Does the choice of starting vertex matter in Prims algorithm?

3 Answers. That is correct. Choosing a different starting node could give you a different spanning tree, but it will always have the same weight: the minimal possible. This is because of uniqueness of minima.

What is minimum spanning tree and explain Prim’s algorithm?

The idea behind Prim’s algorithm is simple, a spanning tree means all vertices must be connected. So the two disjoint subsets (discussed above) of vertices must be connected to make a Spanning Tree. And they must be connected with the minimum weight edge to make it a Minimum Spanning Tree.

Which statement is true for prim algorithm?

Which of the following is true? Explanation: Steps in Prim’s algorithm: (I) Select any vertex of given graph and add it to MST (II) Add the edge of minimum weight from a vertex not in MST to the vertex in MST; (III) It MST is complete the stop, otherwise go to step (II).

What is the minimum cost spanning tree for the given graph using Prim’s algorithm?

The graph produces in the step 4 is the minimum spanning tree of the graph shown in the above figure. The cost of MST will be calculated as; cost(MST) = 4 + 2 + 1 + 3 = 10 units.

Is Prim’s algorithm dynamic programming?

Explanation: Prim’s Minimum Spanning Tree is a Greedy Algorithm. All other are dynamic programming based.

How does Prims algorithm work?

The steps for implementing Prim’s algorithm are as follows: Initialize the minimum spanning tree with a vertex chosen at random. Find all the edges that connect the tree to new vertices, find the minimum and add it to the tree. Keep repeating step 2 until we get a minimum spanning tree.

What is Prims algorithm in data structure?

In computer science, Prim’s algorithm (also known as Jarník’s algorithm) is a greedy algorithm that finds a minimum spanning tree for a weighted undirected graph. This means it finds a subset of the edges that forms a tree that includes every vertex, where the total weight of all the edges in the tree is minimized.

Which of the following is true about Prims and Kruskal algorithm?

Which of the following is true? Explanation: Prim’s algorithm iterates from one node to another, so it can not be applied for disconnected graph. Kruskal’s algorithm can be applied to the disconnected graphs to construct the minimum cost forest.

What is Prim’s algorithm in graph theory?

How is Prim’s algorithm calculated?

How Prim’s algorithm works

1. Initialize the minimum spanning tree with a vertex chosen at random.
2. Find all the edges that connect the tree to new vertices, find the minimum and add it to the tree.
3. Keep repeating step 2 until we get a minimum spanning tree.