Problem 633. Create Circular Perfect Square Sequence

It seems there is a lot of variability depending on your particular search heuristics and the particular value of N. My solution performs in under 30 seconds for 19 out of the 20 cases 31

Hello Richard, Hello Alfonso, Hello @bmtran, Is it possible to solve this kind of problem without recursion ?

In general, sure, you can easily write these sort of heuristic-search algorithms without explicitly using recursion, or you could use non-search-based approaches, such as annealing, integer linear programming, etc. Now if you are asking whether exhaustive or other polynomial-time approaches are possible/practical for this problem I am not really sure about that. I believe this problem reduces to finding a full hamiltonian cycle over an N-node graph, so the only hope of bringing this out of the NP-hard umbrella would be exploiting some properties of these particular networks arising from the properties of perfect numbers, but so far I do not see any useful trick in this regard (so in short, perhaps it is possible but I do not know how; any thoughts?)