Big-O:
- Describes how the algorithm scales and performs, in terms of either the execution time required or the space used.
- Is relative representation of complexity. This allows you to reduce an algorithm to a variable which in turn allows you to easily compare it to another.
- Describes an upper limit on the growth of a function, in the other words the "worst case scenario".
There is also Big-Omega notation which looks at the lower bound / "best case scenario" stating that the algorithm will take at least X amount of time and Big-Theta which is tight bound to both lower and upper / "average".
Some quick observations in determining Big-O:
- A Sequence of statements, or things like conditional checks are constant: O(1)
- A loop of statements result in : O(n) n being the number of loop executions.
- Nested loops are multiplied together: O(n2) where n is the times the outer loop executes and m is the times the inner loop executes.
Comparing the common notation examples:
(Thanks to Algorithms: Big-Oh Notation.)
n | Constant O(1) | O(log n) | Linear O(n) | Linear Logarithmic O(n log n) | Quadractic O(n2) | Cubic O(n3) |
---|---|---|---|---|---|---|
1 | 1 | 1 | 1 | 1 | 1 | 1 |
2 | 1 | 1 | 2 | 2 | 4 | 8 |
4 | 1 | 2 | 4 | 8 | 16 | 64 |
8 | 1 | 3 | 8 | 24 | 64 | 512 |
16 | 1 | 4 | 16 | 64 | 256 | 4,096 |
1,024 | 1 | 10 | 1,024 | 10,240 | 1,048,576 | 1,073,741,824 |
1,048,576 | 1 | 20 | 1,048,576 | 20,971,520 | 1012 | 1016 |
Java code example:
Show examples of notations in the table above.
Common Data Structures and Relative functions: Lists and Sets:
Structure | get | add | remove | contains |
---|---|---|---|---|
ArrayList | O(1) | O(1)* | O(n) | O(n) |
LinkedList | O(n) | O(1) | O(1) | O(n) |
HashSet | O(1) | O(1) | O(1) | O(1) |
LinkedHashSet | O(1) | O(1) | O(1) | O(1) |
TreeSet | O(log n) | O(log n) | O(log n) | O(log n) |
Thanks to reader comments, the add method on an ArrayList should be: O(1) amortized (and O(n) in worse case). Useful reference links:
Maps:
Structure | get | put | remove | containsKey |
---|---|---|---|---|
HashMap | O(1) | O(1) | O(1) | O(1) |
LinkedHashMap | O(1) | O(1) | O(1) | O(1) |
TreeMap | O(log n) | O(log n) | O(log n) | O(log n) |
Algorithmic Complexity and Big-O Notation.
Hi,
ReplyDeletethanks for the post. It was nice to realize that I remember at least something from my CS course :).
<nit-picker>
I have an observation to some values in the last 2 tables though.
It is not 100% true to say that add to ArrayList is O(1). In case underlying arrays requires extension, it will take O(n), where n is the number of elements already present in the array.
As for the maps, O(1) is the case only in approximation. In fact, it's a bit more complex and depends on load factor, hash function distribution and length of the chain per hash value.
</nit-picker>
On the other side, one of key words in post title is "simple", so these comments are really some nerdy stuff :).
Great Article Artificial Intelligence Projects
DeleteProject Center in Chennai
JavaScript Training in Chennai
JavaScript Training in Chennai
Thanks for the comments and from what i read, you're right.
ReplyDeletebut
:) yeah I tried to keep it simple, practical and easy to remember, so wanna stay away from the painfully technical details
You might want to star the ArrayList entry for 'add', and point out the following: add is O(1) amortized, but O(n) worst-case since the array must be resized and copied.
ReplyDeleteSee
http://download.oracle.com/javase/6/docs/api/java/util/ArrayList.html
http://stackoverflow.com/questions/322715/when-to-use-linkedlist-over-arraylist
http://stackoverflow.com/questions/200384/constant-amortized-time
Thanks for the input Philip. Yeah, I'll make mention and add the links you mentioned, very helpful.
ReplyDeleteGreat post mate,one of the best I have read on BigONotation. beauty of this post is simple, clean and concise and relavant example from Java and Collections make it more useful. I would recommend for any Java developer to read this post to get a clear Idea of BigO and that will certainly help them to analyze there Algorithm as well. hope to see some more article from you.
ReplyDeleteThanks
Javin
Why wait() and notify() method must be called from synchronized context
Very nice post. The cleanest I've ever seen so far.
ReplyDeleteThanks.
Alin
Nice summary. While many implementations like to capture the theory of big-O; the associated cost of O(1) is often ignored.
ReplyDeleteThe big-O really depends on the parameters passed to the method/function. For example, if you're dealing with the actual data points it is incorrect to say that any of the LinkedList's operations are O(1). Since given the data, a search to find the list entries is still required.
Have you given thought to the run-time resource usage to get the 'most optimal' performance?
