[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-1-en-105":3,"doc-seo-573428-105":53,"doc-detail-573428-en":125},{"code":4,"msg":5,"data":6},0,"success",[7,14,19,24,29,34,39,44,49],{"id":8,"doc_module":9,"doc_module_name":10,"category_name":11,"show_sort_weight":12,"slug":13},11,1,"Template","Presentations",90,"presentations",{"id":15,"doc_module":9,"doc_module_name":10,"category_name":16,"show_sort_weight":17,"slug":18},12,"Resumes",80,"resumes",{"id":20,"doc_module":9,"doc_module_name":10,"category_name":21,"show_sort_weight":22,"slug":23},14,"Invoices",70,"invoices",{"id":25,"doc_module":9,"doc_module_name":10,"category_name":26,"show_sort_weight":27,"slug":28},15,"Posters",60,"posters",{"id":30,"doc_module":9,"doc_module_name":10,"category_name":31,"show_sort_weight":32,"slug":33},16,"Social Media",50,"social-media",{"id":35,"doc_module":9,"doc_module_name":10,"category_name":36,"show_sort_weight":37,"slug":38},17,"Forms",40,"forms",{"id":40,"doc_module":9,"doc_module_name":10,"category_name":41,"show_sort_weight":42,"slug":43},18,"Letters",30,"letters",{"id":45,"doc_module":9,"doc_module_name":10,"category_name":46,"show_sort_weight":47,"slug":48},21,"Paper Templates",5,"papers-templates",{"id":50,"doc_module":9,"doc_module_name":10,"category_name":51,"show_sort_weight":4,"slug":52},158,"General","general-158",{"code":4,"msg":54,"data":55},"ok",{"site_id":56,"language":57,"slug":58,"title":59,"keywords":60,"description":61,"schema_data":62,"social_meta":118,"head_meta":120,"extra_data":122,"updated_unix":124},105,"en","cs221-algorithms-and-data-structures-big-o-asymptotic-analysis-lecture-3","CS221: Algorithms and Data Structures - Big-O - Asymptotic Analysis Lecture 3","","CS221 lecture on Big-O asymptotic analysis, introducing big-O, big-omega, and big-theta notation with O(•), Ω(•), and Θ(•). It explains how runtime or memory is modeled as a function of input size n, counting basic operations while ignoring constant factors and focusing on large n. The lecture practices proving one function’s asymptotic relationship to another, simplifying expressions, and comparing common complexity orders through example “runtime smackdown” scenarios and algorithm-growth races.",{"@graph":63,"@context":117},[64,80,100],{"@type":65,"itemListElement":66},"BreadcrumbList",[67,71,74,77],{"item":68,"name":69,"@type":70,"position":9},"https://docshare.wps.com","Home","ListItem",{"item":72,"name":10,"@type":70,"position":73},"https://docshare.wps.com/template/",2,{"item":75,"name":11,"@type":70,"position":76},"https://docshare.wps.com/template/presentations/",3,{"item":78,"name":59,"@type":70,"position":79},"https://docshare.wps.com/template/cs221-algorithms-and-data-structures-big-o-asymptotic-analysis-lecture-3/573428/",4,{"url":78,"name":59,"@type":81,"image":82,"author":87,"headline":59,"publisher":90,"fileFormat":93,"inLanguage":57,"description":61,"dateModified":94,"datePublished":94,"encodingFormat":93,"isAccessibleForFree":95,"interactionStatistic":96},"DigitalDocument",{"url":83,"@type":84,"width":85,"height":86},"https://docshare.wps.com/thumbnails/cs221-algorithms-and-data-structures-big-o-asymptotic-analysis-lecture-3/573428.png","ImageObject",442,249,{"name":88,"@type":89},"Jasmine","Person",{"url":68,"name":91,"@type":92},"DocShare","Organization","application/pdf","2026-10-14",true,{"@type":97,"interactionType":98,"userInteractionCount":9},"InteractionCounter",{"@type":99},"ViewAction",{"@type":101,"mainEntity":102},"FAQPage",[103,109,113],{"name":104,"@type":105,"acceptedAnswer":106},"What do big-O, big-omega, and big-theta represent in this lecture?","Question",{"text":107,"@type":108},"They classify the asymptotic growth of a function: big-O is an upper bound, big-omega is a lower bound, and big-theta is a tight bound. The lecture denotes them as O(•), Ω(•), and Θ(•).","Answer",{"name":110,"@type":105,"acceptedAnswer":111},"How does the lecture choose what to count when analyzing algorithms?",{"text":112,"@type":108},"It measures runtime or memory usage as a function of input size n, counting only “basic operations.” Constant factors are ignored because the focus is on behavior as n becomes large.",{"name":114,"@type":105,"acceptedAnswer":115},"Why are runtime comparisons between two computers not enough when algorithms differ?",{"text":116,"@type":108},"Computer-specific performance matters for actual execution time, but asymptotic analysis abstracts away constant factors. It asks which algorithm growth rate “wins” as n approaches infinity, not which machine is faster for small cases.","https://schema.org",{"og:url":78,"og:type":119,"og:title":59,"og:site_name":91,"og:description":61},"article",{"robots":121,"canonical":78},"index,follow",{"doc_id":123,"site_id":56},573428,1792016384,{"code":4,"msg":5,"data":126},{"doc_id":123,"user_id":127,"nickname":88,"user_avatar":128,"doc_module":9,"category_id":8,"category_name":11,"doc_title":59,"doc_description":61,"doc_content":129,"file_id":130,"file_url":131,"file_type":132,"file_size":133,"view_count":9,"is_deleted":4,"is_public":9,"is_downloadable":9,"audit_status":9,"page_count":134,"language":135,"language_code":57,"site_id":56,"html_lang":57,"table_of_contents":136,"faqs":137,"seo_title":138,"seo_description":61,"update_tm":139,"read_time":140},2336478487870,"https://ap-avatar.wpscdn.com/davatar_085a072bc5b1113ac321206ff7593b45","CS221: Algorithms and Data Structures Big-O  \nAlan J. Hu  \n(Borrowing some slides from Steve Wolfman)  \nLearning Goals  \n• Define big-O, big-Omega, and big-Theta: O(•), Ω (•), Θ (•)  \n• Explain intuition behind their definitions .  \n• Prove one function is big-O/Omega/Theta of another function .  \n• Simplify algebraic expressions using the rules of asymptotic analysis .  \n• List common asymptotic complexity orders, and how they compare .  \n• Work some examples .  \nAsymptotic Analysis of Algorithms  \nFrom last time, some key points:  \n• We will measure runtime, or memory usage, or whatever we are comparing, as a function in terms of the input size n.  \n• Because we are comparing algorithms, we only count “basic operations”, and since we don’t knowhow long each basic operation will really take, we ignore constant factors.  \n• We focus only on when n gets big.  \nAsymptotic Analysis of Algorithms  \nFrom last time, some key points:  \n• We will measure runtime, or memory usage, or whatever we are comparing, as a function in terms of the input size n.  \n•  \nBecause we are comparing algorithms, we only count “basic operations”, and since we don’t knowhow long each basic operation will really take, we ignore constant factors.  \n• We focus only on when n gets big.  \nRuntime Smackdown!  \nAlan’s Old Thinkpad x40  \n• Older Laptop  \n• Pentium M 32bit CPU at 1.4Ghz  \n• 1.5 GB of RAM  \nPademelon  \n• 2011 Desktop PC  \n• Core i7-870 64bit CPU at 3Ghz w/ TurboBoost  \n• 16GB of RAM  \nWhich computer is faster? By how much?  \nRuntime Smackdown II!  \nTandy 200  \n• 1984 Laptop  \n• Intel 8085 8bit CPU at 2.4Mhz  \n• 24KB of RAM  \n• Interpreted BASIC  \nPademelon  \n• 2011 Desktop PC  \n• Core i7-870 64bit CPU at 3Ghz w/ TurboBoost  \n• 16GB of RAM  \n• Compiled C++  \nWhich computer is faster? By how much?  \nRuntime Smackdown III!  \nTandy 200  \n• 1984 Laptop  \n• Intel 8085 8bit CPU at 2.4Mhz  \n• 24KB of RAM  \n• Interpreted BASIC  \nPademelon  \n• 2011 Desktop PC  \n• Core i7-870 64bit CPU at 3Ghz w/ TurboBoost  \n• 16GB of RAM  \n• Compiled C++  \nWhich computer is faster? By how much?  \nBut what if we run asymptotically different algorithms?  \nAsymptotic Analysis of Algorithms  \nFrom last time, some key points:  \n• We will measure runtime, or memory usage, or whatever we are comparing, as a function in terms of n.  \n•  \nBecause we are comparing algorithms, we only count “basic operations”, and since we don’t knowhow long each basic operation will really take, we ignore constant factors.  \n• We focus only on when n gets big.  \nSilicon Downs  \nPost \\#1  \nn3 + 2n2  \nn0.1  \nn + 100n0.1  \n5n 5 n-152n /100 82lg n  \nmn3  \nPost \\#2  \n100n2 + 1000 log n  \n2n + 10 log nn!  \n1000n 15  \n3n7 + 7n  \n2mn  \nFor each race, which “horse”grows bigger as n goes to infinity?(Note that in practice, smaller is better.)  \na.Left  \nb.Right  \nc.Tied  \nd.It depends  \ne.I am opposed to algorithm racing.  \n9  \na. Left  \nb. Right  \nc. Tied Race I d. It depends  \nn 3 + 2n 2 vs . 100n 2 + 1000","cbCaisECsXEvZTfR","https://ap.wps.com/l/cbCaisECsXEvZTfR","pdf",143976,55,"English","# Learning Goals\n# Asymptotic Analysis of Algorithms\n# Runtime Smackdown! (Computer Speed Comparisons)\n# Runtime Smackdown II! (Another Comparison)\n# Runtime Smackdown III! (Interpreted vs Compiled)\n# Asymptotically Different Algorithms\n# Silicon Downs (Growth Races)\n## Post #1\n## Post #2","[{\"question\":\"What do big-O, big-omega, and big-theta represent in this lecture?\",\"answer\":\"They classify the asymptotic growth of a function: big-O is an upper bound, big-omega is a lower bound, and big-theta is a tight bound. The lecture denotes them as O(•), Ω(•), and Θ(•).\"},{\"question\":\"How does the lecture choose what to count when analyzing algorithms?\",\"answer\":\"It measures runtime or memory usage as a function of input size n, counting only “basic operations.” Constant factors are ignored because the focus is on behavior as n becomes large.\"},{\"question\":\"Why are runtime comparisons between two computers not enough when algorithms differ?\",\"answer\":\"Computer-specific performance matters for actual execution time, but asymptotic analysis abstracts away constant factors. It asks which algorithm growth rate “wins” as n approaches infinity, not which machine is faster for small cases.\"}]","CS221: Algorithms and Data Structures - Big-O - Asymptotic Analysis Lecture 3 | PDF",1791939575,19]