A balanced search tree O(1) worst-case update time (Q1114387)

A new data structure is described for performing member and neighbor queries in O(log n) time that allows for O(1) worst-case update time once the position of the inserted or deleted element is known. In this way previous solutions that achieved only O(1) amortized time or \(O(\log^* n)\) worst-case time are improved. The method is based on a combinatorial result on the height of piles that are split after some fixed number of insertions. This combinatorial result is interesting in its own right and might have other applications as well.