Asymptotic Analysis

An algorithm’s asymptotic analysis refers to defining the mathematical boundation/framing of its run-time performance. We can very well conclude the best-case, average-case, and worst-case scenarios of an algorithm using asymptotic analysis.

Asymptotic analysis is input bound, which means that if the algorithm receives no input, it is assumed to work in a constant time. Except for the “input,” all other factors are assumed to be constant.

The computation of the running time of any operation in mathematical units of computation is referred to as asymptotic analysis.

The time required by an algorithm is typically classified into three types:

  • Best Case – In the best-case scenario, the time required for program execution is minimal.
  • Average Case – The average time required for program execution.
  • Worst Case -Maximum time required for program execution in the worst-case scenario.

The following are some common asymptotic notations for calculating an algorithm’s running time complexity.

  • O Notation
  • Ω Notation
  • θ Notation
  • Big Oh Notation, O — The formal way to express the upper bound of an algorithm’s running time is with the notation O(n). It calculates the worst-case time complexity, or the longest time an algorithm can take to complete.

For example, for a function f(n)

Ο(f(n)) = { g(n) : there exists c > 0 and n0 such that f(n) ≤ c.g(n) for all  n > n0. }

  • Omega Notation, Ω — The formal way to express the lower bound of an algorithm’s running time is with the notation Ω (n). It calculates the best-case time complexity or the shortest amount of time an algorithm can take to complete.

θ(f(n)) = { g(n) if and only if g(n) =  Ο(f(n)) and g(n) = Ω(f(n)) for all n > n0. }

  • Theta Notation, θ — The notation (n) is used to express both the lower and upper bounds of an algorithm’s running time. It is written as follows:

θ(f(n)) = { g(n) if and only if g(n) =  Ο(f(n)) and g(n) = Ω(f(n)) for all n > n0. }

Common Asymptotic Symptoms

constantΟ(1)
logarithmicΟ(log n)
linearΟ(n)
n log nΟ(n log n)
quadraticΟ(n2)
cubicΟ(n3)
polynomialnΟ(1)
exponential2Ο(n)
0

213 thoughts on “Asymptotic Analysis”

  1. I’ll immediately grab your rss feed as I can not in finding your email subscription hyperlink or newsletter service. Do you have any? Please let me know in order that I may subscribe. Thanks.

    0
  2. Hello there, simply changed into aware of your weblog thru Google, and found that it is really informative. I’m gonna watch out for brussels. I’ll appreciate for those who proceed this in future. A lot of other people will be benefited from your writing. Cheers!

    0
  3. I will right away clutch your rsss feed as
    I can’t to find your email subscription link or e-newsletter
    service. Do you’ve any? Please let me know so that I may just subscribe.
    Thanks.

    My website: Alma

    0
  4. Hiya, I’m really glad I have found this info. Nowadays bloggers publish just about gossips and web and this is really irritating. A good blog with exciting content, that is what I need. Thank you for keeping this web-site, I will be visiting it. Do you do newsletters? Can’t find it.

    0
  5. I am really enjoying the theme/design of your blog. Do you ever run into any browser compatibility problems? A handful of my blog audience have complained about my website not operating correctly in Explorer but looks great in Firefox. Do you have any ideas to help fix this problem?

    0
  6. I’ll right away grab your rss as I can’t find your email subscription link or e-newsletter service. Do you’ve any? Kindly let me know in order that I could subscribe. Thanks.

    0
  7. Hi, i feel that i noticed you visited my web site so i came to “go back the desire”.I am attempting to find things to improve my site!I suppose its good enough to use a few of your concepts!!

    0
  8. I’m often to running a blog and i really respect your content. The article has really peaks my interest. I’m going to bookmark your website and maintain checking for brand new information.

    0
  9. With every thing which appears to be building inside this specific subject material, a significant percentage of perspectives are generally fairly stimulating. Nonetheless, I appologize, but I can not subscribe to your entire suggestion, all be it radical none the less. It seems to everyone that your remarks are generally not entirely rationalized and in fact you are yourself not really totally confident of the point. In any event I did take pleasure in reading through it.

