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...

Full description

Saved in:
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
Tags: Add Tag
No Tags, Be the first to tag this record!
Abstract 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.
AbstractList 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.
Author Gibbons, Jeremy
Author_xml – sequence: 1
  givenname: Jeremy
  surname: Gibbons
  fullname: Gibbons, Jeremy
BookMark eNotjctKAzEAAIMoWGvvHgNeFLprHpvXUUp9QIuH9l6S3URTsolusrb-vQU9zWWYuQLnMUULwA1GdSMZQw96OPrvGmOkaiQkOQMTQimuZEPIJZjlvEcIES4IY3QClmt99P3Yw419720scDP2c7hOUXe-1SH8wLvO5-JDsB0sY0mD12EOD758wJzCWHyK-f4aXDgdsp39cwq2T8vt4qVavT2_Lh5XlWaYVo4jI4jByHSdkMoaw5Rs28ZpbaQRrSaC4MbK9uTRjivrMHOCC2eUtI0idApu_7KfQ_oabS67fRqHeDruCJJccsQ4pb_pGU63
ContentType Paper
Copyright 2011. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
Copyright_xml – notice: 2011. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
DBID 8FE
8FG
ABJCF
ABUWG
AFKRA
AZQEC
BENPR
BGLVJ
CCPQU
DWQXO
HCIFZ
L6V
M7S
PHGZM
PHGZT
PIMPY
PKEHL
PQEST
PQGLB
PQQKQ
PQUKI
PRINS
PTHSS
DOI 10.48550/arxiv.1109.0782
DatabaseName ProQuest SciTech Collection
ProQuest Technology Collection
Materials Science & Engineering Collection
ProQuest Central (Alumni)
ProQuest Central UK/Ireland
ProQuest Central Essentials
ProQuest Central
Technology collection
ProQuest One Community College
ProQuest Central
SciTech Premium Collection
ProQuest Engineering Collection
Engineering Database
ProQuest Central Premium
ProQuest One Academic
Publicly Available Content Database
ProQuest One Academic Middle East (New)
ProQuest One Academic Eastern Edition (DO NOT USE)
ProQuest One Applied & Life Sciences
ProQuest One Academic (retired)
ProQuest One Academic UKI Edition
ProQuest Central China
Engineering Collection
DatabaseTitle Publicly Available Content Database
Engineering Database
Technology Collection
ProQuest One Academic Middle East (New)
ProQuest Central Essentials
ProQuest One Academic Eastern Edition
ProQuest Central (Alumni Edition)
SciTech Premium Collection
ProQuest One Community College
ProQuest Technology Collection
ProQuest SciTech Collection
ProQuest Central China
ProQuest Central
ProQuest One Applied & Life Sciences
ProQuest Engineering Collection
ProQuest One Academic UKI Edition
ProQuest Central Korea
Materials Science & Engineering Collection
ProQuest Central (New)
ProQuest One Academic
ProQuest One Academic (New)
Engineering Collection
DatabaseTitleList Publicly Available Content Database
Database_xml – sequence: 1
  dbid: PIMPY
  name: Publicly Available Content Database
  url: http://search.proquest.com/publiccontent
  sourceTypes: Aggregation Database
DeliveryMethod fulltext_linktorsrc
Discipline Physics
EISSN 2331-8422
Genre Working Paper/Pre-Print
GroupedDBID 8FE
8FG
ABJCF
ABUWG
AFKRA
ALMA_UNASSIGNED_HOLDINGS
AZQEC
BENPR
BGLVJ
CCPQU
DWQXO
FRJ
HCIFZ
L6V
M7S
M~E
PHGZM
PHGZT
PIMPY
PKEHL
PQEST
PQGLB
PQQKQ
PQUKI
PRINS
PTHSS
ID FETCH-LOGICAL-a513-f60b72b10bdd789ebb598cc4faab8b7ca27214e8c60b3d69ef15f767fb98e4923
IEDL.DBID PIMPY
IngestDate Mon Jun 30 09:27:17 EDT 2025
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed false
IsScholarly false
Language English
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-a513-f60b72b10bdd789ebb598cc4faab8b7ca27214e8c60b3d69ef15f767fb98e4923
Notes SourceType-Working Papers-1
ObjectType-Working Paper/Pre-Print-1
content type line 50
OpenAccessLink https://www.proquest.com/publiccontent/docview/2086860563?pq-origsite=%requestingapplication%
PQID 2086860563
PQPubID 2050157
ParticipantIDs proquest_journals_2086860563
PublicationCentury 2000
PublicationDate 20111118
PublicationDateYYYYMMDD 2011-11-18
PublicationDate_xml – month: 11
  year: 2011
  text: 20111118
  day: 18
PublicationDecade 2010
PublicationPlace Ithaca
PublicationPlace_xml – name: Ithaca
PublicationTitle arXiv.org
PublicationYear 2011
Publisher Cornell University Library, arXiv.org
Publisher_xml – name: Cornell University Library, arXiv.org
SSID ssj0002672553
Score 1.4722952
SecondaryResourceType preprint
Snippet 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...