I previously leveraged ArrayList--almost exclusively--due to perceived smaller size and 'constant' access times. I have since retreated from the white rabbit, absent any wounds. The default ArrayList sizes clash with resizing of arrays that kill both performance _and_ resource usage.
There's one part that is either wrong, or I am crazy.
ReplyDeletewhile (startIndex < endIndex) {
int midIndex = (endIndex - startIndex / 2) + startIndex;
int midValue = data[midIndex];
The formula for retrieving the midIndex is the problem. The parenthesis don't actually do anything in this case, the equation will be solved the same without it. Did you mean to write this: int midIndex = (endIndex - startIndex)/2 + startIndex ??
Either way I found this post extremely helpful, I've had trouble finding easy to understand documentation on Big ) notation.
Well written, it was extremely helpful and easy to understand.
ReplyDeleteThanks, nice and clearly explained. Another good one on Big O:
ReplyDeleteBig O Notation
Great article, thank you!
ReplyDeleteOne question:
You wrote: "Nested loops are multiplied together: O(n2) where n is the times the outer loop executes and m is the times the inner loop executes."
Shouldn't it be: "Nested loops are multiplied together: O(n * m) where n is the times the outer loop executes and m is the times the inner loop executes."?
nice post and great information shared
ReplyDelete12th Class Result 2016
keyresult
10th Class Board Exam Result 2016
The issue comes, on the off chance that they just keep a reinforcement on the server. ExcelR Data Science Courses
ReplyDeleteGet your favourite garden sheds and all the household items in Auckland Newzealand on a single click. We provide you quality products and Bed with mattress nz lowest price..!
ReplyDeletewatch your favourite pinoy tambayan replays online in hd. All the pinoy channels and all the replays you will be watch online in hd.
ReplyDeleteThanks for sharing this information. I really like your blog post very much. You have really shared a informative and interesting blog post with people.
ReplyDeleteremote developer jobs
watch all your favourite teleserye shows online on Pinoy Channel Tv free episodes in Single click full pinoy tv replays
ReplyDeleteI was reading your article and wondered if you had considered creating an ebook on this subject.Your writing would sell it fast.You have a lot of writing talent. bigo live diamond
ReplyDelete
ReplyDeleteGet all the latest clicksud online seriale online of clicksud and all the seriale online daily on this blog.
I admire this article for the well-researched content and excellent wording. I got so involved in this material that I couldn’t stop reading. I am impressed with your work and skill. Thank you so much. Tableau Data Blending
ReplyDeleteGreat Content, If you wish to upskill yourself in the latest Technologies Do visit GoLogica Trainings
ReplyDeleteThis comment has been removed by the author.
ReplyDeleteNice post and valuable information thank you.
ReplyDeleteData Analytics Course in Pune
Nice post and valuable information, writing is simply great, thanks for sharing.
ReplyDeleteBusiness Analytics Course in Pune
Business Analytics Training in Pune
After reading your article I was amazed. I know that you explain it very well. And I hope that other readers will also experience how I feel after reading your article.
ReplyDeletedata science course in indore
After reading your article I was amazed. I know that you explain it very well. And I hope that other readers will also experience how I feel after reading your article.
ReplyDeletedata science course in coimbatore
Awesome blog. I enjoyed reading your articles. This is truly a great read for me. I have bookmarked it and I am looking forward to reading new articles. Keep up the good work!
ReplyDeletedata science course in gurgaon
I really enjoy simply reading all of your weblogs. Simply wanted to inform you that you have people like me who appreciate your work. Definitely a great post. Hats off to you! The information that you have provided is very helpful.
ReplyDeletedata science course in bhilai
I feel very grateful that I read this. It is very helpful and very informative and I really learned a lot from it.
ReplyDeletedata science course in nagpur
Really nice and interesting post. I was looking for this kind of information and enjoyed reading this one. Keep posting. Thanks for sharing.data science course in jaipur
ReplyDeleteThis comment has been removed by the author.
ReplyDeleteI feel very grateful that I read this. It is very helpful and very informative and I really learned a lot from it.
ReplyDeletedata science course in nagpur
I finally found great post here.I will get back here. I just added your blog to my bookmark sites. thanks.Quality posts is the crucial to invite the visitors to visit the web page, that's what this web page is providing.
ReplyDeletedata science course in lucknow
I am really enjoying reading your well written articles. It looks like you spend a lot of effort and time on your blog. I have bookmarked it and I am looking forward to reading new articles. Keep up the good work.
ReplyDeletedata science course in kanpur
After reading your article I was amazed. I know that you explain it very well. And I hope that other readers will also experience how I feel after reading your article.
ReplyDeletedata science training in navi mumbai
I just got to this amazing site not long ago. I was actually captured with the piece of resources you have got here. Big thumbs up for making such wonderful blog page!
