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I need a initial post and 2 responses to classmates.

I’ll add my unit 7 discussion post and also 2 classmates posts.

Trees for Modeling Real-World Situations

In this discussion, you will continue considering the real-world contexts presented by you and your classmates in the Unit 7 Discussion Board.

Post 1: Initial Response

Using your graph from the Unit 7 Discussion, start this discussion by addressing the following to explore the modeling of your context even further:

Update your Unit 7 Discussion graph by adding a weight to each of your edges. Present your updated graph with all weighted edges.

Based on the real-world context of your graph, briefly explain what these weights represent.

Present a second illustration where you have identified a spanning tree and its total weight within your weighted graph. Describe how you know this subgraph meets the requirements of a spanning tree.

View Unit 8 Discussion Post 1 example.

Post 2: Reply to a Classmate

Review a classmate’s graph and address all of the following items completely.

Apply either Prim’s algorithm or Kruskal’s algorithm (not presented in the text so you would need to look this up elsewhere) to find a minimum spanning tree for your classmate’s weighted graph. Explain the steps taken and present the minimum spanning tree with a visual.

In the context of your classmate’s real-world context:

What is the total weight of this spanning tree?

What is the difference between your minimum spanning tree and your classmate’s spanning tree (from their initial response)?

How can you interpret the total weight for this spanning tree within the real-world context?

View Unit 8 Discussion Post 2 example.

Post 3: Reply to Another Classmate

Review a different classmate’s graph and address all of the following items completely.

Suppose your objective has been updated from spanning the graph. Now you only need to find an efficient path between any two vertices on your classmate’s weighted graph. Write your own step-by-step process (i.e., in pseudocode or a list of steps) which you propose will find the shortest path between any two vertices. Provide enough detail about the steps so that someone else would be able to apply your idea.

Select a starting and ending vertex (which are not adjacent vertices) on your classmate’s weighted graph. Apply your algorithm and present the path with a visual.

In the context of your classmate’s real-world context:

What is the total weight of your proposed shortest path?

How could the shortest path be useful to your classmate, given the real-world context?

What steps could you take to test whether or not your algorithm works for determining the shortest paths in all graphs (e.g., for graphs other than this one and for different starting/ending vertices)?