    0
  10. A lot of of whatever you state is astonishingly precise and that makes me ponder why I hadn’t looked at this in this light previously. This piece really did switch the light on for me as far as this specific subject goes. Nevertheless at this time there is actually just one issue I am not too comfortable with so whilst I make an effort to reconcile that with the actual main theme of the position, allow me see what all the rest of the visitors have to say.Very well done.

    0
  11. Write more, thats all I have to say. Literally, it seems as though you relied on the video to make your point. You obviously know what youre talking about, why waste your intelligence on just posting videos to your site when you could be giving us something informative to read?

    0
  12. Please let me know if you’re looking for a writer for your site. You have some really great articles and I feel I would be a good asset. If you ever want to take some of the load off, I’d love to write some material for your blog in exchange for a link back to mine. Please send me an email if interested. Thanks!

    0
  13. obviously like your web site however you need to test the spelling on quite a few of your posts. A number of them are rife with spelling issues and I find it very bothersome to tell the truth nevertheless I will definitely come again again.

    0
  14. Hey There. I discovered your weblog the usage of msn. This is a very neatly written article. I will make sure to bookmark it and return to read extra of your helpful info. Thank you for the post. I’ll definitely comeback.

    0
  15. Unquestionably imagine that that you stated. Your favorite reason seemed to be on the internet the simplest factor to take note of. I say to you, I definitely get annoyed whilst other people think about concerns that they just don’t know about. You controlled to hit the nail upon the top as well as outlined out the entire thing with no need side-effects , other folks can take a signal. Will probably be back to get more. Thanks

    0
  16. I love your blog.. very nice colors & theme. Did you create this website yourself? Plz reply back as I’m looking to create my own blog and would like to know wheere u got this from. thanks

    0
  17. This is the right blog for anyone who wants to find out about this topic. You realize so much its almost hard to argue with you (not that I actually would want…HaHa). You definitely put a new spin on a topic thats been written about for years. Great stuff, just great!

    0
  18. I absolutely love your blog and find the majority of your post’s to be what precisely I’m looking for. Do you offer guest writers to write content for you? I wouldn’t mind composing a post or elaborating on some of the subjects you write regarding here. Again, awesome website!

    0
  19. What i don’t realize is actually how you’re not actually much more well-favored than you may be now. You are very intelligent. You understand therefore significantly on the subject of this subject, produced me individually consider it from numerous numerous angles. Its like women and men are not involved until it¦s something to accomplish with Woman gaga! Your individual stuffs excellent. Always maintain it up!

    0
  20. Hi, i feel that i saw you visited my website so i came to “go back the want”.I’m attempting to to find things to enhance my site!I assume its ok to make use of some of your concepts!!

    0
  21. You really make it seem really easy together with your presentation however I find this topic to be actually one thing which I think I might by no means understand. It sort of feels too complex and very wide for me. I am looking ahead for your subsequent submit, I will attempt to get the hold of it!

    0
  22. It is perfect time to make some plans for the future and it is time to be happy. I have read this post and if I could I want to suggest you few interesting things or tips. Perhaps you can write next articles referring to this article. I wish to read even more things about it!

    0
  23. Fantastic beat ! I would like to apprentice while you amend your site, how could i subscribe for a blog site? The account aided me a acceptable deal. I had been a little bit acquainted of this your broadcast provided bright clear concept

    0
  24. You actually make it seem really easy together with your presentation but I in finding this matter to be actually something that I believe I might never understand. It seems too complex and very broad for me. I’m looking ahead on your next post, I¦ll try to get the grasp of it!

    0
  25. I like what you guys are up also. Such smart work and reporting! Carry on the excellent works guys I¦ve incorporated you guys to my blogroll. I think it’ll improve the value of my site 🙂

    0
  26. Thank you for the sensible critique. Me & my neighbor were just preparing to do a little research about this. We got a grab a book from our area library but I think I learned more from this post. I am very glad to see such excellent info being shared freely out there.

    0
  27. I got what you intend, regards for posting.Woh I am lucky to find this website through google. “Success is dependent on effort.” by Sophocles.

