Depth-First Search Algorithm: Comprehensive Node Traversal in Networks

Depth-First Search (DFS) is a classical algorithm used for traversing or searching tree and graph structures. When traversing network nodes, DFS explores paths as deeply as possible before backtracking, systematically visiting all unvisited nodes along branches until the entire network is covered.

### Core DFS Algorithm Workflow Start Node Initialization: Select a starting node as the search origin and mark it as visited using a boolean array or visited set. Recursive Neighbor Exploration: From the current node, recursively visit all unvisited adjacent nodes using a stack-based approach (either implicit via recursion or explicit stack data structure). Backtracking Mechanism: When no unvisited neighbors remain, backtrack to the previous node and explore alternative branches using stack pop operations. Termination Condition: The algorithm completes when all nodes have been visited, verified through the visited tracking system.

### Time Complexity Analysis DFS traversal time primarily depends on network structure parameters. For networks with n nodes and m edges, the algorithm achieves O(n + m) complexity since each node and edge is processed exactly once during adjacency list traversal.

### Implementation Optimizations Visit Tracking: Utilize boolean arrays or hash sets to mark visited nodes, preventing redundant processing in cyclic graphs. Stack-Based Iteration: Replace recursion with explicit stack structures (e.g., deque in Python or Stack class in Java) to prevent stack overflow in deep networks. Path Recording: Maintain traversal stacks or timestamp arrays to track visit order for applications requiring path reconstruction or topological sorting.

DFS finds extensive applications in network analysis, maze solving, and topological sorting scenarios. Its "depth-first" exploration strategy makes it ideal for tasks requiring complete node traversal while maintaining linear time complexity relative to network size.