Triple Edge Swap Simple Algorithm

In computer science, the Hamiltonian Cycle Problem is classified as an NP-complete problem, meaning that finding a Hamiltonian cycle requires computational time that grows exponentially with problem size. This code implements a simple algorithm based on triple edge swaps designed to handle practical real-world instances. The algorithm operates by iteratively modifying three edges in the current path to potentially improve the cycle, using techniques like local search and neighborhood exploration. For example, in circuit design, Hamiltonian cycles can traverse each circuit node to ensure electrical integrity and stability - the algorithm's edge swapping mechanism helps optimize such traversals. Furthermore, the application extends to domains like logistics and transportation route planning, where the algorithm can optimize paths and reduce costs through successive edge modifications. The implementation includes key functions for cycle validation, edge selection, and swap operations, providing a practical approach to this complex problem. Overall, this code offers a straightforward method for addressing Hamiltonian cycle problems with broad practical applications.