AVL Tree

2,288 Comments / Trending / December 30, 2022

It has been discovered that the worst-case performance of BST is similar to that of linear search algorithms, namely O (n). We cannot forecast data patterns and frequencies in real-time data. As a result, there is a need to balance out the present BST.

AVL trees are height-balancing binary search trees named after their inventors Adelson, Velski, and Landis. The AVL tree compares the heights of the left and right sub-trees and ensures that the difference is less than one. This distinction is known as the Balance Factor.

Here we see that the first tree is balanced and the next two trees are not balanced −

Unbalanced AVL Trees

The left subtree of C in the second tree has a height of 2 and the right subtree has a height of 0, hence the difference is 2. The difference is 2 again in the third tree, since the right subtree of A has height 2 and the left is missing, therefore it is 0. The AVL tree allows only one difference (balancing factor).
BalanceFactor = height(left-subtree) − height(right-subtree)

AVL Rotations

To balance itself, an AVL tree may perform the following four kinds of rotations −

  • Left rotation
  • Right rotation
  • Left-Right rotation
  • Right-Left rotation

Left Rotation

If a tree becomes unbalanced, when a node is inserted into the right subtree of the right subtree, then we perform a single left rotation −

Left Rotation

In our example, node A has become unbalanced as a node is inserted in the right subtree of A’s right subtree. We perform the left rotation by making A the left-subtree of B.

Right Rotation

AVL tree may become unbalanced, if a node is inserted in the left subtree of the left subtree. The tree then needs a right rotation.

Right Rotation

As depicted, the unbalanced node becomes the right child of its left child by performing a right rotation.

Left-Right Rotation

Double rotations are slightly complex version of already explained versions of rotations. To understand them better, we should take note of each action performed while rotation. Let’s first check how to perform Left-Right rotation. A left-right rotation is a combination of left rotation followed by right rotation.

StateAction
Right RotationA node has been inserted into the right subtree of the left subtree. This makes C an unbalanced node. These scenarios cause AVL tree to perform left-right rotation.
Left RotationWe first perform the left rotation on the left subtree of C. This makes A, the left subtree of B.
Left RotationNode C is still unbalanced, however now, it is because of the left-subtree of the left-subtree.
Right RotationWe shall now right-rotate the tree, making B the new root node of this subtree. C now becomes the right subtree of its own left subtree.
Balanced Avl TreeThe tree is now balanced.

Right-Left Rotation

The second type of double rotation is Right-Left Rotation. It is a combination of right rotation followed by left rotation.

StateAction
Left Subtree of Right SubtreeA node has been inserted into the left subtree of the right subtree. This makes A, an unbalanced node with balance factor 2.
Subtree Right RotationFirst, we perform the right rotation along C node, making C the right subtree of its own left subtree B. Now, B becomes the right subtree of A.
Right Unbalanced TreeNode A is still unbalanced because of the right subtree of its right subtree and requires a left rotation.
Left RotationA left rotation is performed by making B the new root node of the subtree. A becomes the left subtree of its right subtree B.
Balanced AVL TreeThe tree is now balanced.
Share on Facebook
Tweet
0

Related posts:

  1. Linked List
  2. Tree
  3. Tree Traversal
  4. Binary Search Tree

2,288 thoughts on “AVL Tree”

  1. zoritoler imol

    There are actually lots of details like that to take into consideration. That is a great level to bring up. I offer the ideas above as common inspiration however clearly there are questions like the one you convey up where crucial factor will probably be working in trustworthy good faith. I don?t know if greatest practices have emerged around issues like that, however I am positive that your job is clearly identified as a good game. Each boys and girls really feel the impression of only a moment’s pleasure, for the remainder of their lives.

    0
    Reply
  2. Becky Kelty

    You actually make it seem really easy together with your presentation but I to find this matter to be really one thing which I believe I’d by no means understand. It kind of feels too complex and very large for me. I am having a look ahead to your next submit, I¦ll attempt to get the cling of it!

    0
    Reply
  3. cbd vape canada

    I am very happy to read this. This is the kind of manual that needs to be given and not the accidental misinformation that’s at the other blogs. Appreciate your sharing this greatest doc.

    0
    Reply
  5. Cory Ronchetto

    Its such as you read my mind! You appear to know a lot about this, like you wrote the guide in it or something. I think that you could do with a few percent to force the message house a bit, however other than that, this is excellent blog. A great read. I will certainly be back.

    0
    Reply
  6. tlovertonet

    Thank you, I’ve recently been searching for information about this subject for ages and yours is the best I have discovered so far. But, what about the conclusion? Are you sure about the source?

