What is the time complexity of binary search trees?

Can you explain the time complexity of binary search trees?

Sure! The time complexity of binary search trees (BST) depends on the tree's height. In a balanced BST, the average time complexity for search, insert, and delete operations is O(log n). However, in the worst case, it can degrade to O(n) if the tree becomes unbalanced.

What makes a binary search tree balanced?

A balanced binary search tree maintains its height to be logarithmic relative to the number of nodes. This can be achieved through various self-balancing techniques, such as AVL trees or Red-Black trees, which ensure that the tree remains balanced after insertions and deletions.

How do AVL trees maintain balance?

AVL trees maintain balance by ensuring that the heights of the two child subtrees of any node differ by no more than one. When an insertion or deletion causes this property to be violated, rotations are performed to restore balance.

Can you give an example of a rotation?

Certainly! A right rotation is performed when a left-heavy subtree needs balancing. For example, if a node's left child has a left child, a right rotation on the node will make the left child the new root of that subtree, promoting it and demoting the original root.