AVL-Tree | AVL Tree Implementation in C | Dataset library
kandi X-RAY | AVL-Tree Summary
kandi X-RAY | AVL-Tree Summary
AVL Tree is a self-balancing binary search tree which guarantees O(logN) time complexity for insertion, deletion, and look-up operations. This version is implemented in C++ language, and allows multiple elements with same values. It means the tree can be used as multiset. The tree can store any type of data which has greater than (>) operator. Build-in types such as int, long long, and std::string are well-tested, however user-defined structures, even has > operator, may cause some exceptions. For competitive programmers, onefile.cpp contains all functions in one. As we know that std::multiset in standard template library (STL) is based on Red Black Trees (RB Trees) and both RB Trees and AVL Trees support insertion, deletion and look-up in guaranteed O(logN) time. However, AVL Trees are more rigidly balanced, it means that AVL Trees need more rotations in insertion and deletion, but provide faster look-up. So you are strongly recommended to use AVL Trees for look-up intensive tasks, otherwise RB Trees (also std::multiset) are more convenient. In look-up and deletion operations, containers have 100.000 elements.
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Trending Discussions on AVL-Tree
QUESTION
AVL tree is a binary search tree that is balanced i.e height = O(log(n)). This is achieved by making sure every node follows the AVL tree property:
Height of the left subtree(LST) - Height of the right subtree(RST) is in the range [-1, 0, 1]
where Height(LST) - Height(RST) is called Balance factor(BF) for a given node.
The height of the node is usually defined as, "length of the path(#edges) from that node to the deepest node" eg:
By this definition, height of leaf is 0. But almost everytime while discussing AVL trees, people consider height of the leaf to be 1.
My question is, can we take the height of leaf to be 0? This will make following BSTs also AVL trees, right?
Height concept confuses me because of these articles:
- https://www.geeksforgeeks.org/minimum-number-of-nodes-in-an-avl-tree-with-given-height/
- https://www.tutorialspoint.com/minimum-number-of-nodes-in-an-avl-tree-with-given-height-using-cplusplus
Firstly, they start the height with 0. Then they say, minimum number of nodes required for avl tree of height 2 to be 4 BUT if height is starting with zero, I can have the following AVL trees too, right?
...ANSWER
Answered 2022-Jan-14 at 10:58By this definition, height of leaf is 0.
This is correct.
BUT if height is starting with zero, I can have the following AVL trees too, right?
No, the parent of the leaf has height 1, as the path from that node to the leaf has 1 edge.
So it should be:
QUESTION
I got the bug when adding 13 to the tree, the left and right pointer of node 10 have reference back to the root, and create cycle reference.
I think it's because I understand Javascript syntax wrong.
code (open the console)
...ANSWER
Answered 2021-Oct-01 at 18:07The problem is that you don't use the returned node reference from the recursive call of insert. insert may return a different node than the one it got as argument. By not assigning it back to node.left or node.right, the latter will keep a reference to the non-cloned node, giving you an inconsistent tree.
So change this:
QUESTION
I'm trying to do a search function for an AVL-tree, when i try to search for a number that is in the tree the code works fine, but i'm getting the error
AttributeError: 'NoneType' object has no attribute 'search'
when a try to search for a number that isn't in the tree
This is the search function
...ANSWER
Answered 2021-Apr-13 at 20:54 def search(self, data):
if self is None:
return "the key doesn't exist"
elif data < self.data:
return self.left.busca(data)
elif data > self.data:
return self.right.busca(data)
else:
return "the key exist"
QUESTION
Below is a code snippet out of an AVL-tree implementation. It worked fine back in the days, but now it doesn't work any longer. The cause seems to be casting Object to Integer.
So the Avl structure handles Object as data, and the user (in this case main() ) does the casting. What I wanted to achieve was a generic AVL-tree with comparable objects. Actually I insert Objects alongside with a key to be able to distinguish what to sort for. They are internally put in a local class called KeyData.
Here is the code:
...ANSWER
Answered 2021-Mar-06 at 04:55...so what's the story?
The short version is that your find method doesn't return an Integer value. So you can't cast it to an Integer.
It worked fine back in the days, but now it doesn't work any longer.
Well, you must have changed something significant in your code between then and now. (Hint: the Java language or its implementations have not changed in ways that would cause this!)
So lets take a look at your find method.
QUESTION
Structures like AVL-Tree and RB-Tree should be fast enough for most uses. But is there any room for optimization if there is no need for deletion?