ReplyDeletedata science course in kochi
Really nice and interesting post. I was looking for this kind of information and enjoyed reading this one. Keep posting. Thanks for sharing.
ReplyDeletedata science course in pune
Nice post and great information thank you. waiting for the next update.
ReplyDeleteData Science Course in Pune
Data Science Training in Pune
Awesome blog. I enjoyed reading your articles. This is truly a great read for me. I have bookmarked it and I am looking forward to reading new articles. Keep up the good work!
ReplyDeleteData Science Institute in Bangalore
Nice post and great information thank you. waiting for the next update.
ReplyDeleteData Science Course in Pune
Data Science Training in Pune
I have to search sites with relevant information ,This is a
ReplyDeletewonderful blog,These type of blog keeps the users interest in
the website, i am impressed. thank you.
Data Science Course in Bangalore
I feel really happy to have seen your webpage and look forward to so many more entertaining times reading here. Thanks once more for all the details.
ReplyDeleteBusiness Analytics Training in Hyderabad | Artificial Intelligence Course in Hyderabad | Business Analytics Course in Hyderabad
Very informative post! Here is a lot of information that can help any business start a successful social media campaign!
ReplyDeleteData Science Course
I feel very grateful that I read this. It is very helpful and very informative and I really learned a lot from it.
ReplyDeleteData Analytics Course in Pune
Data Analytics Training in Pune
I am impressed by the information that you have on this blog. It shows how well you understand this subject.
ReplyDeleteBusiness Analytics Course in Pune
Business Analytics Training in Pune
I want to say thanks to you. I have bookmark your site for future updates.
ReplyDeletedata science course
I like viewing web sites which comprehend the price of delivering the excellent useful resource free of charge. I truly adored reading your posting. Thank you!
ReplyDeletebusiness analytics course in hyderabad
data science course hyderabad
data analytics courses in hyderabad
Excellent Blog! I would like to thank for the efforts you have made in writing this post. I am hoping the same best work from you in the future as well. I wanted to thank you for this websites! Thanks for sharing. Great websites!
ReplyDeleteArtificial Intelligence Training In Hyderabad
Clicksud este platforma de divertisment finală pentru seriale online și filme online. Divertismentul digital din întreaga lume este acoperit de clicksud și ne îndreptăm spre una dintre cele mai bune platforme online care înțelege nevoia publicului și oferă exact lucrurile vizitatorilor, ceea ce le face unice pentru noi.
ReplyDeleteI’m excited to uncover this page. I need to to thank you for ones time for this particularly fantastic read!! I definitely really liked every part of it and i also have you saved to fav to look at new information in your site.
ReplyDeleteData Science Training in Hyderabad | Data Science Course in Hyderabad
You are in point of fact a just right webmaster. The website loading speed is amazing. It kind of feels that you're doing any distinctive trick. Moreover, The contents are masterpiece. you have done a fantastic activity on this subject!
ReplyDeleteBusiness Analytics Course in Hyderabad | Business Analytics Training in Hyderabad
I feel really happy to have seen your webpage and look forward to so many more entertaining times reading here. Thanks once more for all the details.
ReplyDeleteData Science Training in Hyderabad | Data Science Course in Hyderabad
Nice blog. I finally found great post here Very interesting to read this article and very pleased to find this site. Great work!
ReplyDeleteData Science Training in Pune
Data Science Course in Pune
this blog was really great, never seen a great blog like this before. i think im gonna share this to my friends..
ReplyDeletedata science course in guwahati
Very interesting blog. Many blogs I see these days do not really provide anything that attracts others, but believe me the way you interact is literally awesome.You can also check my articles as well.
ReplyDeleteData Science In Banglore With Placements
Data Science Course In Bangalore
Data Science Training In Bangalore
Best Data Science Courses In Bangalore
Data Science Institute In Bangalore
Thank you..
I really like your take on the issue. I now have a clear idea on what this matter is all about.. buy like
ReplyDeleteI have to search sites with relevant information ,This is a
ReplyDeletewonderful blog,These type of blog keeps the users interest in
the website, i am impressed. thank you.
Data Science Course in Bangalore | Data Science Training in Bangalore
Clicksud shows: www.pinoy1channel.com/, TVpenet shows, rulare shows, Romanian shows full hd episodes online for free.
ReplyDeleteIt has fully emerged to crown Singapore's southern shores and undoubtedly placed her on the global map of residential landmarks. I still scored the more points than I ever have in a season for GS. I think you would be hard pressed to find somebody with the same consistency I have had over the years so I am happy with that.
ReplyDeleteData Science Course in Bangalore
You might comment on the order system of the blog. You should chat it's splendid. Your blog audit would swell up your visitors. I was very pleased to find this site.I wanted to thank you for this great read!!
