What are the limitations of binary search trees?

What are the limitations of binary search trees?

Binary search trees (BSTs) have several limitations, including:

1. Unbalanced Trees: If the tree becomes unbalanced, operations can degrade to O(n) time complexity.
2. Space Complexity: They require additional space for pointers, which can be significant for large datasets.
3. Inefficient for Range Queries: BSTs are not optimal for range queries compared to other data structures like segment trees.
4. Complexity in Deletion: Deleting nodes can be complex, especially when dealing with nodes that have two children.

What happens if a BST becomes unbalanced?

If a BST becomes unbalanced, the time complexity for operations like search, insert, and delete can degrade from O(log n) to O(n). This happens because the tree may resemble a linked list, making it inefficient.

Are there any alternatives to BSTs?

Yes, there are several alternatives to binary search trees, including:

1. AVL Trees: Self-balancing BSTs that maintain O(log n) height.
2. Red-Black Trees: Another type of self-balancing BST with specific properties to ensure balance.
3. B-Trees: Used in databases and file systems, optimized for disk storage.
4. Hash Tables: Provide average O(1) time complexity for search operations, but do not maintain order.

How can I balance a BST?

You can balance a BST using various techniques, such as:

1. Rotations: Perform left or right rotations to maintain balance after insertions or deletions.
2. Rebuilding: Convert the BST to a sorted array and then build a balanced BST from that array.
3. Self-Balancing Trees: Use self-balancing trees like AVL or Red-Black trees that automatically maintain balance during operations.