    0
  28. What Is Neotonics? Neotonics is a skin and gut supplement made of 500 million units of probiotics and 9 potent natural ingredients to support optimal gut function and provide healthy skin.

    0
  29. What Is ZenCortex? ZenCortex is a natural supplement that promotes healthy hearing and mental tranquility. It’s crafted from premium-quality natural ingredients, each selected for its ability to combat oxidative stress and enhance the function of your auditory system and overall well-being.

    0
  30. You actually make it seem really easy along with your presentation but I to find this topic to be actually one thing that I feel I would never understand. It sort of feels too complex and very extensive for me. I’m taking a look forward in your next publish, I will try to get the hold of it!

    0
  31. I have not checked in here for a while since I thought it was getting boring, but the last several posts are good quality so I guess I will add you back to my everyday bloglist. You deserve it my friend 🙂

    0
  32. whoah this blog is excellent i love reading your articles. Keep up the good work! You know, lots of people are looking around for this information, you can aid them greatly.

    0
  33. Aw, this was a really nice post. In idea I wish to put in writing like this moreover – taking time and actual effort to make an excellent article… however what can I say… I procrastinate alot and in no way seem to get one thing done.

    0
  34. Hey! I know this is kinda off topic however , I’d figured I’d ask. Would you be interested in trading links or maybe guest writing a blog post or vice-versa? My blog addresses a lot of the same subjects as yours and I think we could greatly benefit from each other. If you happen to be interested feel free to send me an email. I look forward to hearing from you! Terrific blog by the way!

    0
  35. You are my inspiration, I have few blogs and infrequently run out from brand :). “Analyzing humor is like dissecting a frog. Few people are interested and the frog dies of it.” by E. B. White.

    0
  36. Hi, just required you to know I he added your site to my Google bookmarks due to your layout. But seriously, I believe your internet site has 1 in the freshest theme I??ve came across. It extremely helps make reading your blog significantly easier.

    0
  37. Howdy, i read your blog from time to time and i own a similar one and i was just wondering if you get a lot of spam remarks? If so how do you prevent it, any plugin or anything you can advise? I get so much lately it’s driving me insane so any help is very much appreciated.

    0
  38. We’re a group of volunteers and opening a new scheme in our community. Your site offered us with valuable information to work on. You have done an impressive job and our entire community will be thankful to you.

    0
  39. I intended to send you a tiny note to say thanks as before on your magnificent pointers you have shown on this site. It’s tremendously generous of people like you to deliver freely what exactly a few people could possibly have made available for an electronic book to earn some cash for their own end, specifically given that you could have done it in the event you decided. These tricks additionally served as the great way to comprehend someone else have the identical keenness like mine to figure out very much more with regard to this issue. I think there are a lot more pleasant moments in the future for those who find out your website. sumatra slim belly tonic reviews

    0
  40. I wanted to write you one very little observation to help say thank you over again on your fantastic views you’ve featured at this time. It has been quite generous of people like you to supply extensively all many of us would’ve made available for an e book to get some money on their own, precisely considering that you might have done it in case you decided. The basics in addition acted to provide a easy way to be sure that other individuals have the same interest just like mine to know a lot more with respect to this issue. I know there are thousands of more fun moments ahead for many who looked over your website. phenq

    0
  41. I needed to write you one little note to thank you yet again on the beautiful secrets you’ve documented on this website. It is simply strangely generous with people like you to supply without restraint what exactly most of us would’ve marketed for an ebook to get some profit for themselves, chiefly seeing that you might well have done it in the event you desired. These ideas additionally acted like a fantastic way to be sure that many people have the identical zeal similar to my own to grasp significantly more on the subject of this issue. I’m sure there are numerous more enjoyable occasions ahead for people who scan through your blog post. boostaro

    0
  42. I intended to draft you the very small remark to finally say thank you once again on your pleasing information you’ve documented on this page. It was certainly open-handed with you giving extensively exactly what a few people would have advertised for an electronic book to end up making some dough on their own, most notably since you might well have done it if you decided. The secrets likewise worked as a good way to realize that many people have similar zeal really like mine to realize good deal more in regard to this problem. I am sure there are many more fun moments up front for many who find out your website. lottery defeated