ReplyDeleteData Science Training in Bangalore
Then the article considers three obstacles that often discourage companies from making their ERP dream a reality: (1) companies must find the right software partner, (2) they need to review their current business processes, and (3) they have to deal with the cost factor. But first, let us look into the considerable benefits of ERP software, ultimately, trumping any challenges. download google input tool offline
ReplyDeleteI will really appreciate the writer's choice for choosing this excellent article appropriate to my matter. Here is deep description about the article matter which helped me more.
ReplyDeleteBest Institute for Cyber Security in Bangalore
Very nice blog and articles. I am really very happy to visit your blog. Now I am found which I actually want. I check your blog everyday and try to learn something from your blog. Thank you and waiting for your new post.
ReplyDeleteCyber Security Training in Bangalore
Thumbs up guys your doing a really good job. It is the intent to provide valuable information and best practices, including an understanding of the regulatory process.
ReplyDeleteCyber Security Course in Bangalore
After reading your article I was amazed. I know that you explain it very well. And I hope that other readers will also experience how I feel after reading your article.
ReplyDeleteEthical Hacking Course in Bangalore
This comment has been removed by the author.
ReplyDeleteWow! Such an amazing and helpful post this is. I really really love it. I hope that you continue to do your work like this in the future also.
ReplyDeleteEthical Hacking Training in Bangalore
I am impressed by the information that you have on this blog. Thanks for Sharing
ReplyDeleteEthical Hacking in Bangalore
Actually I read it yesterday but I had some thoughts about it and today I wanted to read it again because it is very well written.
ReplyDeletedata science course
data analytics course
business analytics course in hyderabad
https://digitalweekday.com/
ReplyDeletehttps://digitalweekday.com/
https://digitalweekday.com/
https://digitalweekday.com/
https://digitalweekday.com/
https://digitalweekday.com/
https://digitalweekday.com/
https://digitalweekday.com/
https://digitalweekday.com/
ReplyDeletehttps://digitalweekday.com/
https://digitalweekday.com/
https://digitalweekday.com/
https://digitalweekday.com/
https://digitalweekday.com/
https://digitalweekday.com/
https://digitalweekday.com/
Very interesting blog. Many blogs I see these days do not really provide anything that attracts others, but believe me the way you interact is literally awesome.You can also check my articles as well.
ReplyDeleteRowe Rowe
Rowe Rowe
Rowe Rowe
Rowe Rowe
Thank you..
If your looking for Online Illinois license plate sticker renewals then you have need to come to the right place.We offer the fastest Illinois license plate sticker renewals in the state.data science course in malaysia
ReplyDeleteThe Basics You Have Explained Was Good.Thanks For Sharing The Content With Us.
ReplyDeletePython Training Course Institute in Hyderabad
Very impressive and interesting blog found to be well written in a simple manner that everyone will understand and gain the enough knowledge from your blog being much informative is an added advantage for the users who are going through it. Once again nice blog keep it up.
ReplyDeleteVery impressive and interesting blog found to be well written in a simple manner that everyone will understand and gain the enough knowledge from your blog being much informative is an added advantage for the users who are going through it. Once again nice blog keep it up.
ReplyDeleteData Science Course in raipur
Very impressive and interesting blog found to be well written in a simple manner that everyone will understand and gain the enough knowledge from your blog being much informative is an added advantage for the users who are going through it. Once again nice blog keep it up.
ReplyDeleteDigital Marketing Course in raipur
If your looking for Online Illinois license plate sticker renewals then you have need to come to the right place.We offer the fastest Illinois license plate sticker renewals in the state.
ReplyDelete360digitmg
Found your post interesting to read. I cant wait to see your post soon. Good Luck for the upcoming update. This article is really very interesting and effective, data science courses
ReplyDeletePinoy Channel Filipino teleserye replays channel to watch all pinoy lambingan and pinoy tambayan , free and online pinoy tv .
ReplyDeleteI see some amazingly important and kept up to length of your strength searching for in your on the site
ReplyDeleteartificial intelligence course in delhi
Our website serves as the best site where people can easily enjoy all the Pinoy TV and We gave them a chance to add a bookmark to their favorite site.
ReplyDeleteI have to search sites with relevant information ,This is a
ReplyDeletewonderful blog,These type of blog keeps the users interest in
the website, i am impressed. thank you.
pmp training in bangalore
I wanted to leave a little comment to support you and wish you a good continuation. Wishing you the best of luck for all your blogging efforts.
ReplyDeletedata science training in Hyderabad
it’s really nice and meanful. it’s really cool blog. Linking is very useful thing.you have really helped lots of people who visit blog and provide them usefull information.
ReplyDeleteData Science Training in Hyderabad
I am really happy to say it’s an interesting post to read . I learn new information from your article , you are doing a great job . Keep it up
Devops Training in USA
Hadoop Training in Hyderabad
Python Training in Hyderabad
That's certainly a massive amount, isn't it! Now just think what would happen if owing to some system malfunction or any other issue, all this data gets lost. data science course syllabus
ReplyDeleteI have been searching to find a comfort or effective procedure to complete this process and I think this is the most suitable way to do it effectively.
