Description: Depth-First Search (DFS) is a fundamental algorithm in graph theory that allows for traversing or searching data structures such as trees and graphs. Its operation is based on exploring as far as possible along each branch before backtracking. It starts at a root node and delves into adjacent nodes, marking visited nodes to avoid cycles and repetitions. This approach can be implemented recursively or using an explicit stack, allowing for efficient control over the traversal. Depth-First Search is particularly useful in situations where all possibilities need to be explored before making a decision, such as in maze solving or in searching for solutions in puzzles or games. Its time complexity is O(V + E), where V is the number of vertices and E is the number of edges, making it suitable for various types of graphs. Additionally, Depth-First Search can be adapted to find paths, cycles, or connected components within a graph, making it a versatile tool in the analysis of complex structures.
