What is the time complexity of detecting a cycle in an undirected graph using DFS?O(V)O(V+E)O(ElogV)O(V^2)
Question
What is the time complexity of detecting a cycle in an undirected graph using DFS?
- O(V)
- O(V + E)
- O(E log V)
- O(V^2)
Solution
The time complexity of detecting a cycle in an undirected graph using Depth-First Search (DFS) is O(V + E), where V is the number of vertices and E is the number of edges in the graph.
Here's a step-by-step explanation:
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DFS traversal starts by picking a source node and visiting as far as possible along each branch before backtracking.
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DFS visits each vertex once and scans through all the corresponding edges of the vertex.
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Therefore, the time complexity of DFS is O(V) for visiting all vertices and O(E) for scanning all edges.
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Hence, the total time complexity of detecting a cycle in an undirected graph using DFS is O(V + E).
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