In the BinarySearch Tree, we discussed what should be an efficient find algorithm; with the worst-case performance it achieves for the various operations is linear time, which is no better than the performance of list-based and array-based tree implementations. The simple correction is to add a rule to the binary search tree definition that maintains a logarithmic height for the tree. The rule we consider in this section is the following height-balance property, which characterizes the structure of a binary search tree T in terms of the heights of its internal nodes.
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