    0
    Reply
  8. Kristy

    hey there and thank you for your information – I’ve certainly picked up
    sometging new from rijght here. I did however expertise several technical issues
    using this site, as I experienced to reload the web site many times previous to I could get it to load correctly.
    I had been wondering if yokur web host is OK?
    Not that I am complaining, but slugvgish loading instances times
    will often affeect your plaement in google and can damage your high
    quality score if ads and marketing with Adwords.

    Anyway I am adding this RSS to my e-mail and
    cold look oout for much more of your respective interesting content.
    Ensure that you updage this again vrry soon.

    my web pave :: Kristy

    0
    Reply
  9. Slotbom88

    I do agree with all of the ideas you have presented in your post. They’re very convincing and will certainly work. Still, the posts are very short for starters. Could you please extend them a bit from next time? Thanks for the post.

    0
    Reply
  15. Warung138

    With havin so much content and articles do you ever run into any problems of plagorism or copyright infringement? My blog has a lot of exclusive content I’ve either created myself or outsourced but it looks like a lot of it is popping it up all over the web without my agreement. Do you know any methods to help stop content from being ripped off? I’d really appreciate it.

    0
    Reply
  17. Slotbom77

    I have been exploring for a little for any high quality articles or blog posts on this sort of house . Exploring in Yahoo I ultimately stumbled upon this site. Studying this info So i’m satisfied to convey that I have a very just right uncanny feeling I came upon just what I needed. I most definitely will make certain to don’t put out of your mind this site and provides it a look on a relentless basis.

    0
    Reply
  18. KKSLOT777

    You could certainly see your expertise in the work you write. The world hopes for even more passionate writers like you who are not afraid to say how they believe. Always go after your heart.

    0
    Reply
  47. sklep

    Hi, Neat post. There’s a problem along with your web site in web explorer, would test this?
    IE still is the market leader and a huge part of other people will pass over your fantastic
    writing due to this problem. I saw similar here: %random_link% and also here: %random_link%

    0
    Reply
  55. vorbelutr ioperbir

    you’re really a excellent webmaster. The web site loading speed is incredible. It sort of feels that you are doing any unique trick. In addition, The contents are masterwork. you’ve performed a great process on this subject!

    0
    Reply
  58. dobry sklep

    Hey there! I know this is somewhat off-topic however I had
    to ask. Does operating a well-established blog such
    as yours require a lot of work? I’m completely new to blogging however I do
    write in my diary daily. I’d like to start a blog so I can easily share my experience and views online.
    Please let me know if you have any kind of suggestions or
    tips for new aspiring blog owners. Appreciate it!!

    0
    Reply
  105. hire a hacker for facebook

    I love your blog.. very nice colors & theme. Did you make this website yourself or did you hire someone to do it for you? Plz reply as I’m looking to design my own blog and would like to find out where u got this from. kudos

    0
    Reply
  108. расследование qiwi

    Have you lost money on your QIWI wallet?
    We know how disheartening that can be.

    Don’t despair—we specializes in retrieving lost funds from QIWI wallets.

    Boasting an experienced team, we’re positive we can help out.

    Contact us and let’s get to work of restoring your balance.

    0
    Reply
  110. вернуть деньги qiwi

    Retrieving your lost funds shouldn’t be complicated.
    That’s why our methodology is simple and open.
    Just provide us with some basic information, and
    we’ll handle everything else.

    Don’t let a simple mistake keep you from your hard-earned money.
    Our goal is to assist you in reclaiming every penny.

    0
    Reply
  115. dobry sklep

    Good day! Do you know if they make any plugins to
    help 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. Many thanks!

    You can read similar art here: E-commerce

    0
    Reply
  117. najlepszy sklep

    Hey there! Do you know if they make any plugins to help with SEO?
    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. Thank you!
    You can read similar blog here: Dobry sklep

    0
    Reply
  127. Java Burn

    My brother suggested I might like this website. He was entirely right. This post actually made my day. You cann’t imagine just how much time I had spent for this info! Thanks!

    0
    Reply
  132. Fitspresso review

    Howdy very cool site!! Man .. Beautiful .. Amazing .. I’ll bookmark your site and take the feeds additionally…I am satisfied to seek out a lot of helpful information right here in the post, we need work out more strategies in this regard, thanks for sharing.

    0
    Reply
  135. Sumatra Slim Belly Tonic

    I have been browsing on-line greater than 3 hours these days, yet I by no means discovered any interesting article like yours. It is beautiful price enough for me. In my view, if all web owners and bloggers made excellent content as you probably did, the internet will likely be a lot more useful than ever before.

    0
    Reply
  137. Sugar defender drops review

    I’ve been browsing on-line more than 3 hours lately, yet I by no means found any interesting article like yours. It’s pretty price sufficient for me. In my opinion, if all webmasters and bloggers made just right content material as you probably did, the net can be a lot more helpful than ever before. “No nation was ever ruined by trade.” by Benjamin Franklin.

