Maximum Segment Sum, Monadically (distilled tutorial, with solutions)

The maximum segment sum problem is to compute, given a list of integers, the largest of the sums of the contiguous segments of that list. This problem specification maps directly onto a cubic-time algorithm; however, there is a very elegant linear-time solution too. The problem is a classic exercise...

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Bibliographic Details
Published in:	arXiv.org
Main Author:	Gibbons, Jeremy
Format:	Paper
Language:	English
Published:	Ithaca Cornell University Library, arXiv.org 18.11.2011
Subjects:	Algorithms Functional programming Integers
ISSN:	2331-8422
Online Access:	Get full text
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Summary:	The maximum segment sum problem is to compute, given a list of integers, the largest of the sums of the contiguous segments of that list. This problem specification maps directly onto a cubic-time algorithm; however, there is a very elegant linear-time solution too. The problem is a classic exercise in the mathematics of program construction, illustrating important principles such as calculational development, pointfree reasoning, algebraic structure, and datatype-genericity. Here, we take a sideways look at the datatype-generic version of the problem in terms of monadic functional programming, instead of the traditional relational approach; the presentation is tutorial in style, and leavened with exercises for the reader.
Bibliography:	SourceType-Working Papers-1 ObjectType-Working Paper/Pre-Print-1 content type line 50
ISSN:	2331-8422
DOI:	10.48550/arxiv.1109.0782