Act as a senior software engineer with 10+ years of experience in algorithm design and optimization. Explain how to implement a depth-first search (DFS) algorithm in [PROGRAMMING_LANGUAGE] for traversing or searching [DATA_STRUCTURE]. Provide a step-by-step breakdown, including how to handle [SPECIFIC_CASE] (e.g., cycles in graphs or backtracking). Include code snippets with comments, time/space complexity analysis, and best practices for optimization. Tailor the explanation for a [TARGET_AUDIENCE] (e.g., beginners, intermediate coders, or competitive programmers).