By Thomas E. Gerasch
Communications of the ACM,
Vol. 31 No. 5, Pages 579-585
This paper presents an insertion algorithm for maintaining a binary search tree with minimal internal path length. The insertion algorithm maintains minimal internal path length by displacing keys when necessary, in an inorder fashion, until a vacant position is found in the last incomplete level of the tree. The algorithm produces trees that are optimal for searching while exhibiting a runtime behavior that is between logarithmic and linear in the number of nodes in the tree, with linear time being its worst-case behavior.
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