ReplyDeletebest institutes for digital marketing in hyderabad
This is a wonderful article, Given so much info in it, These type of articles keeps the users interest in the website, and keep on sharing more ... good luck. 360DigiTMG
ReplyDeleteTremendous blog quite easy to grasp the subject since the content is very simple to understand. Obviously, this helps the participants to engage themselves in to the subject without much difficulty. Hope you further educate the readers in the same manner and keep sharing the content as always you do.
ReplyDeleteData Science training in Bhilai
Truly incredible blog found to be very impressive due to which the learners who ever go through it will try to explore themselves with the content to develop the skills to an extreme level. Eventually, thanking the blogger to come up with such an phenomenal content. Hope you aarrive with the similar content in future as well.
ReplyDeleteDigital Marketing Course in Bhilai
Fantastic blog extremely good well enjoyed with the incredible informative content which surely activates the learners to gain the enough knowledge. Which in turn makes the readers to explore themselves and involve deeply in to the subject. Wish you to dispatch the similar content successively in future as well.
ReplyDeleteartificial intelligence course in bhilai
Through this post, I realize that your great information in playing with all the pieces was exceptionally useful. I advise this is the primary spot where I discover issues I've been scanning for. You have a smart yet alluring method of composing.
ReplyDeletedata science course in noida
I am genuinely thankful to the holder of this web page who has shared this wonderful paragraph at at this place
ReplyDeleteartificial intelligence course training in hyderabad
This is a wonderful article, Given so much info in it, These type of articles keeps the users interest in the website, and keep on sharing more ... good luck. contact us
ReplyDelete
ReplyDeleteThank you for helping people get the information they need. Great stuff as usual. Keep up the great work!!!
360digitmg
Incredibly all around intriguing post. I was searching for such a data and completely appreciated inspecting this one. Continue posting. A commitment of gratefulness is all together for sharing.data science course in Hyderabad
ReplyDeleteI will really appreciate the writer's choice for choosing this excellent article appropriate to my matter.Here is deep description about the article matter which helped me more.
ReplyDeletedata science training in Hyderabad
You actually make it look so easy with your performance but I find this matter to be actually something which I think I would never comprehend. It seems too complicated and extremely broad for me. I'm looking forward for your next post, I’ll try to get the hang of it!
ReplyDeletebest data science courses in hyderabad
Excellent Blog! I would like to thank for the efforts you have made in writing this post. I am hoping the same best work from you in the future as well. I wanted to thank you for this websites! Thanks for sharing. Great websites!
ReplyDeletedata science course in India
I have express a few of the articles on your website now, and I really like your style of blogging. I added it to my favorite’s blog site list and will be checking back soon…
ReplyDeletedata science course in Hyderabad
ReplyDeleteI'm really thankful that I read this.
Data Science Course In India
ReplyDeleteVery wonderful article. I liked reading your article. Very wonderful share. Thanks ! .
Data Science Course Syllabus
I have bookmarked your website because this site contains valuable information in it. I am really happy with articles quality and presentation. Thanks a lot for keeping great stuff. I am very much thankful for this site.
ReplyDeletedata science training in Hyderabad
I have to search sites with relevant information ,This is a
ReplyDeletewonderful blog,These type of blog keeps the users interest in
the website, i am impressed. thank you.
Data Science Course in Bangalore
I am really happy to say it’s an interesting post to read . I learn new information from your article , you are doing a great job . Keep it up
ReplyDeleteDevops Training in USA
Hadoop Training in Hyderabad
Python Training in Hyderabad
Just the way I have expected. Your website really is interesting. ExcelR Data Analytics Course
ReplyDeleteAivivu đại lý vé máy bay
ReplyDeletevé máy bay giá rẻ tết 2021
Vé máy bay đi Mỹ
kinh nghiệm mua vé máy bay giá rẻ đi Pháp
giá vé máy bay đi hàn quốc hôm nay
vé máy bay sang nhật bản
giá vé máy bay đi Anh Vietnam Airline
đặt vé máy bay giá rẻ ở đâu
This comment has been removed by the author.
ReplyDeleteI am genuinely thankful to the holder of this web page who has shared this wonderful paragraph at at this place Great Business
ReplyDeletewow, great, I was wondering how to cure acne naturally. and found your site by google, learned a lot, now i’m a bit clear. I’ve bookmark your site and also add rss. keep us updated.
ReplyDelete360digitmg
I’m happy I located this blog! From time to time, students want to cognitive the keys of productive literary essays composing. Your first-class knowledge about this good post can become a proper basis for such people. nice one Water Softener System
ReplyDeleteYour blog is so impressive to us. Thanks for sharing this post. Good content delivery.
