đŗ Tree Algorithms
Master tree traversals, binary search trees, and advanced tree operations. Trees are fundamental in databases, compilers, and AI.
Overview
What are Tree Algorithms?
Key Tree Algorithms
Inorder Traversal
Left â Root â Right. Produces sorted order for BSTs.
Preorder Traversal
Root â Left â Right. Used for copying trees.
Postorder Traversal
Left â Right â Root. Used for deleting trees.
Level Order Traversal
BFS on tree, visit nodes level by level.
BST Search
Efficient search in a binary search tree.
Lowest Common Ancestor
Find LCA of two nodes in a binary tree.
Interactive Visualizer
Tree Visualization
Inorder Traversal Tree Visualizer
Watch nodes being traversed with highlights showing the current node and direction.
Deep Dive: Inorder Traversal
Time Complexity
Time: O(n)Space Complexity
Space: O(h)Method
Recursive/IterativeAlgorithm Approach
python
def inorder(node):
if not node: return
inorder(node.left)
print(node.val)
inorder(node.right)Choose Traversal
Select order based on what you need: inorder for sorted, preorder for copy, postorder for deletion.
Handle Base Case
If node is null, return (do nothing). This is the foundation of recursive traversal.
Recursive Calls
Make recursive calls in the correct order with left and right children.
Process Node
Print, collect, or transform node value at the appropriate point in the recursion.
Real-World Applications
File Systems
Hierarchical directory/folder structures are trees
HTML DOM
Browser represents HTML as a tree (Document Object Model)
Databases
B-Trees and B+ Trees index database records efficiently
Compilers
Abstract Syntax Trees (ASTs) represent program structure
Network Routing
Spanning trees prevent loops in network broadcasts
AI Decision Trees
Decision trees and random forests for classification
Interview Questions
What's the difference between a binary tree and BST?
Binary tree: each node has at most 2 children, no ordering. BST: for each node, left subtree has smaller values, right subtree has larger values. BST enables O(h) search.
How do you check if a binary tree is balanced?
Check that height difference between left and right subtrees ⤠1 for every node. Can be done with a recursive function that returns height and checks balance simultaneously (postorder).
What is tree serialization?
Serialization converts a tree to a string (e.g., for network transmission). Preorder traversal with null markers works well. Deserialization reconstructs the tree from the string.
Knowledge Check
1. Which traversal produces sorted order in BST?
2. Height of a balanced BST with n nodes is:
3. Which traversal is used to delete a tree?
4. What traversal mimics BFS?
5. What is the space complexity of level order traversal?