SourceID proquest
SourceType Aggregation Database
SubjectTerms Algorithms
Functional programming
Integers
Title Maximum Segment Sum, Monadically (distilled tutorial, with solutions)
URI https://www.proquest.com/docview/2086860563
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV1JTwIxFG4UNPHkHhckPXjQhJHZ2zmZaCB6gEyEA55IV0MyLM4AwX9vXxnwYOLJpLf28NL2Lf3e6_cQuhUQ9LoBcyTl0gk1NzoXBdKhzFXCuAjjNahtNkG6XToYJGn5Pbooyyo3NtEa6jXbM9RtGyPclFMBiLl5stOYmkg8Dh5nnw70kIJca9lQYxdVgXjLraBq-tpJ37eYix8TE0EH62ylpfJqsnw1WlrazQdwlr8ssnUz7cP_FfDICMZmKj9GO2pygvZtsacoTlGrw1aj8WKMe-oDwEHcW4wb2Gg3s0mb7AvfSVD9LFMSz4HkwFzSBgbIFm-v6v0Z6rdb_ecXp2yn4LDICxwdu5z43HO5lIQmivMooUKEmjFOORHMN4_BUFFh1gUyTpT2Ik1ionlCFdC4naPKZDpRFwiHkXATN2TaHG1I4oT6HjdxjwZ2P645u0S1zRYNS5Uohj87cvX39DU6sMAtDFpDlXm-UDdoTyznoyKvo-pTq5u-1aFIs1cvT_gbVsK2dQ
linkProvider ProQuest
linkToHtml http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V3JSgNBEC1iVPTkjkvUPigoZHQya89BPGhCQhYCySGeQq8SyGY2k4_yH62eLB4EbzkIc-th6JmqelX1qqcK4EaYoNd2mSUpl5anOdqc70qLMlsJdBHoNWg8bCKsVGijEVUT8LX8F8Ycq1xiYgzUsicMR45JOg0oxt6B-9z_sMzUKFNdXY7QmKtFUc0-MWUbPhVeUb63jpPL1l_y1mKqgMX8jGvpwOahwzM2lzKkkeLcj6gQnmaMUx4K5mBO5Ckq8D5XBpHSGV-HQah5RJXpZoaP3YBND3XdTsJmtVCuvq1IHScIMUR35-XQuFfYIxtMW5O4r-eD8ca_ID_2Y7m9f_YF9vHNWV8NDiChuoewHR9XFcMjyJbZtNUZd0hNvRt6k9TGnTRBfGJx2ak9I3fSgFe7rSQZmTYNaGZpYkhnsjK2-2Oor2PjJ5Ds9rrqFIjnCzuyPaZROb0wiKiT4Ri5adOfkGvOziC1lEFzYdTD5o8Azv9evoadfL1capYKleIF7MY0tLloCpKjwVhdwpaYjFrDwdVCgQg01yywb3TQBi4
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Maximum+Segment+Sum%2C+Monadically+%28distilled+tutorial%2C+with+solutions%29&rft.jtitle=arXiv.org&rft.au=Gibbons%2C+Jeremy&rft.date=2011-11-18&rft.pub=Cornell+University+Library%2C+arXiv.org&rft.eissn=2331-8422&rft_id=info:doi/10.48550%2Farxiv.1109.0782