The path length of binary trees
More than twenty years ago Nievergelt and Wong obtained a number of new bounds on the path length of binary trees in both the weighted and unweighted cases.
For the unweighted case, the novelty of their approach was that the bounds were applicable to all trees, not just the extremal ones. To obtain these “adaptive” bounds they introduced what came to be known as the weight balance of a tree, subsequently used as the basis of weight-balanced trees.
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