ReplyDeletedevops culture
java mobile app development
adwords campaign
is web design a good career
seo interview questions and answers
A decent blog dependably concocts new and energizing data and keeping in mind that understanding I have feel that this blog is truly have each one of those quality that qualify a blog to be a one. 토토사이트
ReplyDeleteI found that site very usefull and this survey is very cirious, I ' ve never seen a blog that demand a survey for this actions, very curious... windshield replacement san diego
ReplyDeleteI just want to let you know that I just check out your site and I find it very interesting and informative motorcycles for sale san diego
ReplyDeleteReally appreciate this wonderful post that you have provided for us.Great site and a great topic as well i really get amazed to read this. Its really good motorcycle dealer
ReplyDeleteExcellent and very exciting site. Love to watch. Keep Rocking. real estate agent vanier
ReplyDeleteLovely article mate! real estate agent vanier
ReplyDeleteCool stuff you have got and you keep update all of us cybersécurité
ReplyDeleteTo start with You got an awesome blog .I will be keen on more comparative points. I see you got extremely exceptionally valuable themes, I will be continually checking your blog much appreciated resistance heating
ReplyDeleteWhat a information of un-ambiguity and preserveness of valuable familiarity concerning unexpected feelings. real estate broker aylmer
ReplyDeleteHi buddies, it is great written piece entirely defined, continue the good work constantly shipping from china to us
ReplyDeleteI am always searching online for articles that can help me. There is obviously a lot to know about this. I think you made some good points in Features also. Keep working, great job! buy web traffic
ReplyDelete여기에 나열된 것이 중요하다는 것을 배우고 유용한 웹 페이지에 링크를 제공합니다. 토토사이트
ReplyDeleteI want you to thank for your time of this wonderful read!!! I definately enjoy every little bit of it and I have you bookmarked to check out new stuff of your blog a must read blog! 토토사이트
ReplyDeleteThanks for another wonderful post. Where else could anybody get that type of info in such an ideal way of writing? 메이저사이트
ReplyDeleteI recently found many useful information in your website especially this blog page. Among the lots of comments on your articles. Thanks for sharing 먹튀커뮤니티
ReplyDeleteI have added and shared your site to my social media accounts to send people back to your site because I am sure they will find it extremely helpful too. freelancer malta
ReplyDeleteĐặt mua vé máy bay tại Aivivu, tham khảo
ReplyDeletevé máy bay đi Mỹ Vietnam Airline
cách săn vé máy bay giá rẻ tết 2021
vé máy bay rẻ đi canada
vé máy bay đi Pháp
bay từ việt nam sang Anh mất bao lâu
vé máy bay giá rẻ khứ hồi
vé máy bay đi San Francisco
vé máy bay đi Los Angeles bao nhiêu tiền
combo intercontinental phú quốc
mua combo vinpearl nha trang
좋은 사이트가 있습니다. 정말 쉽고 탐색하기 좋은 웹 사이트가 훌륭하고 멋져 보이고 따라 가기 매우 쉽다고 생각합니다. 출장샵
ReplyDeleteHello, I really enjoyed reading your post. Actually I'm doing something similar to yours. You and I have a lot in common. Like you, I have posted a lot of articles on my website. If you are interested, please visit and read. Thank you. Have a nice day. 토토사이트
ReplyDeleteI truly like you're composing style, incredible data, thankyou for posting 토토사이트
ReplyDeleteThanks for providing recent updates regarding the concern, I look forward to read more. 먹튀검증
ReplyDeleteThis is most informative and also this post most user-friendly and super navigation to all posts.
ReplyDeleteOnline Data Science Classes
Selenium Training in Pune
AWS Online Classes
Python Online Classes
Excellent post and I am very happy to read this blog. Keep doing...!
ReplyDeletePrimavera Training in Chennai
Embedded System Course in Chennai
Embedded Training in Coimbatore
Embedded Training in Chennai
Your content is very unique and understandable useful for the readers keep update more article like this.
ReplyDeletedata science training in noida
Thanks for the information about Blogspot very informative for everyone
ReplyDeletedata scientist malaysia
Nice & Informative Blog !
ReplyDeleteIn case you face any technical issue in QuickBooks, call us at QuickBooks Customer Support Number 1-855-974-6537 and get instant solutions for QuickBooks problems.
Really satisfied with all the information I have found in this article. It gives immense knowledge on physical education, it is very helpful and quite generous to spread a good message. The author has done카지노
ReplyDeletea brilliant job on summing all the points here. You just made a new fan with your writing skills. Cheers!
Really satisfied with all the information I have found in this article. It gives immense knowledge on physical education, it is very helpful and quite generous to spread a good message.바카라커뮤니티
ReplyDeleteThe author has done a brilliant job on summing all the points here. You just made a new fan with your writing skills. Cheers!