    0
  43. I wanted to compose you this bit of observation to finally give thanks as before over the pleasant thoughts you’ve documented here. This has been quite incredibly open-handed with people like you to present unreservedly all that some people could have sold as an e book to generate some profit on their own, chiefly given that you could have tried it if you ever considered necessary. Those points in addition acted to become a good way to recognize that some people have the same interest just as my very own to understand a lot more around this matter. I’m sure there are some more fun moments ahead for individuals that examine your website. smart hemp gummies australia

    0
  44. Needed to write you that very little observation to say thank you again with your incredible tricks you have contributed on this website. This has been certainly wonderfully generous of people like you to give easily all that many people could have offered for sale as an ebook to earn some money for themselves, most notably now that you could have done it if you ever decided. These suggestions additionally worked to become a great way to realize that some people have a similar zeal much like my personal own to figure out very much more with regard to this condition. I think there are numerous more pleasurable occasions up front for individuals who look over your website. tonic greens reviews

    0
  45. I needed to send you the very small remark to say thanks a lot once again on your magnificent information you have contributed on this website. This has been surprisingly generous of people like you to make easily precisely what a number of us could possibly have offered for sale as an electronic book to generate some money for their own end, and in particular seeing that you might well have done it if you ever decided. These solutions additionally worked like a good way to fully grasp that someone else have similar keenness the same as my very own to grasp a good deal more in regard to this problem. I’m certain there are thousands of more enjoyable occasions up front for individuals that scan through your blog post. tonic greens reviews

    0
  46. Needed to create you one very little remark to be able to thank you yet again on the lovely advice you’ve contributed on this page. It has been really tremendously open-handed of people like you to grant without restraint precisely what many individuals could have distributed as an e-book to help make some profit for their own end, notably now that you could possibly have done it in case you considered necessary. Those smart ideas additionally served like a good way to understand that other individuals have the identical fervor just like my own to grasp many more on the topic of this issue. I believe there are several more pleasurable sessions up front for individuals that scan through your blog post. sight care reviews

    0
  47. Needed to write you a tiny observation to help give many thanks once again on your precious things you’ve provided in this case. It has been so unbelievably open-handed of people like you giving freely what exactly a few people would’ve marketed for an electronic book to get some profit for themselves, notably since you might have done it in the event you decided. These basics additionally acted as a great way to understand that other individuals have the identical interest really like my very own to figure out very much more in regard to this issue. I’m certain there are lots of more pleasant moments ahead for those who look over your website. nitric boost reviews

    0

  48. I wanted to post you the very small note to help say thanks a lot as before for those pleasing tactics you have contributed at this time. It has been certainly wonderfully generous of you to give extensively what exactly some people would’ve marketed as an ebook to make some dough for their own end, most notably considering that you might well have tried it in case you considered necessary. The creative ideas as well acted to be the great way to recognize that other people have the same fervor much like my own to understand great deal more around this issue. I’m certain there are a lot more pleasant times in the future for many who read through your blog. alpha bites

    0
  49. I wanted to create you the little word to help give thanks the moment again relating to the amazing tips you’ve featured in this article. It was simply strangely generous of people like you to provide freely all many people would have distributed for an e-book to generate some bucks on their own, specifically seeing that you might well have done it if you ever wanted. These principles in addition worked like the easy way to be certain that many people have similar eagerness the same as my personal own to figure out whole lot more in regard to this problem. I think there are many more fun occasions in the future for folks who scan through your blog post. provadent

    0
  50. Needed to send you the very small remark just to say thanks a lot once again for your exceptional views you’ve shown at this time. It has been quite remarkably open-handed of you to grant freely what exactly a lot of folks would have distributed for an ebook to end up making some money for their own end, particularly given that you might well have tried it if you wanted. The things as well acted to become a great way to recognize that many people have similar passion the same as mine to know good deal more around this issue. I am certain there are a lot more enjoyable situations up front for folks who go through your blog. prodentim reviews

