Eulerian and Hamiltonian Path Algorithms

[JohnnyWan1123]

Description

Implement algorithms to check for and find Eulerian paths/circuits and Hamiltonian paths/circuits. Note: Hamiltonian is NP-complete, so focus on small graphs and verification.

Tasks

• Implement Eulerian path/circuit existence check (degree conditions)
• Implement Eulerian path/circuit finder (Fleury's or Hierholzer's algorithm)
• Implement Hamiltonian path/circuit verification (check if given path is valid)
• Add Hamiltonian existence check with timeout for small graphs
• Support both directed and undirected graphs for Eulerian
• Write comprehensive unit tests
• Add clear feedback for why Eulerian path doesn't exist

Acceptance Criteria

• Eulerian algorithms work correctly for all graph types
• Hamiltonian verification works for any graph size
• Hamiltonian existence check works for graphs up to 10 nodes
• Clear feedback when paths don't exist
• Unit tests cover all edge cases