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A greedy algorithm for dropping digits

Part of: JFP Functional Pearls

Published online by Cambridge University Press:  04 November 2021

RICHARD BIRD Open the ORCID record for RICHARD BIRD [Opens in a new window]  and
SHIN-CHENG MU Open the ORCID record for SHIN-CHENG MU [Opens in a new window]
RICHARD BIRD
Affiliation:
Department of Computer Science, University of Oxford, Oxford OX1 3QD, UK (e-mail: richard.bird@cs.ox.ac.uk)
SHIN-CHENG MU
Affiliation:
Institute of Information Science, Academia Sinica, Taipei, Taiwan (e-mail: scm@iis.sinica.edu.tw)
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Abstract

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Consider the following puzzle: given a number, remove k digits such that the resulting number is as large as possible. Various techniques are employed to derive a linear-time solution to the puzzle: we justify the structure of a greedy algorithm by predicate logic, give a constructive proof of the greedy condition using a dependently typed proof assistant and calculate the greedy step as well as the final, linear-time optimisation by equational reasoning.

Type
Functional Pearl
Information
Journal of Functional Programming , Volume 31 , 2021 , e29
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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