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Heap-like data structure with fast random access?

If few members are affected when the best entity is grabbed, then you might be able to improve the runtime by using a linked list and an unordered map (each with the original set of entities), and a max heap. After removing the best entity from the end of the linked list you'll use the map to locate the affected entities, removing them from the list and adding the non-worthless entities to the max heap. Thereafter, the next best entity is the greater of the entity at the end of the list or the max entity in the heap. The advantage of this setup is that removal from the linked list is a constant time operation, and insertion into the max heap will be a relatively small (compared to the total number of entities) log time operation.

Because entities' values can only get worse, you can lazily remove them from the linked list - if the item is worthless then remove it, and if its value has changed then flag it as "changed." Check the "changed" flag on the entity at the end of the linked list, and if it's "true" then remove the entity and add it to the max-heap. The advantage of lazy updates is that you usually won't need to update items that are in the heap (you'll just need to update the value of items in the linked list), and if an item is changed and then later made worthless then you can remove it from the linked list without ever having to add it to the heap.

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Heap-like data structure with fast random access?
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