I think you are missing the point. OP presented a linear time algorithm. You did not. The point of algorithms is solving problems where the input can change -

I think you are missing the point. OP presented a linear time algorithm. You did not. The point of algorithms is solving problems where the input can change - here it's n, the size of the board. Your solution, as stated, works only for a specific n. It's not an algorithm, at least by common definitions. You could adapt the solution to handle some finite number of possible inputs with: n_queens_answer = [ ... array of answers...]; for (int i = 0; i < n_queens_answer[n].length; i++) { place_queen(n_queens_answer[n][i]); This is also missing the point - obviously every finite function can be written with a lookup table. The point of algorithms is solving problems with potentially infinitely many possible inputs. In fact, time complexity terms such as "linear time" usually mean asymptotic complexity, where the time for any finite number of inputs is irrelevant. Every algorithm could be said to take linear time - even constant time - if you limit allowed length of the input! That's not useful. Even though real world computers have limited memory, the asymptotic behavior, theoretically irrelevant to practice, usually agrees with reality. In the case of n-queens, finding a pattern that solves the problem for arbitrary n does solve the puzzle. That might be disappointing or contradict intuition, but that's how computer science works. We want an asymptotically fast algorithm that outputs a correct answer, it does not matter that the answer is dull.