What are BST rotations and why are they important?

What are BST rotations and why are they important?

BST rotations are operations that change the structure of a binary search tree (BST) to maintain its balanced state. They are crucial for ensuring efficient search, insert, and delete operations.

Can you explain the different types of rotations?

Sure! There are two main types of rotations: left rotation and right rotation. Left rotation is used when a right-heavy subtree needs balancing, while right rotation is used for left-heavy subtrees.

How do these rotations affect the tree's height?

Rotations help maintain the height of the tree, ensuring it remains logarithmic in size. This keeps operations efficient, ideally around O(log n) time complexity.

Can you give an example of a left rotation?

Absolutely! In a left rotation, the right child of a node becomes the new root of that subtree, and the original root becomes the left child of the new root.

What happens if I don't perform rotations?

If rotations are not performed, the BST can become unbalanced, leading to degraded performance for search, insert, and delete operations, potentially reaching O(n) time complexity.