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#### A best possible bound for the weighted path length of binary search trees

##### MPS-Authors
http://pubman.mpdl.mpg.de/cone/persons/resource/persons45021

Mehlhorn,  Kurt
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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##### Citation

Mehlhorn, K. (1977). A best possible bound for the weighted path length of binary search trees. SIAM Journal on Computing, 6, 235-239.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0014-AFA7-A
##### Abstract
The weighted path length of optimum binary search trees is bounded above by $\sum \beta_i + 2\sum \alpha_j + H$ where $H$ is the entropy of the frequency distribution, $\sum \beta _i$ is the total weight of the internal nodes, and $\sum \alpha_j$ is the total weight of the leaves. This bound is best possible. A linear time algorithm for constructing nearly optimal trees is described.