[Solved] CS 300 Homework 5

Question 1

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

Question 2

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

Question 3

Trace the operations of Kruskals minimum spanning tree algorithm on the graph given in Figure 1.

Question 4

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

Figure 2: A directed weighted graph.

Question 5

Given Figure 2 and starting from S,

1. Trace the operations of depth-first traversal.
2. Give the post-order numbers for all the nodes.
3. Give the pre-order numbers for all the nodes.
4. List the tree arcs, cross arcs, forward arcs, and backward arcs.

Question 6

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

Figure 3: An example DAG