Depth-First Search Algorithm MATLAB Source Code with Randomness Enhancement

This text presents a MATLAB implementation of the depth-first search algorithm. The program performs node traversal and cycle detection, following standard DFS principles. The key enhancement involves introducing randomness at branch points - when encountering multiple possible paths, the algorithm randomly selects the next node, transforming it into a randomized depth-first search algorithm. The implementation maintains the core DFS functionality using stack-based traversal and visited node tracking. The random selection mechanism utilizes MATLAB's randperm or randi functions to choose among available branches, adding probabilistic path exploration. This modification enhances algorithm flexibility and applicability, making it particularly useful for scenarios requiring non-deterministic exploration or when dealing with graphs where branch order doesn't affect correctness. The algorithm employs adjacency list or matrix representation for graph structure, with main functions handling stack operations, neighbor identification, and cycle detection through back-edge identification. The randomness implementation occurs specifically in the node selection phase while preserving the fundamental DFS backtracking mechanism. For detailed understanding of the underlying algorithm and implementation specifics, users should consult the original English comments which explain the core DFS mechanics, time complexity (O(V+E)), and memory management approaches.