To be specific, I wonder if there is a container type optimized for the scenario described below:
- It's set-like, i.e. it stores unique values.
- It's based on comparison, e.g.
<operator, rather than hash. - It support insertion and lookup, i.e. checking whether it contains a value or not.
- There is no need for deletion, i.e. values will never be remove from it.
ANSWER
Answered 2020-Sep-15 at 14:49In theory, no, since the Ω(log n) bound on comparisons still applies to comparison-based sets without deletion.
In practice, I'm not aware of any comparison-based structures that yield an empirical improvement, other than that deletion is often more complicated than insertion, and you don't have to code it. (Bloom filters are an example of a hash-based data structure where not having deletion yields a performance improvement.)
QUESTION
In this post, it says the LL Rotation is a single left Rotation.
https://www.freecodecamp.org/news/avl-tree-insertion-rotation-and-balance-factor/
However, from the wiki of tree rotation, https://en.wikipedia.org/wiki/Tree_rotation, I think that is a single right Rotation?
What is more, I also see,
https://www.codingeek.com/data-structure/avl-tree-introduction-to-rotations-and-its-implementation/. This says it is a RR Rotation and it is a single right Rotation?
I am confused for the different opinions. Can anyone tell me the truth for the above picture?
- Is it a LL Rotation?
- Is it a single left rotation or a single right rotation?
ANSWER
Answered 2020-Aug-21 at 14:27First of all, all the referenced websites agree that the depicted example represents a single right rotation.
You write:
As this for example, LL tree rotation
In this post, it says the LL Rotation is a single left Rotation https://www.freecodecamp.org/news/avl-tree-insertion-rotation-and-balance-factor/
Indeed, although there is no ambiguity for what the terms "left rotation" and "right rotation" mean, there seem to be two contradictory interpretations floating around for what "LL rotation" and "RR rotation" stand for.
However, from the wiki of tree rotation, https://en.wikipedia.org/wiki/Tree_rotation, I think that is a single right Rotation?
Well the Wikipedia article does not use the term "LL rotation". But it does also agree that the depicted example represents a right rotation. There is so far no ambiguity for the terms "left rotation" and "right rotation".
Can anyone tell me the truth for the above picture?
Like all those sites explain: it is a single right rotation.
LL, RRThe ambiguity arises in the use of the terms "LL rotation" and "RR rotation":
The acronyms "LL" and "RR" make more sense in describing the imbalance before any rotation is performed. The Wikipedia article categorises imbalanced trees in 4 categories (4 columns):
In each column you see the original state at the top, and then below it the result of the rotation(s) that should be performed to bring the tree in balance.
So for a tree in the Left Left case, we need a right rotation. And for a tree in the Right Right case we need a left rotation.
The following notes of an ICS course at University of California, Irvine, explain where the letters LL, RR, LR, RL come from:
The rotation is chosen considering the two links along the path below the node where the imbalance is, heading back down toward where you inserted a node. (If you were wondering where the names LL, RR, LR, and RL come from, this is the answer to that mystery.)
- If the two links are both to the left, perform an LL rotation rooted where the imbalance is.
- If the two links are both to the right, perform an RR rotation rooted where the imbalance is.
- If the first link is to the left and the second is to the right, perform an LR rotation rooted where the imbalance is.
- If the first link is to the right and the second is to the left, perform an RL rotation rooted where the imbalance is.
But I feel speaking of LL rotation can trigger confusion, as here we see that the double LL describes the imbalance of the original state, and does not describe the action. It would have been cleaner to speak of an LL state (or imbalance) and then name the resolving action a "right rotation". With that in mind, I think the Wikipedia article takes a good position, as it avoids the term "LL rotation".
This misunderstanding does not arise with LR and RL rotations. You can say that the initial state is LR (the imbalance was caused by giving a left leaf a right child), and you can also say that first a left rotation is needed, and then a right rotation. In both cases the abbreviation LR makes sense. So no ambiguity there.
ConclusionThe terms left rotation and right rotation are clear.
There are different traditions for which of these rotations to call an LL or RR rotation. In my opinion we should avoid talking about "LL rotation" or "RR rotation", as these letters do not describe the act of the rotation, but the initial state. It is better to speak of the "LL case" or "LL imbalance".
With those terms we can say:
- A tree with an LL imbalance needs a right rotation
- A tree with a RR imbalance needs a left rotation
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