I'd never heard of Big O until this thread, but from what I can tell it'll only be when a solution is in the O(logn) that "running time will get less significan

I'd never heard of Big O until this thread, but from what I can tell it'll only be when a solution is in the O(logn) that "running time will get less significant as n gets larger". This is simply the way you describe logarithmic growth, so maybe that's where you got confused. Also, wouldn't it be fair to say that a logarithm (nlogn) is a lower order term than mn? In which case your definition stands. At any rate, I wanted to test this out, so I made a naive benchmark for running these functions. The dict solution was ten times faster (0.0011s vs 0.015s) than the list version with ~1350 words. The dict solution ran in 0.13s at ~162,000 words, while I waited a couple minutes before killing the list version on that input.