Binary Search Tree (BST)
Master the properties and operations of Binary Search Trees: the efficient way to store and retrieve ordered data.
Master the properties and operations of Binary Search Trees: the efficient way to store and retrieve ordered data. This hands-on tutorial focuses on practical implementation of binary search tree (bst) concepts.
Binary Search Tree (BST)
A Binary Search Tree is a binary tree with a special ordering property:
- The left subtree contains only nodes with values less than the root.
- The right subtree contains only nodes with values greater than the root.
- Both subtrees must also be binary search trees.
1. Structure of a BST
2. Core Operations
A. Search
To find a value, we compare it with the root and move left or right. This takes O(log n) in a balanced tree.
B. Insertion
Similar to search, find the correct null spot and attach the new node.
C. Deletion
Three cases:
- No children: Just remove.
- One child: Replace with its child.
- Two children: Replace with the Inorder Successor (smallest in the right subtree).
3. Implementation in Python
Comparison: Array vs BST
| Operation | Unsorted Array | Balanced BST |
|---|---|---|
| Search | O(n) | O(log n) |
| Insert | O(1) | O(log n) |
| Delete | O(n) | O(log n) |
[!WARNING] In the worst case (skewed tree), a BST can behave like a linked list with O(n) complexity. This is why self-balancing trees (AVL, Red-Black) are used in production.
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Quiz
Quiz
Question 1 of 2In a BST, where would you find the value larger than the root?