Depth-first search

Depth-first search (DFS) is an algorithm for traversing or searching tree or graph data structures. The algorithm starts at the root node (selecting some arbitrary node as the root node in the case of a graph) and explores as far as possible along each branch before backtracking. Extra memory, usually a stack, is needed to keep track of the nodes discovered so far along a specified branch which helps in backtracking of the graph.

Depth-first search

Order in which the nodes are visited
Class	Search algorithm
Data structure	Graph
Worst-case performance	${\displaystyle O(|V|+|E|)}$ for explicit graphs traversed without repetition, ${\displaystyle O(b^{d})}$ for implicit graphs with branching factor b searched to depth d
Worst-case space complexity	${\displaystyle O(|V|)}$ if entire graph is traversed without repetition, O(longest path length searched) = ${\displaystyle O(bd)}$for implicit graphs without elimination of duplicate nodes
Optimal	no (does not generally find shortest paths)

A version of depth-first search was investigated in the 19th century by French mathematician Charles Pierre Trémaux as a strategy for solving mazes.