Depth-first search

Depth-first search is a graph traversal algorithm that follows one path as far as possible before backtracking to explore alternatives. It can be implemented with recursion or an explicit stack.

Stack (abstract data type): A collection that adds and removes items at one end, following last-in, first-out order. DFS uses this order to resume the most recently explored path after reaching a dead end.
Topological sorting: A linear ordering of a directed acyclic graph's vertices in which every edge points forward. Reverse DFS finish order produces a topological ordering when the graph has no directed cycle.
Breadth-first search: A graph traversal algorithm that explores vertices in increasing distance from a starting vertex. Unlike DFS, it explores a whole frontier before moving to greater depths.
Graph theory: The mathematical study of vertices, edges, and the structures and relationships they form. DFS operates on this broader mathematical structure.
Recursion: A technique in which a function solves a problem by calling itself on smaller or related inputs. Recursive DFS stores unfinished visits in the program's call stack.
Tarjan's strongly connected components algorithm: A linear-time DFS algorithm that finds all strongly connected components of a directed graph. It augments DFS with discovery indices and low-link values to identify components.
Dijkstra's algorithm: An algorithm that finds shortest paths from a source in a graph with nonnegative edge weights. DFS does not account for path costs and cannot guarantee shortest paths.
Graph traversal: The systematic process of visiting vertices or edges in a graph. DFS is one of the two standard strategies for traversing a graph.
Backtracking: A search strategy that abandons a path when it cannot lead to a desired result and returns to an earlier choice. DFS backtracks when the current vertex has no unvisited neighbors.
Kosaraju's algorithm: A two-pass graph algorithm that finds strongly connected components using DFS and the graph's transpose. It uses DFS finish order to choose the sequence for its second traversal.

Linked from 19 pages