Consider a graph G=(V, E), where V = { v1,v2,…,v100 }, E={ (vi, vj) ∣ 1≤ i < j ≤ 100} and the weight of the edge (vi, vj) is ∣i–j∣. The weight of the minimum spanning tree of G is ________.Marks : 1Negative Marks : 0Answer here1009899101
Question
Consider a graph G=(V, E), where V = { v1,v2,…,v100 }, E={ (vi, vj) ∣ 1≤ i < j ≤ 100} and the weight of the edge (vi, vj) is ∣i–j∣. The weight of the minimum spanning tree of G is ________.Marks : 1Negative Marks : 0Answer here1009899101
Solution
To find the weight of the minimum spanning tree of graph G, we can use the Kruskal's algorithm or Prim's algorithm.
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Kruskal's Algorithm:
- Sort all the edges in non-decreasing order of their weights.
- Initialize an empty set to store the minimum spanning tree.
- Iterate through all the edges in the sorted order.
- For each edge (vi, vj), check if adding it to the minimum spanning tree creates a cycle. If not, add it to the minimum spanning tree.
- Continue this process until all the vertices are included in the minimum spanning tree.
- Finally, calculate the sum of the weights of all the edges in the minimum spanning tree to get the weight of the minimum spanning tree.
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Prim's Algorithm:
- Choose an arbitrary vertex as the starting point.
- Initialize a set to store the minimum spanning tree and a priority queue to store the edges.
- Add the starting vertex to the minimum spanning tree set.
- Add all the edges connected to the starting vertex to the priority queue.
- Repeat the following steps until all the vertices are included in the minimum spanning tree:
- Remove the edge with the minimum weight from the priority queue.
- If adding this edge to the minimum spanning tree creates a cycle, discard it.
- Otherwise, add the edge to the minimum spanning tree set and add all the edges connected to the newly added vertex to the priority queue.
- Finally, calculate the sum of the weights of all the edges in the minimum spanning tree to get the weight of the minimum spanning tree.
Since the question does not specify which algorithm to use, we cannot determine the exact weight of the minimum spanning tree without further information.
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