Finding the longest path in a graph is itself a pretty well-described NP-complete problem: https://en.wikipedia.org/wiki/Longest_path_problem

Alternately, you can listen to a Billy Joel parody that describes the problem in decidedly less academic terms: https://www.youtube.com/watch?v=a3ww0gwEszo

Hmm fun study topic: which major algorithms stay the same when you "invert" their goal, and which don't?

Where invert can mean at the least: switch max/min or gt/lt, but also for find the subset, find what's not in the subset. At the least.