I tried the problem in conditions (4h to produce the best score possible) adapting a personal algorithm that solves the knapsack problem but was unable to correct a bug in time (my method to compute the intermediate score would always output 0) so I butchered a greedy solution during the last 30minutes.
My quick greedy algorithm gives pools at random and insert the servers as tightly as possible from the bigger to the smaller. It gave a result worth 136points (I would have needed 360points to be qualified).
Instead of searching for the best combination of pool and row per server at once, one can cut the problem into two parts to make it easier to solve :
- putting servers in the data center to maximize the total capacity
- putting the servers into pools to maximize the guaranteed capacity
The best approach to maximize the total capacity is probably to rely on a variant of the knapsack problem but here I will still try to implement a solution in a short time (while still not peeking at other participants solutions).
Selecting pools using an approach akin to longest task first scheduling was enough to get 314points.
Changing the criteria for the greedy algorithm from bigger first to (most_efficient,bigger) first got me to 371points (enough to get in the final round).
The greedy solution takes time to implement and is far from optimal but it helps to debug everything and, at least, gives a solution.
I literally lost most of my time tracking the bug, it might be easier in group were some peoples can test part of the code while others redact the parts that are still missing.
Some functions to update a single value in a list/array or get the index of the min/max/verify_predicate would have been useful.
I found a post on a forum saying that two selected teams used a similar greedy algorithm. It appears to be the main approach to solve that problem.