The solution to this problem is widely known and my first assumption was that the default recursive solution would fail for bigger inputs. Then I followed the tail recursive solution that going from the bottom up calculates intermediate steps to remember which path it should follow going back (memoization).

It probably could be simplified to collect all the data while going up, without the intermediate step of collecting the Path and to follow it to collect the exact values from the nodes. But this way it seemed easier to implement and to be more readable than having it done in one go. The most difficult part, performance wise, is while we're looking for the path, not getting the values, anyway.

sbt run

And then provide the file name, e.g.:
input

sbt test