July 2018
Beginner
202 pages
5h 4m
English
Content preview from Beginning Java Data Structures and Algorithms
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Cycle Detection
A useful application of DFS is determining whether or not a graph is acyclic (that is, it does not contain cycles). In order to do so, it's important to define four types of edges in terms of the depth-first forest produced by DFS. They are as follows:
- Tree edges: They are edges in the depth-first forest. An edge can only be a tree edge if it was the one explored when first discovering a vertex.
- Back edges: They are edges connecting a vertex to an ancestor in a depth-first tree. Self-loops (which may occur in directed graphs) are back edges.
- Forward edges: They are edges that do not belong to a depth-first tree but connect a vertex to one of its descendants in a depth-first tree. Forward edges are therefore edges that weren't ...
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