Self-adjusting binary search trees
Journal of the ACM (JACM)
Randomized binary search trees
Journal of the ACM (JACM)
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
Concrete Math
A New Method for Balancing Binary Search Trees
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
A dichromatic framework for balanced trees
SFCS '78 Proceedings of the 19th Annual Symposium on Foundations of Computer Science
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This paper presents a new method to balance binary search trees, which has the following properties. (i) The only information stored for the balance is the size of every subtree. (ii) Inserting or deleting an element can be done in the most traditional way: first, the element is recursively inserted (deleted) in (from) the appropriate subtree; afterwards, a single or double rotation takes place if necessary. (iii) Checking whether or not those rotations are required is computable in constant time per visited node. (iv) The worst-case height of these trees is never worse than approximately 1.44042log"2n, where n is the number of elements.