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Intermediate 20 min readModule: Module 7: Binary Trees & Binary Search Trees (BST)

Binary Search Trees (BST) & Tree Traversals

Perform O(log n) searches, insertions, and in-order traversals on Binary Search Trees.

What You Will Learn in This Lesson

  • The BST invariant: Left child < Root < Right child
  • Tree traversals: In-Order (sorted), Pre-Order, and Post-Order
  • Binary search tree insertion and lookup in O(h) time

Introduction & Core Concept

A Binary Search Tree (BST) is a rooted binary tree data structure whose internal nodes each store a key greater than all the keys in the node's left subtree and less than those in its right subtree.
WHY DOES THIS MATTER IN THE REAL WORLD?

In-Order traversal on a BST produces elements in strictly ascending sorted order automatically in O(n) time!

BST Node & In-Order Traversal

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javascript
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class TreeNode {
  constructor(val, left = null, right = null) {
    this.val = val; this.left = left; this.right = right;
  }
}
 
function inOrder(root, result = []) {
  if (!root) return result;
  inOrder(root.left, result);
  result.push(root.val);
  inOrder(root.right, result);
  return result;
}
 
const tree = new TreeNode(20, new TreeNode(10), new TreeNode(30));
console.log("Sorted Traversal:", inOrder(tree));

Line-by-Line Technical Breakdown

1Unbalanced BSTs can degenerate into O(n) linked lists; self-balancing trees (AVL, Red-Black) maintain O(log n) height.

Try It Yourself (Interactive Editor)

Modify the code in real-time and click Run to test live browser output and console logs.

Intelligent Code Runner & Live Sandbox[JAVASCRIPT]
JAVASCRIPT SOURCE EDITOR
Interactive Live Code

Industry Best Practices & Professional Standards

  • Use tree structures for hierarchical data like DOM trees and file systems.

Lesson Summary & Core Takeaways

  • BSTs combine the rapid search of sorted arrays with the dynamic insertion of linked lists.