To paraphrase, the problem asks for a data structure with the following operations
* use_resources(name, quantity) which does resources[name] += quantity

* get_approximate_max() which returns name1 such that max(resources[name]) / 2 <=  resources[name1] <= max(resources[name])

* get_approximate_top() which returns name1 such that max(resources[name]) / 2 <=  resources[name1] <= max(resources[name])

Using a map in combination with heap gives us a solution with O(log n) time for each of the two operations. Can we do better?

Using a map in combination with a hash table gets a solution that has O(log n) complexity for use_resources and get_approximate
_top which is too slow.