    0
    Reply
  142. pinealxt review

    Appreciating the time and energy you put into your blog and detailed information you offer. It’s awesome to come across a blog every once in a while that isn’t the same old rehashed information. Great read! I’ve bookmarked your site and I’m including your RSS feeds to my Google account.

    0
    Reply
  144. The Genius Wave

    You actually make it seem so easy with your presentation but I find this topic to be really something that I think I would never understand. It seems too complex and extremely broad for me. I am looking forward for your next post, I will try to get the hang of it!

    0
    Reply
  151. sugar defender review

    Hey would you mind sharing which blog platform you’re using? I’m planning to start my own blog soon but I’m having a difficult time selecting between BlogEngine/Wordpress/B2evolution and Drupal. The reason I ask is because your design seems different then most blogs and I’m looking for something unique. P.S Apologies for being off-topic but I had to ask!

    0
    Reply
  277. Fitspresso

    Hello! I just would like to give a huge thumbs up for the great info you have here on this post. I will be coming back to your blog for more soon.

    0
    Reply
  281. Lottery Defeater

    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
    Reply

  327. Pingback: A Glimpse Inside The Secrets Of Sleeper Sofa With Storage - worldhealthstock

  356. Lottery defeater reviews

    We are a group of volunteers and opening a new scheme in our community. Your website provided us with valuable info to work on. You have done a formidable job and our whole community will be thankful to you.

    0
    Reply
  380. Javaburn reviews

    Very interesting details you have noted, thankyou for putting up. “I don’t know what you could say about a day in which you have seen four beautiful sunsets.” by John Glenn.

    0
    Reply
  381. Javaburn review

    Hi, Neat post. There’s an issue along with your website in web explorer, would check this?K IE still is the marketplace leader and a huge component to other folks will leave out your excellent writing due to this problem.

    0
    Reply
  394. Java Burn

    Terrific work! This is the type of info that should be shared around the internet. Shame on the search engines for not positioning this post higher! Come on over and visit my site . Thanks =)

    0
    Reply
  405. easy install air conditioner

    When I originally commented I clicked the -Notify me when new surveys are added- checkbox and from now on whenever a comment is added I am four emails sticking with the same comment. Perhaps there is any way you can get rid of me from that service? Thanks!

    0
    Reply
  408. air conditioning unit installation

    I admit, I have not been on this webpage in a long time… however it was one more joy to see It is such an significant topic and also ignored by so many, even professionals. I thank you to support making people more aware of possible issues.

    0
    Reply
  409. qualified gas engineer

    I am often to blogging and that i really appreciate your content regularly. The article has truly peaks my interest. I’m going to bookmark your website and maintain checking for brand spanking new data.

    0
    Reply
  411. Fitspresso

    I know this if off topic but I’m looking into starting my own weblog and was wondering what all is required to get set up? I’m assuming having a blog like yours would cost a pretty penny? I’m not very internet savvy so I’m not 100 sure. Any suggestions or advice would be greatly appreciated. Thank you

    0
    Reply
  415. gas safe central heating

    Thank you, I have recently been searching for info about this topic for a while and yours is the best I’ve discovered till now. However, what in regards to the bottom line? Are you certain about the supply?

    0
    Reply
  416. register boiler on gas safe

    One other important aspect is that if you are an elderly person, travel insurance regarding pensioners is something you ought to really take into consideration. The old you are, greater at risk you are for making something terrible happen to you while overseas. If you are not covered by quite a few comprehensive insurance coverage, you could have some serious problems. Thanks for sharing your guidelines on this blog site.

    0
    Reply
  430. hvac heat exchanger replacement

    I just want to tell you that I’m very new to weblog and honestly liked this web site. More than likely I’m planning to bookmark your blog post . You certainly come with exceptional articles and reviews. Bless you for sharing your web site.

    0
    Reply
  432. air duct cleaning

    Attractive section of content. I just stumbled upon your blog and in accession capital to assert that I get in fact enjoyed account your weblog posts. Anyway I will be subscribing to your augment and even I achievement you access consistently rapidly.

    0
    Reply
  435. 24 hour air conditioning service near me

    You are not the average website article writer, gentleman. You certainly have got some thing powerful to increase the net. Your own style is really robust that you could almost pull off being a negative article writer, yet you’re even amazing at articulating what you have to point out. Keep in the great work gentleman!

    0
    Reply
  437. Residential AC unit installation

    I don’t really get how there is much different between the New York Times publishing this or some online site. Content such as this needs to be pushed out more frequently. I would hope that citizens in America would take a stand like this.

    0
    Reply
  444. escape rooms review

    Hey there! Do you know if they make any plugins to assist with Search Engine Optimization? I’m trying
    to get my website to rank for some targeted keywords but I’m not seeing very good results.
    If you know of any please share. Appreciate it! You can read similar article here: Escape rooms

    0
    Reply