When is an avl tree unbalanced

The search operation in the AVL tree is similar to the search operation in a Binary search tree. We use the following steps to search an element in AVL tree In an AVL tree, the insertion operation is performed with O log n time complexity. In AVL Tree, a new node is always inserted as a leaf node. The insertion operation is performed as follows But after every deletion operation, we need to check with the Balance Factor condition.

If the tree is balanced after deletion go for next operation otherwise perform suitable rotation to make the tree Balanced. The perfect place for easy learning Place your ad here. Previous Next. Step 1 - Read the search element from the user. Step 2 - Compare the search element with the value of root node in the tree.

The recursive code itself travels up and visits all the ancestors of the newly inserted node. Update the height of the current node. To check whether it is left left case or not, compare the newly inserted key with the key in left subtree root. To check whether it is Right Right case or not, compare the newly inserted key with the key in right subtree root. Write node. Updating the height and getting the balance factor also takes constant time.

The AVL trees are more balanced compared to Red-Black Trees, but they may cause more rotations during insertion and deletion. So if your application involves many frequent insertions and deletions, then Red Black trees should be preferred. And if the insertions and deletions are less frequent and search is the more frequent operation, then AVL tree should be preferred over Red Black Tree. Following is the post for delete. Skip to content. Change Language. Related Articles.

Table of Contents. Save Article. Improve Article. Right Rotation. A single rotation applied when a node is inserted in the left subtree of a left subtree.

In the given example, node C now has a balance factor of 2 after the insertion of node A. By rotating the tree right, node B becomes the root resulting in a balanced tree. Left Rotation. A single rotation applied when a node is inserted in the right subtree of a right subtree. If balance factor of any node is -1, it means that the left sub-tree is one level lower than the right sub-tree.

An AVL tree is given in the following figure. Due to the fact that, AVL tree is also a binary search tree therefore, all the operations are performed in the same way as they are performed in a binary search tree. Searching and traversing do not lead to the violation in property of AVL tree. However, insertion and deletion are the operations which can violate this property and therefore, they need to be revisited.

AVL tree controls the height of the binary search tree by not letting it to be skewed. The time taken for all operations in a binary search tree of height h is O h. However, it can be extended to O n if the BST becomes skewed i. By limiting this height to log n, AVL tree imposes an upper bound on each operation to be O log n where n is the number of nodes.

There are basically four types of rotations which are as follows:. For a tree to be unbalanced, minimum height must be at least 2, Let us understand each rotation. When BST becomes unbalanced, due to a node is inserted into the right subtree of the right subtree of A, then we perform RR rotation, RR rotation is an anticlockwise rotation, which is applied on the edge below a node having balance factor In above example, node A has balance factor -2 because a node C is inserted in the right subtree of A right subtree.

We perform the RR rotation on the edge below A. When BST becomes unbalanced, due to a node is inserted into the left subtree of the left subtree of C, then we perform LL rotation, LL rotation is clockwise rotation, which is applied on the edge below a node having balance factor 2.

In above example, node C has balance factor 2 because a node A is inserted in the left subtree of C left subtree. We perform the LL rotation on the edge below A. Double rotations are bit tougher than single rotation which has already explained above. As already discussed, that double rotations are bit tougher than single rotation which has already explained above.