How to Use
- Insert: Enter a value and click "Insert"
- Delete: Enter a value and click "Delete"
- Search: Enter a value and click "Search"
- Random Tree: Click to generate a random tree
- Reset: Click to clear the tree
Binary Tree Concept
Binary Tree is a hierarchical data structure where each node has at most two children: left child and right child.
Key Properties:
- Each node has at most 2 children
- Left and right subtrees are also binary trees
- No ordering constraint (unlike BST)
- Flexible insertion and structure
Binary Tree is the foundation for many specialized tree structures like BST, AVL, and Red-Black trees.
Tree Traversals:
- Pre-order: Root → Left → Right
- In-order: Left → Root → Right
- Post-order: Left → Right → Root
Binary Tree Setup
Binary Tree Operations
Tree Visualization
(Binary Tree allows flexible node placement)
Operation Steps
Purpose & Applications
- Expression trees
- Decision trees
- Huffman coding
- File system hierarchies
- Syntax trees in compilers
Time & Space Complexity
| Operation | Average Case | Worst Case |
|---|---|---|
| Insert | O(log n) | O(n) |
| Delete | O(log n) | O(n) |
| Search | O(log n) | O(n) |
| Space | O(n) | O(n) |
Strengths & Limitations
Strengths:
- Flexible structure
- Foundation for specialized trees
- Efficient traversals
Limitations:
- No ordering guarantee
- Can become unbalanced