You totally coordinate our desire and the assortment of our data.
ReplyDeletedata analytics course in yelahanka
Doramasmp4 esperamos que la estés pasando genial viendo. DoramasMP4 siempre será el primero en tener el episodio, así que por favor marque y agréguenos en Facebook para actualizarlo.
ReplyDeletehttps://doramas-sub-espanol.jimdosite.com/
Organic Chemistry tutor
ReplyDeleteOrganic chemistry
online tutor
Hello there to everyone, here everybody is sharing such information, so it's fussy to see this webpage, and I used to visit this blog day by day
ReplyDeletedata science course in noida
Săn vé máy bay tại Aivivu, tham khảo
ReplyDeleteVe may bay di My
vé máy bay từ mỹ về việt nam hãng ana
khi nào có chuyến bay từ anh về việt nam
mua vé máy bay giá rẻ từ pháp về việt nam
Happy to visit your blog, I am by all accounts forward to more solid articles and I figure we as a whole wish to thank such huge numbers of good articles, blog to impart to us.
ReplyDeletedata scientist certification
Thanks for Sharing This Article.It is very so much valuable content. I hope these Commenting lists will help to my website
ReplyDeletedata science courses in noida
It's like you understand the topic well, but forgot to include your readers. Maybe you should think about it from several angles.
ReplyDeleteData Science Course in Pune
Really Nice Information It's Very Helpful All courses Checkout Here.
ReplyDeletebest data science course
Your content is very unique and understandable useful for the readers keep update more article like this.
ReplyDeletecertification of data science
Nice article. I liked very much. All the information given by you are really helpful for my research. keep on posting your views.
ReplyDeletedata science course
"Very Nice Blog!!!
ReplyDeletePlease have a look about "data science course in delhi ncr
"Very Nice Blog!!!
ReplyDeletePlease have a look about "data science courses in noida
Wow, amazing post! Really engaging, thank you.
ReplyDeletebest data science course in delhi
Very awesome!!! When I seek for this I found this blog at the top of all blogs in search engine. 먹튀검증
ReplyDeleteI really want to thank you for yet another great informative post, I’m a loyal reader to this blog and I can’t stress enough how much valuable information I’ve learned from reading your content. I really appreciate all the effort you put into this great site. 이기자벳
ReplyDeleteHelpful info. Lucky me I discovered your site by chance, and I’m 토토사이트
ReplyDeleteHi, This is a nice article you shared great information I have read it thanks for giving such a wonderful Blog for the reader. 토토
ReplyDelete읽어 주셔서 감사합니다 !! 나는 모든 작은 부분을 확실히 좋아했습니다. 귀하가 게시하는 새로운 콘텐츠를 확인하기 위해 귀하의 사이트를 북마크했습니다. 먹튀검증
ReplyDeleteAre you looking for custom packaging for your CBD boxes? Well, look no further Because Custom CBD Boxes is here for you. There are two major reasons as to why you should use a customized box for your CBD boxes; market size and CBD unique position in society.
ReplyDeleteI've been using this kind of hobby lately, so take a look.먹튀검증
ReplyDeleteI recently came across your article and have been reading along. I want to express my admiration of your writing skill and ability to make readers read from the beginning to the end. I would like to read newer posts and to share my thoughts with you. Primavera Training in Chennai | Primavera online course
ReplyDeleteI am really enjoying reading your well written articles. It looks like you spend a lot of effort and time on your blog. I have bookmarked it and I am looking forward to reading new articles. Keep up the good work.
ReplyDeleteartificial intelligence course in pune
Fantastic blog with excellent information and valuable content just added your blog to my bookmarking sites thank for sharing.
ReplyDeleteData Science Course in Chennai
Hello. I'm subscribed to your posts. You inspire me a lot.카지노사이트I am so grateful.
ReplyDeleteI really enjoy every part and have bookmarked you to see the new things you post. Well done for this excellent article. Please keep this work of the same quality.
ReplyDeleteArtificial Intelligence course in Chennai
Amazing Article ! I would like to say thank you for the efforts you had made for writing this awesome article. This article inspired me to read more your blogs. keep it up.
ReplyDeleteAffiliate Marketing Training In Telugu
Affiliate Marketing Means In Telugu
Digital Marketing Training In Telugu
Blogging In Telugu
Podcast Meaning In telugu
SEO Meaning In Telugu
1000 Social BookMarking Sites List
I am very impressed with your writing온라인포커 I couldn't think of this, but it's amazing! I wrote several posts similar to this one, but please come and see!
ReplyDeleteIt is late to find this act. At least one should be familiar with the fact that such events exist. I agree with your blog and will come back to inspect it further in the future, so keep your performance going.
