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Asked: 2026-05-29T05:29:07+00:00

I have solved the more generic N Queens problem, but now I am looking

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I have solved the more generic N Queens problem, but now I am looking for an algorithm to solve the N Queens Domination problem.

“Given an n×n board, find the domination number, which is the minimum number of queens (or other pieces) needed to attack or occupy every square. For the 8×8 board, the queen’s domination number is 5.” – Wikipedia

I have searched extensively and cannot find anything but scholarly papers on this problem, nothing remotely understandable.

My first thoughts are to just place a Queen down and then place the next Queen in the place that can attack the most other squares, and so on. However, while this may generate a solution, I cannot figure out a way to guarantee that that solution is the minimal solution.

Any help would be appreciated, thanks.

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1 Answer

  1. Editorial Team

    Using your algorithm, you can generate all possible combinations and take minimum from it.
    Hints: Use recursion for this and don’t process similar conditions (or cache it) like symmetric placement, the same order and so on.

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