Cycle Detection and Analysis

[JohnnyWan1123]

Description

Implement algorithms to detect cycles, find all cycles, detect negative cycles, and compute graph girth (shortest cycle length).

Tasks

• Implement basic cycle detection using DFS
• Implement negative cycle detection (Bellman-Ford)
• Implement shortest cycle finder (girth)
• Add option to find all cycles (with size limits)
• Handle directed and undirected graphs
• Write unit tests for various cycle scenarios
• Add performance optimizations for large graphs

Acceptance Criteria

• Cycle detection works for both directed and undirected graphs
• Negative cycles are correctly identified in weighted graphs
• Girth computation works for graphs with cycles
• All cycles can be found for small graphs (<15 nodes)
• Proper handling of acyclic graphs