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Which of the following algorithms can be used to find the minimum spanning tree (MST) of an undirected graph?
- a)Dijkstra's algorithm
- b)Bellman Ford algorithm
- c)Kruskal's algorithm
- d)Ford Fulkerson algorithm
Correct answer is option 'C'. Can you explain this answer?
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Which of the following algorithms can be used to find the minimum span...
Explanation:
To find the minimum spanning tree (MST) of an undirected graph, we can use the Kruskal's algorithm. This algorithm follows a greedy approach to find the MST by selecting edges with the minimum weight and adding them to the MST until all vertices are included.
Kruskal's Algorithm:
1. Sort all the edges of the graph in non-decreasing order of their weights.
2. Initialize an empty graph to store the MST.
3. Iterate through the sorted edges and for each edge:
- If including the edge does not create a cycle in the MST, add it to the MST.
- Otherwise, discard the edge.
4. Continue this process until all vertices are included in the MST.
Comparison with other algorithms:
- Dijkstra's algorithm: Dijkstra's algorithm is used to find the shortest path from a single source vertex to all other vertices in a weighted graph. It does not directly find the minimum spanning tree.
- Bellman Ford algorithm: Bellman Ford algorithm is used to find the shortest paths from a single source vertex to all other vertices in a weighted graph. It can also handle negative edge weights. It does not directly find the minimum spanning tree.
- Ford Fulkerson algorithm: Ford Fulkerson algorithm is used to find the maximum flow in a flow network. It does not directly find the minimum spanning tree.
Therefore, the correct algorithm to find the minimum spanning tree (MST) of an undirected graph is Kruskal's algorithm.
To find the minimum spanning tree (MST) of an undirected graph, we can use the Kruskal's algorithm. This algorithm follows a greedy approach to find the MST by selecting edges with the minimum weight and adding them to the MST until all vertices are included.
Kruskal's Algorithm:
1. Sort all the edges of the graph in non-decreasing order of their weights.
2. Initialize an empty graph to store the MST.
3. Iterate through the sorted edges and for each edge:
- If including the edge does not create a cycle in the MST, add it to the MST.
- Otherwise, discard the edge.
4. Continue this process until all vertices are included in the MST.
Comparison with other algorithms:
- Dijkstra's algorithm: Dijkstra's algorithm is used to find the shortest path from a single source vertex to all other vertices in a weighted graph. It does not directly find the minimum spanning tree.
- Bellman Ford algorithm: Bellman Ford algorithm is used to find the shortest paths from a single source vertex to all other vertices in a weighted graph. It can also handle negative edge weights. It does not directly find the minimum spanning tree.
- Ford Fulkerson algorithm: Ford Fulkerson algorithm is used to find the maximum flow in a flow network. It does not directly find the minimum spanning tree.
Therefore, the correct algorithm to find the minimum spanning tree (MST) of an undirected graph is Kruskal's algorithm.
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Which of the following algorithms can be used to find the minimum span...
Kruskal's algorithm is used to find the minimum spanning tree (MST) of an undirected graph.
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Which of the following algorithms can be used to find the minimum spanning tree (MST) of an undirected graph?a)Dijkstras algorithmb)Bellman Ford algorithmc)Kruskals algorithmd)Ford Fulkerson algorithmCorrect answer is option 'C'. Can you explain this answer?
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