ReplyDeleteData Science Course in Pune
I'm writing on this topic these days, , but I have stopped writing because there is no reference material. Then I accidentally found your article. I can refer to a variety of materials, so I think the work I was preparing will work! Thank you for your efforts. 토토커뮤니티
ReplyDeleteI really enjoyed your writing. You should come and see mine.카지노사이트
ReplyDeleteA very awesome blog post. 토토사이트 We are really grateful for your blog post. combat, law enforcement You will find a lot of approaches after visiting your post. I was exactly searching for. Thanks for such post and please keep it up. Great work.
ReplyDeletebespoke packaging boxes uk At Bespoke Packaging UK we strongly believe in the interests of bespoke packaging, which has multiple benefits.
ReplyDeleteI needed several examples to write an article on this subject, and your article was of great help to me.바카라사이트
ReplyDeleteI seriously love your website.. Excellent colors & theme.
ReplyDeleteDid you create this amazing site yourself? Please reply back as I’m attempting to create my own site
and want to know where you got this from or just what the theme is named.
Cheers!국산야동
I want to start a blog to write about everything that happens at school and
ReplyDeletewith friends…anonymously…any sugestions?.해외선물
ReplyDeleteI am really happy to say it’s an interesting post to read . I learn new information from your article , you are doing a great job . Keep it up
Devops Training in Hyderabad
Hadoop Training in Hyderabad
Python Training in Hyderabad
Tableau Training in Hyderabad
Selenium Training in Hyderabad
This article is very interesting information. It has helped me a lot. Thank you very much for providing this quality information in an easy-to-understand manner. Our site also provides high-quality information, so it will be helpful for your site. 토토사이트
ReplyDeleteI read your article it is very interesting and every concept is very clear, thank you so much for sharing. AWS Certification Course in Chennai
ReplyDeleteThis is one very interesting post. I like the way you write and I will bookmark your blog to my favorites. 온라인홀덤
ReplyDeleteThis is very interesting, You are a very skilled blogger. I've joined your rss feed and look forward to seeking more of your wonderful 메이저놀이터. Also, I have shared your website in my social networks!
ReplyDeleteYou did a great job writing. I have the same interests, so please bear with me here.카지노사이트
ReplyDeleteHello, I read the post well. 토토커뮤니티 It's a really interesting topic and it has helped me a lot. In fact, I also run a website with similar content to your posting. Please visit once
ReplyDeleteHello, I read the post well. 토토커뮤니티 It's a really interesting topic and it has helped me a lot. In fact, I also run a website with similar content to your posting. Please visit once
ReplyDeleteIt's so interesting.카지노사이트Let's enjoy it together.
ReplyDeleteThanks for always being willing to lend a hand to provide the best knowledge.
ReplyDeletehttps://360digitmg.com/course/certification-program-on-digital-marketing
I simply couldn’t leave your site prior to suggesting that I really loved the usual This is a brilliant blog! I'm very happy with the comments!wholesale cosmetic boxes | wholesale cosmetic boxes
ReplyDeleteYour writing is perfect and complete. 온라인바둑이 However, I think it will be more wonderful if your post includes additional topics that I am thinking of. I have a lot of posts on my site similar to your topic. Would you like to visit once?
ReplyDeleteI seriously love your website.. Excellent colors & theme.
ReplyDeleteDid you create this amazing site yourself? Please reply back as I’m attempting to create my own site
and want to know where you got this from or just what the theme is named.
Cheers!오피사이트
It took me a while to read all the reviews, but I really enjoyed the article. This has proven to be very helpful to me and I'm sure all the reviewers here! It's always nice to be able to not only be informed, but also have fun!
ReplyDeleteDigital Marketing Course in Bangalore
Excellent exchange of information ... I am very happy to read this article ... thank you for giving us information. Fantastic. I appreciate this post.
ReplyDeleteBusiness Analytics Course
With so many books and articles appearing to usher in the field of making money online and further confusing the reader on the real way to make money.
ReplyDeleteBest Data Science Courses in Bangalore
Wonderful blog post. It's absolute magic on your part! I have never seen a more wonderful article than this. You really made my day today with this. Hope you continue like this!
ReplyDeleteData Analytics Course in Bangalore
Hi there, I simply hopped over in your website by way of StumbleUpon. Now not one thing I’d typically learn, but I favored your emotions none the less. Thank you for making something worth reading. 토토사이트
ReplyDeleteIt's really great. Thank you for providing a quality article. There is something you might be interested in. Do you know 온라인홀덤 ?
ReplyDeleteLecithin Market
ReplyDelete나는 주어진 주제에 대한 관련 정보를 가지고 사이트를 검색해서 우리의 의견과 기사를 선생님에게 제공해야 합니다.토토사이트
ReplyDeleteThank a lot. You have done excellent job. I enjoyed your blog . Nice efforts
ReplyDeleteData Science Certification in Hyderabad
It's really great. Thank you for providing a quality article. 사설토토
ReplyDelete