Binary Search Trees
Introduction
- Binary search trees (BST) are an extension of binary trees.
- A binary tree is a tree data structure where each node has up to two children.
- BST adds properties that allow for efficient data access.
Properties of Binary Search Trees
- Nodes are organized such that:
- All nodes in the left subtree of a node have lesser values than the node itself.
- All nodes in the right subtree have greater values.
- This ordering makes it possible to search, insert, and delete items efficiently.
Data Types
- Can be used with any data type that can be ordered (e.g., ints, floats, strings).
- Allows for comparison operations to maintain order.
Advantages
- Faster search operations compared to unsorted lists.
- Search operations have a time complexity of O(log n) in balanced trees.
Implementation
- Start with a simple binary tree structure.
Insertion in BST
- Insertion is done recursively:
- If the tree is empty (root is null), insert the new node.
- If the value is already present, do not insert again.
- Recursively find the correct spot in the left or right subtree based on the value.
- Use double pointers to adjust root pointers.
Search in BST
- Search operation is also recursive:
- Check if the root is null (tree is empty).
- If the value is equal to the root, it's found.
- Otherwise, recursively search the left or right subtree based on the value.
Edge Cases
- A degenerate or skewed BST can degrade to O(n) search complexity, resembling a linked list.
- Balanced trees (e.g., using AVL or Red-Black trees) maintain O(log n) efficiency.
Coding Example
- Code snippets provided for constructing, inserting, and searching in BSTs.
- Example illustrated with integer data.
Conclusion
- BSTs are effective for fast searching and data management.
- Consider balance of the tree for optimal performance.
- Alternative balanced BSTs can automatically maintain balance.
Further Topics
- AVL Trees and Red-Black Trees (self-balancing)
- Binary search on sorted arrays as a comparison
Note: Detailed code examples and source code are available through the video creator's Patreon.