Do you mean "incrementally by 1 each iteration" where you wrote "monotontically", in your reference to Stormbringer's algorithm?
Mathematically, I do not see how any solution could beat Stormbringer's, by considering the cases where tolerance = k+0.5 and tolerance = ((kk +k)/2+0.5, which shows that the set of tolerances for a building of height > (kk+k)/2 requires >= k+1 drops to validate. But I have not been quite formal in my analysis.
Mathematically, I do not see how any solution could beat Stormbringer's, by considering the cases where tolerance = k+0.5 and tolerance = ((kk +k)/2+0.5, which shows that the set of tolerances for a building of height > (kk+k)/2 requires >= k+1 drops to validate. But I have not been quite formal in my analysis.
(Argh, asterisks!)