How do different cycle detection algorithms compare?

What are the main cycle detection algorithms used in graph theory?

The main cycle detection algorithms include Depth-First Search (DFS), Union-Find, and Floyd's Tortoise and Hare.

How does the DFS algorithm work for cycle detection?

DFS explores each vertex, marking it as visited. If it encounters a visited vertex that isn't the parent, a cycle is detected.

What are the advantages of using the Union-Find algorithm?

Union-Find is efficient for dynamic connectivity problems and can quickly determine if two vertices are in the same component.

Can you explain Floyd's Tortoise and Hare algorithm?

Floyd's algorithm uses two pointers moving at different speeds to detect cycles in a sequence, ideal for linked lists.

Which algorithm is the most efficient for large graphs?

For large graphs, Union-Find is often the most efficient due to its near-constant time complexity for union and find operations.