What is the complexity of cycle detection in graphs?
An example of an AI chatbot conversation about the complexity of cycle detection in graphs.
What is the complexity of cycle detection in graphs?
The complexity of cycle detection in graphs depends on the algorithm used. For example, Depth-First Search (DFS) can detect cycles in O(V + E) time.
Can you explain how DFS detects cycles?
Sure! DFS explores each vertex and keeps track of visited nodes. If it encounters a visited node that isn't the parent, a cycle is detected.
Are there other algorithms for cycle detection?
Yes, besides DFS, you can use algorithms like Union-Find for undirected graphs or Floyd's Tortoise and Hare for directed graphs.
What about the space complexity of these algorithms?
The space complexity for DFS is O(V) due to the recursion stack, while Union-Find can be O(V) as well, depending on the implementation.
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