Yeah I think the trivial solution is always harder complexity and the main challenge is to lower it. Either from NP to P or from n*2 to n log n.

> or from n*2 to n log n.

I guess you mean n^2 (or maybe n**2, if you're a fellow Pythonista). Many of these — especially the ones where the intended solution is characterized as using a "dynamic programming" technique — are reducible to n.