Algorithms, Data Structures, and Complexity: A Complexity-First Pedagogical Framework

Algorithms, Data Structures, and Complexity: A Complexity-First Pedagogical Framework | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Algorithms, Data Structures, and Complexity: A Complexity-First Pedagogical Framework Valeriu Ungureanu This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9006105/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Algorithms and Data Structures (ADS) constitute a foundational pillar of computer science education; however, traditional instruction often emphasizes functional correctness while leaving scalability reasoning implicit or secondary. This paper proposes a pedagogical reframing termed ADSC (Algorithms, Data Structures, and Complexity) , in which multi-layered cost models become the central explanatory lens for algorithmic understanding. The ADSC framework introduces the concept of Scalability Literacy , defined as the learner’s ability to anticipate feasibility limits, empirically validate efficiency claims, and detect complexity leaks hidden within high-level abstractions or AI-generated code. Sorting algorithms are employed as a didactic laboratory through which algorithmic cost is operationalized using complementary metrics: comparison counts (C), element movements (M), theoretical auxiliary memory usage (S peak ), and large-scale execution time (up to n = 2 x 10 6 ). This multidimensional evaluation enables students to systematically distinguish between (i) asymptotic growth behavior, (ii) implementation-dependent constant factors, and (iii) paradigm-specific cost models, including allocation and memory management penalties characteristic of functional programming styles. Validated through sustained university-level teaching practice, the ADSC approach shifts learning from the mechanical reproduction of algorithmic templates toward algorithmic auditing . By foregrounding explicit cost reasoning, the framework equips future software engineers with the analytical rigor required to design, evaluate, and trust scalable systems in an ecosystem increasingly shaped by automated and AI-assisted code generation. Theoretical Computer Science Educational Philosophy and Theory Computer science education Algorithm education Scalability literacy Computational complexity Sorting algorithms Empirical learning Cost models Programming paradigms Algorithm auditing Full Text Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-9006105","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":599037329,"identity":"398504d5-e7f4-44fc-80dc-ea3c536af4ce","order_by":0,"name":"Valeriu Ungureanu","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA90lEQVRIiWNgGAWjYFAC5gYGBgNkAfYGMMXYgFMLI7oWngPEaEEBEgn4tRgcP9j4uKLgMIPB7fZr0hUVdnkGN98Yf7rBsE0Wp5Yzic2GZwyAWu6cKZM8cya52OB2jpl0DsNtY1xaJBsS2yQbQFpu5KRJNrYxJ24AamEGaknEqaX/YftPhJZ/9Ykbbp4x/oxPC79EYhsjREv6McnGhsOJG27wGEjj1/KwGeiwdB7JGznMlg3HjifOPJNWJp1jgNsvbPzJBz82/LGW47uR/vBmQ011Yt/xw5s/51TcxhliMMADRMgRaoBTJTJgf0CUslEwCkbBKBh5AACX8V+gUYPTlgAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0000-0001-5184-0040","institution":"Moldova State University","correspondingAuthor":true,"prefix":"","firstName":"Valeriu","middleName":"","lastName":"Ungureanu","suffix":""}],"badges":[],"createdAt":"2026-03-02 06:00:56","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-9006105/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9006105/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":103792962,"identity":"85058e4e-a249-4d03-9c2a-d44f5a372fe1","added_by":"auto","created_at":"2026-03-03 02:55:46","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":460213,"visible":true,"origin":"","legend":"","description":"","filename":"ADSCPreprint.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9006105/v1_covered_dd863ba5-4c34-4600-9884-4da574a1f2a0.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eAlgorithms, Data Structures, and Complexity: A Complexity-First Pedagogical Framework\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Moldova State University","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Computer science education, Algorithm education, Scalability literacy, Computational complexity, Sorting algorithms, Empirical learning, Cost models, Programming paradigms, Algorithm auditing","lastPublishedDoi":"10.21203/rs.3.rs-9006105/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9006105/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eAlgorithms and Data Structures (ADS) constitute a foundational pillar of computer science education; however, traditional instruction often emphasizes functional correctness while leaving scalability reasoning implicit or secondary. 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Sorting algorithms are employed as a didactic laboratory through which algorithmic cost is operationalized using complementary metrics: comparison counts (C), element movements (M), theoretical auxiliary memory usage (S\u003csub\u003epeak\u003c/sub\u003e), and large-scale execution time (up to n = 2 x 10\u003csup\u003e6\u003c/sup\u003e).\u003c/p\u003e\n\u003cp\u003e\t\u003c/p\u003e\n\u003cp\u003e\tThis multidimensional evaluation enables students to systematically distinguish between (i) asymptotic growth behavior, (ii) implementation-dependent constant factors, and (iii) paradigm-specific cost models, including allocation and memory management penalties characteristic of functional programming styles. Validated through sustained university-level teaching practice, the ADSC approach shifts learning from the mechanical reproduction of algorithmic templates toward \u003cstrong\u003ealgorithmic auditing\u003c/strong\u003e. 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