[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-86336-en":3,"doc-seo-86336-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},86336,7971461741311,"Ophelia","https://ap-avatar.wpscdn.com/avatar/74000253aff267980c6?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779345379180704826",8,"Research & Report","Need for Speed Sort: A Recursive Distribution-Based Sorting Algorithm","Need for Speed Sort (NFS Sort) is a recursive distribution-based sorting algorithm for numeric arrays. It partitions values into equal-width intervals, scatters elements into buckets, recursively refines dense buckets, and propagates analytical interval bounds to prevent repeated min/max scans. For small buckets it defers work to a final insertion-sort cleanup, and when recursion cannot shrink the problem it activates a comparison-based fallback to preserve worst-case guarantees. Evaluation on synthetic inputs and SOSD benchmark datasets compares against leading sorters, showing competitive or better results across distributions and sizes.","Need for Speed Sort: A Recursive Distribution-Based Sorting  \nAlgorithm  \nFran Sučić  \nIndependent Researcher Croatia  \n[fransucic46@gmail.com](fransucic46@gmail.com)  \nLeo Vitasović  \nIT University of Copenhagen Denmark [leov@itu.dk](leov@itu.dk)  \nNikola Petrušić  \nIndependent Researcher Croatia  \n[nikola.petrusic221@gmail.com](nikola.petrusic221@gmail.com)  \narXiv :2607 . 1 1850v 1 [ cs .DS] 13 Jul 2026  \nAbstract  \nWe present Need for Speed Sort (NFS Sort), a recursive distributionbased sorting algorithm designed for numeric arrays. The algorithm partitions elements into equal-width value intervals, recursively refines dense buckets, and propagates analytical interval bounds between recursive calls, avoiding repeated scans for local minima and maxima. NFS Sort combines a fragment-based, cache-conscious scatter procedure for large subarrays with a lower-overhead auxiliaryarray approach for smaller inputs. Small buckets are deferred toa final insertion-sort cleanup, while a comparison-based fallback is activated when recursive partitioning repeatedly fails to reduce the problem size. This mechanism guarantees a worst-case running time of O(􀀽 log􀀽) and auxiliary space usage of O(log􀀽) . Experimental evaluation on synthetic inputs and real-world datasets from the SOSD benchmark suite compares NFS Sort with Balanced Learned Sort, IPS4o, Boost Spreadsort, PDQSort, and std::sort. The results show that NFS Sort is competitive or better than established state-of-the-art sorting methods across dataset sizes and distributions, outperforming the learned baseline particularly on smaller inputs while retaining strong performance at larger scales. Overall, NFS Sort combines efficient recursive distribution, practical memory management, and robust worst-case guarantees for high-performance numeric sorting.  \n1 Introduction  \nSorting is a fundamental problem in computer science and a core component of many software systems. Comparison-based algorithms such as quicksort, mergesort, heapsort, and introsort are robust and widely used, but they are limited by the Ω (􀀽 log􀀽) lower bound in the comparison model [2] . For numeric values, distribution-based methods can avoid this bound by exploiting the structure of the value range [2, 5] .  \nWe introduce Need for Speed Sort (NFS Sort), a recursive distributionbased sorting algorithm for numeric arrays. At each recursive step, NFS Sort divides the current value range into equally spaced buckets, scatters elements into those buckets, and recursively processes only those that remain larger than the set threshold. Small buckets are left for a final insertion-sort pass, which is efficient because all remaining disorder is confined to bounded-size regions.  \nNFS Sort combines ideas from existing distribution sorters. Inspired by Flashsort [8], it maps elements to buckets according to their relative position in the observed value range. Unlike a single-pass approach, it recursively refines dense regions. Its implementation also uses memory-management techniques inspired by IPS4 o [1] .  \nTo avoid repeated memory accesses, NFS Sort propagates analytical bucket bounds instead of recomputing minima and maxima  \nduring recursion. It also includes a fallback mechanism: if recursion repeatedly fails to reduce the size of a bucket, that bucket is sorted using a comparison-based sort. This preserves a worstcase O(􀀽 log􀀽) bound while retaining the practical advantages of distribution sorting.  \nThis paper describes the algorithm, analyses its time and space complexity, discusses adversarial inputs, and evaluates its empirical performance against established sorting methods.  \nTo facilitate reproducibility, the source code for NFS Sort and the accompanying benchmark implementation are publicly available at [https://github.com/fsucic/need-for-speed-sort](https://github.com/fsucic/need-for-speed-sort).  \nThe remainder of the paper is organized as follows. Section 2 discusses related work. Section 3 describes the al","cbCaia6awS8WLGzh","https://ap.wps.com/l/cbCaia6awS8WLGzh","pdf",1689011,3,1,13,"English","en",105,"# Introduction\n## Related Work\n# Algorithm\n## Theoretical Behavior\n## Experimental Results\n# Conclusion","[{\"question\":\"What problem does NFS Sort solve and what type of inputs does it target?\",\"answer\":\"NFS Sort targets sorting of numeric arrays. It is designed around distribution-based processing of value ranges rather than only comparison operations.\"},{\"question\":\"How does NFS Sort perform recursive sorting internally?\",\"answer\":\"It partitions the current value range into equal-width buckets, scatters elements into these buckets, and recursively refines only those buckets that remain larger than a threshold. Small buckets are left for a final insertion-sort cleanup.\"},{\"question\":\"What prevents NFS Sort from degrading on adversarial cases?\",\"answer\":\"NFS Sort propagates analytical bucket bounds to avoid repeated scans, and includes a fallback mechanism: if recursive partitioning repeatedly fails to reduce a bucket’s size, that bucket is sorted using a comparison-based method to preserve worst-case running time.\"}]",1784210550,33,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"need-for-speed-sort-a-recursive-distribution-based-sorting-algorithm","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,50],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":20},"https://docshare.wps.com/document/research-report/",{"item":51,"name":13,"@type":43,"position":52},"https://docshare.wps.com/document/need-for-speed-sort-a-recursive-distribution-based-sorting-algorithm/86336/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-25","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What problem does NFS Sort solve and what type of inputs does it target?","Question",{"text":75,"@type":76},"NFS Sort targets sorting of numeric arrays. It is designed around distribution-based processing of value ranges rather than only comparison operations.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does NFS Sort perform recursive sorting internally?",{"text":80,"@type":76},"It partitions the current value range into equal-width buckets, scatters elements into these buckets, and recursively refines only those buckets that remain larger than a threshold. Small buckets are left for a final insertion-sort cleanup.",{"name":82,"@type":73,"acceptedAnswer":83},"What prevents NFS Sort from degrading on adversarial cases?",{"text":84,"@type":76},"NFS Sort propagates analytical bucket bounds to avoid repeated scans, and includes a fallback mechanism: if recursive partitioning repeatedly fails to reduce a bucket’s size, that bucket is sorted using a comparison-based method to preserve worst-case running time.","https://schema.org",{"og:url":51,"og:type":87,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":89,"canonical":51},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":21,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]