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Home/ Questions/Q 8740255
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Editorial Team
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Editorial Team
Asked: June 13, 20262026-06-13T11:05:57+00:00 2026-06-13T11:05:57+00:00

I am trying to solve the Hamiltonian Cycle problem. I am able to find

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I am trying to solve the Hamiltonian Cycle problem. I am able to find a path with all the vertices, but unable to complete the cycle.

Can someone provide me with an algorithm to find the cycle?

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  1. Editorial Team
    Editorial Team
    2026-06-13T11:05:58+00:00Added an answer on June 13, 2026 at 11:05 am

    Determining if a graph has a Hamiltonian Cycle is a NP-complete problem. This means that we can check if a given path is a Hamiltonian cycle in polynomial time, but we don’t know any polynomial time algorithms capable of finding it.

    The only algorithms that can be used to find a Hamiltonian cycle are exponential time algorithms. Some of them are

    • Brute force search
    • Dynamic programming
    • Other exponential but nevertheless faster algorithms that you can find here
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