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An optimal, purely functional implementation of the Garsia–Wachs algorithm

Part of: JFP Functional Pearls

Published online by Cambridge University Press:  21 January 2020

RICHARD S. BIRD Open the ORCID record for RICHARD S. BIRD [Opens in a new window]
RICHARD S. BIRD*
Affiliation:
Department of Computer Science, Oxford University, Wolfson Building, Parks Road, Oxford, OX1 3QD, UK (e-mail: bird@cs.ox.ac.uk)
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The Garsia–Wachs algorithm is an algorithm for building a binary leaf tree whose cost is as small as possible. The problem and the algorithm are described in more detail below, but the task is essentially the same as that of building a Huffman coding tree with the added constraint that the fringe of the tree has to be exactly the given list of inputs (in Huffman coding, the fringe of the tree can be any permutation of the input). As we will show below, the Garsia–Wachs algorithm can be implemented with a linearithmic running time—a running time of O (n log n) steps for an input of length n, the same time bound as for Huffman coding.

Type
Functional Pearl
Information
Journal of Functional Programming , Volume 30 , 2020 , e3
Copyright
© Cambridge University Press 2020

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