Depth-first search (DFS) is based on LIFO (last-in, first-out). A recursion is implemented with LIFO stack data structure. Thus, 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.

A depth-first search (DFS) algorithm is a technique used in computer science and artificial intelligence to traverse or search through a graph or tree data structure. In DFS, the algorithm starts at a selected node (usually the root node) and explores as far as possible along each branch before backtracking. This means that it goes as deep as possible in one direction before it has to backtrack and explore other branches.

Here’s a more detailed explanation:

Starting Point: Begin with a selected starting node.
Exploration: Explore as far as possible along each branch from the starting node.
Backtracking: If a dead end is reached (i.e., a node with no unvisited adjacent nodes), backtrack to the most recent node with unexplored branches and continue exploration.
Repeat: Repeat steps 2 and 3 until all nodes have been visited or the goal node is found.

DFS is commonly implemented using either recursion or a stack data structure. It is often used in various applications such as solving puzzles, topological sorting, graph traversal, and pathfinding algorithms like maze solving.

The key characteristics of DFS are its simplicity and the fact that it requires relatively little memory compared to breadth-first search (BFS), making it particularly useful for large, sparse graphs or trees. However, DFS may not always find the shortest path to the goal, especially if the search space is infinite or the goal is located deep in a branch far from the starting point.