1. Write down a non-deterministic algorithm that solves the Hamiltonian Path Problem (HPP), and runs in polynomial-time. Deduce that HPP is NP. 2. Define a polynomial time-reduction of HPP to HCP (Hamiltonian Circuit Problem). 3. Define a polynomail time-reduction of HCP to HPP. 4. Assuming that HCP is NP-complete, prove that HPP is also NP-complete.
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