the operations of the Dijkstra’s weighted shortest path algorithm on the graph given in Figure 1.

Question 2 (15 points)

Starting from G, trace the operations of the Prim’s minimum spanning tree algorithm on the graph given in Figure 1.

Question 3 (15 points)

Trace the operations of Kruskal’s minimum spanning tree algorithm on the graph given in Figure 1.

Question 4 (15 points)

Starting from S, trace the operations of breadth-first traversal on the graph given in Figure 2.

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Figure 2: A directed weighted graph.

Question 5 (20 points)

Given Figure 2 and starting from S,

  1. Trace the operations of depth-first traversal.

  1. Give the post-order numbers for all the nodes.

  1. Give the pre-order numbers for all the nodes.

  1. List the tree arcs, cross arcs, forward arcs, and backward arcs.

Question 6 (15 points)

Find a topological ordering of the graph given in Figure 3.

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Figure 3: An example DAG.

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