What are the properties of binary search trees?

What are the properties of binary search trees?

Binary search trees (BSTs) have several key properties: 1. Each node has at most two children. 2. The left child contains only nodes with values less than the parent node. 3. The right child contains only nodes with values greater than the parent node. 4. Both the left and right subtrees must also be binary search trees.

Can you explain how these properties affect search efficiency?

Certainly! The properties of BSTs allow for efficient searching. On average, searching for a value takes O(log n) time, where n is the number of nodes. This is because each comparison allows you to eliminate half of the remaining nodes.

What happens if a BST becomes unbalanced?

If a BST becomes unbalanced, its efficiency can degrade to O(n) in the worst case, resembling a linked list. This happens when nodes are added in a sorted order, leading to a skewed tree.

How can we maintain balance in a binary search tree?

To maintain balance, you can use self-balancing trees like AVL trees or Red-Black trees. These trees automatically adjust their structure during insertions and deletions to keep the height balanced.