Heap insertion time
When looking for data structure projects, you want to encounter distinct problems being solved with creative approaches. One such unique research question concerns the average case insertion time for binary heap data structures. According to some online sources, it is constant time, while others imply that it is log(n) time.
But Bollobas and Simon give a numerically-backed answer in their paper entitled,
Repeated random insertion into a priority queue. First, they assume a scenario where you want to insert n elements into an empty heap. There can be n! possible orders for the same. Then, they adopt the average cost approach to prove that the insertion time is bound by a constant of 1.7645.
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