    0
  51. Needed to write you one tiny note to help thank you so much again for the lovely basics you’ve discussed in this case. This has been really surprisingly open-handed with you to grant publicly just what many individuals could possibly have offered for sale for an e book to get some money for their own end, chiefly considering the fact that you might have tried it in the event you desired. These good tips as well acted as the great way to fully grasp someone else have a similar eagerness similar to my very own to figure out more and more pertaining to this issue. Certainly there are lots of more fun situations ahead for many who read your blog post. lottery defeater

    0
  52. I have not checked in here for a while because I thought it was getting boring, but the last few posts are great quality so I guess I¦ll add you back to my everyday bloglist. You deserve it my friend 🙂

    0
  53. Wow that was strange. I just wrote an incredibly long comment but after I clicked submit my comment didn’t appear. Grrrr… well I’m not writing all that over again. Anyways, just wanted to say excellent blog!

    0
  54. Oh my goodness! an amazing article dude. Thank you Nonetheless I am experiencing challenge with ur rss . Don’t know why Unable to subscribe to it. Is there anyone getting an identical rss problem? Anyone who knows kindly respond. Thnkx

    0
  55. Good day I am so glad I found your blog, I really found you by error, while I was researching on Digg for something else, Anyways I am here
    now and would just like to say thank you for a incredible post and a all round interesting blog (I also love the theme/design), I don’t
    have time to go through it all at the moment but I have bookmarked it and
    also included your RSS feeds, so when I have time
    I will be back to read more, Please do keep up the excellent job.

    Also visit my web site; fitspresso

    0
  56. Have you ever thought about creating an e-book or guest authoring on other sites?
    I have a blog centered on the same ideas you discuss and would really
    like to have you share some stories/information. I know my audience would enjoy your work.
    If you are even remotely interested, feel free to send me an email.

    Visit my homepage :: what is pronerve 6

    0
  57. I don’t know whether it’s just me or if perhaps everyone else encountering problems with your blog.
    It appears as if some of the written text within your posts are running off the screen. Can somebody else please provide feedback and let me know if
    this is happening to them too? This may be a issue with my internet browser because I’ve had this happen before.

    Kudos

    My webpage; provadent bbb reviews

    0
  58. My developer is trying to persuade me to move to .net from PHP.
    I have always disliked the idea because of the expenses.

    But he’s tryiong none the less. I’ve been using WordPress on numerous
    websites for about a year and am anxious about switching to another platform.

    I have heard very good things about blogengine.net.
    Is there a way I can import all my wordpress content into it?
    Any kind of help would be really appreciated!

    Feel free to visit my web page the growth matrix ryan

    0
  59. I blog often and I really thank you for your information. This article has really peaked my interest.
    I am going to take a note of your blog and keep checking for new details about once a week.

    I opted in for your RSS feed as well.

    my blog post :: lung pro clear

    0
  60. Howdy, I do believe your web site could possibly be having internet browser compatibility problems.

    Whenever I take a look at your web site in Safari, it looks fine but when opening in IE,
    it has some overlapping issues. I simply wanted to give you a quick heads up!
    Apart from that, great website!

    Also visit my web page … testofuel vs testoprime

    0
  61. Hello there! Do you know if they make any plugins to assist with Search Engine Optimization? I’m trying to get my blog to
    rank for some targeted keywords but I’m not seeing very good results.
    If you know of any please share. Appreciate it!

    Here is my website :: endoboost pro

    0
  62. hey there and thank you for your information – I’ve definitely picked up anything new from right
    here. I did however expertise some technical issues using this web site, since I experienced to reload the site lots of times previous to I could get it to load properly.
    I had been wondering if your web hosting is OK? Not that
    I am complaining, but sluggish loading instances times will very frequently
    affect your placement in google and can damage your high-quality score if ads and marketing with Adwords.
    Well I’m adding this RSS to my email and can look
    out for much more of your respective interesting content. Make sure you update this again soon.

    Feel free to visit my web-site; fitspresso customer reviews

    0
  63. I’m really inspired with your writing talents as smartly as
    with the structure for your weblog. Is this a paid subject
    matter or did you modify it your self? Anyway keep up the
    nice high quality writing, it’s rare to peer a great blog like this
    one nowadays..

