Explain  depth-first search (DFS).

Depth-First Search (DFS) is a fundamental algorithm used to explore nodes and edges of a graph or tree by traversing as far as possible along each branch before backtracking. It is useful for various graph and tree operations and has distinct characteristics compared to Breadth-First Search (BFS).

Time and Space Complexity:

• Time Complexity: $O(V + E)$, where $V$ is the number of vertices and $E$ is the number of edges. Each vertex and edge is processed once.
• Space Complexity: $O(V)$, due to the space required for the stack and the set/list of visited nodes. The space complexity can also be impacted by the depth of the recursion stack in recursive implementations.