Prim\'s algorithm for finding minimum spanning tree. a. Run Prim\'s algorithm on

Question

Prim's algorithm for finding minimum spanning tree. a. Run Prim's algorithm on the graph below. For simplicity we use a distance array rather than a priority queue. Label each tree edge by the order in which it was selected. Use the table below to show the contents in the two arrays D (for distance) and P (for parent vertex) after each update. Please start vertex h. b. If the edges of the graph remain the same, but all the edge weights are increased by the same constant value, do you have to re-run the Prim's algorithm to find a minimum spanning tree? c. If the edges of the graph remain the same, but all the edge weights are multiplied by the same constant factor, do you have to re-run the Prim's algorithm to find a minimum spanning tree?

Explanation / Answer

C)No need of re-run the Prim's algorithm to find a minimum spanning tree.

Prim's algorithm:Find the edge which is having less weight from current node.Add that node to minimum spanning tree.

If suppise A->B weight 3

A->C weight 2

A->D weight 1

as per Prim's algorithm we add A->D to our MST

Suppose i multiply those edge weights with some constant i.e,5

A->B updated weight 15

A->C updated weight 10

A->D updated weight 5

Still we are having same edge to our MST.so,no need of executing Prim's algorithm.

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