Depth-first search (DFS) is an algorithm that is based on LIFO (last-in, first-out). Since recursion is implemented with LIFO stack data structure, the nodes are in a different order than in BFS. The path is stored in each iteration from root to leaf nodes in a linear fashion with space requirement.

The Depth-first Search (DFS) algorithm is a fundamental technique used in graph traversal. It explores as far as possible along each branch before backtracking. Here’s the breakdown of how it works:

Start at a Vertex: The algorithm starts at a chosen vertex (or node) in a graph.
Explore Adjacent Vertices: It explores one of the adjacent vertices of the current vertex as deeply as possible.
Backtrack When Necessary: If the algorithm reaches a dead-end (i.e., a vertex with no unvisited adjacent vertices), it backtracks along the path until it finds a vertex with unexplored neighbors.
Repeat Until All Vertices are Visited: This process continues until all vertices in the graph are visited.

Here’s a brief description of the process in pseudo-code:

vbnet

DFS(vertex):

    Mark vertex as visited

    For each neighbor of vertex:

        If neighbor is not visited:

            Call DFS(neighbor)

DFS is often implemented using a stack data structure, either explicitly or implicitly through recursion.

It’s essential to note that DFS may not necessarily visit all vertices in a connected graph (a graph where every vertex is reachable from every other vertex). If you require visiting all vertices, you might need to modify the algorithm slightly.

DFS has various applications, including finding connected components in a graph, detecting cycles, and solving puzzles like mazes. It’s a crucial algorithm in both graph theory and artificial intelligence.