Describe step-by-step how a Prover can convince a Verifier that they know a Hamiltonian Cycle for a large graph without revealing the cycle itself. Detail the interactive protocol used, ensuring that the property of 'Zero-Knowledge' is met (simulator). Explain why this proof is computationally sound and how it could be converted into a non-interactive zero-knowledge proof (NIZKP) using the Fiat-Shamir heuristic. Discuss the computational complexity of this proof generation and verification compared to simply revealing the solution.