Delayed Work

This problem asks us to optimize the number of painters that need to be hired to most cheaply paint a house.

One notices that even if X is 1 and P and K are 10k, we will still only <10k painters (since the next one still costs a dollar, but saves us 10000/100001 dollars, so it's already diminishing returns). Given that result, we can iterate over all counts and find the min.

We could also ternary search or binary search.

We can also compute an exact result

Cost = XM + P*K/M

dCost/dM = X - PK/M^2

X = PK/M^2

M = sqrt(PK/X)

And evaluate cost(floor/ceil(M))