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The most efficient algorithm for finding the number of connected components in an undirected graph on n vertices and m edges has time complexity.
- a)θ(n)
- b)θ(m)
- c)θ(m + n)
- d)θ(mn)
Correct answer is option 'C'. Can you explain this answer?
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The most efficient algorithm for finding the number of connected compo...
Connected components can be found in O(m + n) using Tarjan’s algorithm. Once we have connected components, we can count them.
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The most efficient algorithm for finding the number of connected compo...
The most efficient algorithm for finding the number of connected components in an undirected graph on n vertices and m edges has a time complexity of O(n + m).
One common algorithm for finding connected components is Depth-First Search (DFS). In this algorithm, we start from a vertex and explore all its neighboring vertices recursively. We mark each visited vertex as visited and continue until all vertices have been visited.
The time complexity of DFS is O(n + m), where n is the number of vertices and m is the number of edges. This is because each vertex is visited exactly once, and for each vertex, we visit all its neighboring vertices. The total number of operations is therefore proportional to the number of vertices and edges.
Other algorithms for finding connected components, such as Breadth-First Search (BFS) and Union-Find, also have a time complexity of O(n + m) in the worst case.
Therefore, the most efficient algorithm for finding the number of connected components in an undirected graph on n vertices and m edges has a time complexity of O(n + m).
One common algorithm for finding connected components is Depth-First Search (DFS). In this algorithm, we start from a vertex and explore all its neighboring vertices recursively. We mark each visited vertex as visited and continue until all vertices have been visited.
The time complexity of DFS is O(n + m), where n is the number of vertices and m is the number of edges. This is because each vertex is visited exactly once, and for each vertex, we visit all its neighboring vertices. The total number of operations is therefore proportional to the number of vertices and edges.
Other algorithms for finding connected components, such as Breadth-First Search (BFS) and Union-Find, also have a time complexity of O(n + m) in the worst case.
Therefore, the most efficient algorithm for finding the number of connected components in an undirected graph on n vertices and m edges has a time complexity of O(n + m).
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