Exponential tree

An exponential tree is almost identical to a binary search tree, with the exception that the dimension of the tree is not the same at all levels. In a normal binary search tree, each node has a dimension (d) of 1, and has 2d children. In an exponential tree, the dimension equals the depth of the node, with the root node having a d = 1. So the second level can hold four nodes, the third can hold eight nodes, the fourth 16 nodes, and so on.

Exponential tree
Typetree
Invented1995
Invented byArne Andersson
Time complexity in big O notation
Algorithm Average Worst case
Space O(n) O(n)
Search O(min(log n, log n/log w+ log log n, log w log log n)) O(min(log n, log n/log w+ log log n, log w log log n))
Insert O(min(log n, log n/log w+ log log n, log w log log n)) O(min(log n, log n/log w+ log log n, log w log log n))
Delete O(min(log n, log n/log w+ log log n, log w log log n)) O(min(log n, log n/log w+ log log n, log w log log n))
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