    0
  64. Wonderful goods from you, man. I have bear in mind your stuff prior to and you are simply too excellent. I actually like what you’ve obtained right here, really like what you are stating and the way in which during which you assert it. You’re making it enjoyable and you continue to take care of to keep it sensible. I can not wait to learn far more from you. This is really a tremendous website.

    0
  65. Fantastic items from you, man. I have take note your stuff previous to and you’re just too wonderful.
    I actually like what you’ve got right here,
    really like what you are saying and the way through which you are saying it.
    You make it enjoyable and you continue to care for to keep it smart.
    I cant wait to learn far more from you. This is actually
    a terrific site.

    Also visit my blog post: lottery defeated software

    0
  66. Please let me know if you’re looking for a article author for
    your site. You have some really great posts and I believe I would
    be a good asset. If you ever want to take some of the load off, I’d absolutely love to write some material for
    your blog in exchange for a link back to
    mine. Please send me an e-mail if interested. Regards!

    Here is my web site – provadent where to buy

    0
  67. Hey just wanted to give you a quick heads up. The words in your post seem to be running off the
    screen in Safari. I’m not sure if this is a formatting issue or something
    to do with browser compatibility but I thought I’d post to let you know.
    The design and style look great though!
    Hope you get the issue resolved soon. Many thanks

    Here is my blog post :: alpha bites reviews

    0
  68. I’ve been surfing online more than 2 hours today, yet I never found any interesting article
    like yours. It’s pretty worth enough for me. Personally, if all webmasters
    and bloggers made good content as you did, the web will
    be a lot more useful than ever before.

    Here is my page: testoprime near me

    0
  69. This design is spectacular! You most certainly know
    how to keep a reader entertained. Between your wit
    and your videos, I was almost moved to start my own blog (well, almost…HaHa!) Wonderful job.
    I really loved what you had to say, and more than that, how
    you presented it. Too cool!

    My web blog UltraK9 Pro

    0
  70. Thanks for your personal marvelous posting!

    I actually enjoyed reading it, you can be a great author.I will always bookmark your blog
    and may come back down the road. I want to encourage you to definitely continue your
    great work, have a nice morning!

    Here is my web site :: fitspresso reorder

    0
  71. Hello just wanted to give you a quick heads up.
    The text in your content seem to be running off the screen in Chrome.

    I’m not sure if this is a formatting issue or
    something to do with web browser compatibility but I figured I’d post to let you
    know. The layout look great though! Hope you get the problem
    solved soon. Thanks

    Also visit my page :: jungle beast pro reviews

    0
  72. I do accept as true with all the concepts you have presented for
    your post. They’re very convincing and will definitely work.
    Still, the posts are too short for starters. Could you please
    lengthen them a bit from next time? Thanks for the post.

    Feel free to visit my web blog http://www.prodentim

    0
  73. I needed to create you one very little remark to say thanks once again for all the stunning techniques you’ve shared above. It’s quite remarkably generous of people like you to allow without restraint what exactly a few individuals could have made available for an e-book to help make some dough on their own, especially now that you could have tried it in case you desired. The concepts also worked like the great way to comprehend some people have a similar keenness the same as my very own to figure out significantly more in regard to this matter. I am certain there are millions of more enjoyable periods ahead for individuals who view your blog. tonic greens reviews

    0
  74. Hello! I know this is somewhat off-topic but I had to ask.

    Does running a well-established website like yours require a massive amount work?
    I’m completely new to operating a blog but I do write in my journal every day.

    I’d like to start a blog so I will be able to share my own experience and feelings online.

    Please let me know if you have any kind of ideas or tips for new aspiring bloggers.

    Appreciate it!

    My web site; according to the bcg growth market share matrix

    0
  75. I am really enjoying the theme/design of your website.
    Do you ever run into any web browser compatibility problems?
    A small number of my blog audience have complained about my blog not operating
    correctly in Explorer but looks great in Opera. Do you have any ideas to
    help fix this issue?

    Look at my webpage; tonic greens benefits

    0

Leave a Comment

Your email address will not be published. Required fields are marked *