An AVL tree is a self-balancing binary search tree. Here is an example algorithm for creating an AVL tree:
1. Create an empty AVL tree.
2. For each node to be inserted into the tree:
a. Insert the node into the tree using the standard binary search tree insertion algorithm.
b. Starting from the inserted node, perform the following steps until the tree is balanced:
i. If the current node is unbalanced, perform the appropriate rotation to balance it (either a left-right rotation, a right-left rotation, a left-left rotation, or a right-right rotation).
ii. Update the height of the current node, if necessary.
iii. Move to the parent node of the current node and repeat the steps from ii.
This algorithm ensures that the resulting AVL tree is balanced, with the height of any node in the tree being at most O(log n), where n is the number of nodes in the tree. This allows for efficient search and insertion operations in the tree.
An AVL tree is a self-balancing binary search tree. Here is an example algorithm for creating an AVL tree:
1. Create an empty AVL tree.
2. For each node to be inserted into the tree:
a. Insert the node into the tree using the standard binary search tree insertion algorithm.
b. Starting from the inserted node, perform the following steps until the tree is balanced:
i. If the current node is unbalanced, perform the appropriate rotation to balance it (either a left-right rotation, a right-left rotation, a left-left rotation, or a right-right rotation).
ii. Update the height of the current node, if necessary.
iii. Move to the parent node of the current node and repeat the steps from ii.
This algorithm ensures that the resulting AVL tree is balanced, with the height of any node in the tree being at most O(log n), where n is the number of nodes in the tree. This allows for efficient search and insertion operations in the tree.