We show that the cost of an optimal binary search tree can vary substantially, depending only on the left-to-right order imposed on the probabilities. We also prove that the costs of some common classes of near-optimal trees cannot be bounded above by the cost of an optimal tree plus a constant.
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⋆ This work was supported by the National Research Council of Canada, while the author was at the University of Waterloo
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Allen, B. On the costs of optimal and near-optimal binary search trees. Acta Informatica 18, 255–263 (1982). https://doi.org/10.1007/BF00263193
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