BST Property and Why It Matters in DSA Javascript - Execution Trace

Concept Flow - BST Property and Why It Matters

Start at root node

↓

Compare value to node

↓

Go left

↓

Repeat until

↓

Null child found

↓

Insert new node here

The BST property guides where to place or find values by comparing and moving left for smaller or right for larger values until the correct spot is found.

Execution Sample

DSA Javascript

class Node {
  constructor(val) {
    this.val = val;
    this.left = null;
    this.right = null;
  }
}

Defines a simple node structure for a BST with value and left/right pointers.

Execution Table

Step	Operation	Current Node Value	Compare With	Pointer Changes	Visual State
1	Start at root	10	Insert 5	None	10
2	Compare 5 < 10	10	5 < 10 is True	Move left pointer	10 / ?
3	Left child is null	null	Insert 5 here	root.left = Node(5)	10 / 5
4	Start at root	10	Insert 15	None	10 / 5
5	Compare 15 > 10	10	15 > 10 is True	Move right pointer	10 / 5 ?
6	Right child is null	null	Insert 15 here	root.right = Node(15)	10 / \ 5 15
7	Start at root	10	Insert 12	None	10 / \ 5 15
8	Compare 12 > 10	10	12 > 10 is True	Move right pointer	10 / \ 5 15 ?
9	Compare 12 < 15	15	12 < 15 is True	Move left pointer	10 / \ 5 15 / ?
10	Left child is null	null	Insert 12 here	15.left = Node(12)	10 / \ 5 15 / 12
11	End	N/A	All inserted	No changes	10 / \ 5 15 / 12

💡 Insertion stops when a null child pointer is found where the new node is attached.

Variable Tracker

Variable	Start	After Step 3	After Step 6	After Step 10	Final
root	Node(10)	Node(10) with left=Node(5)	Node(10) with left=Node(5), right=Node(15)	Node(10) with left=Node(5), right=Node(15 with left=Node(12))	Same as After Step 10
current	Node(10)	null (inserted 5)	null (inserted 15)	null (inserted 12)	null
left child of 10	null	Node(5)	Node(5)	Node(5)	Node(5)
right child of 10	null	null	Node(15)	Node(15)	Node(15)
left child of 15	null	null	null	Node(12)	Node(12)

Key Moments - 3 Insights

Why do we move left when the new value is smaller than the current node?

Because the BST property says smaller values go to the left subtree, as shown in steps 2 and 3 where 5 < 10 leads us left.

What happens if the child pointer is not null when inserting?

We continue moving down the tree following the BST property until we find a null child pointer to insert, as in steps 8 and 9 for inserting 12.

Why is the insertion stopped when we find a null child pointer?

Because that is the correct empty spot to place the new node, ensuring the BST property remains true, as seen in steps 3, 6, and 10.

Visual Quiz - 3 Questions

Look at the execution table, what is the visual state after step 6?

A 10 with left child 5 and right child 15

B 10 with right child 15 only

C 10 with left child 5 only

D 10 with left child 12 and right child 15

💡 Hint

Check the Visual State column at step 6 showing both children attached to 10.

At which step does the insertion of the node with value 12 happen?

A Step 8

B Step 9

C Step 10

D Step 11

💡 Hint

Look for the step where the left child of 15 changes from null to Node(12).

If we tried to insert 20 instead of 12, which direction would we move after step 7?

A Right of 10

B Right of 15

C Left of 15

D Left of 10

💡 Hint

Compare 20 with 10 and 15 following the BST property in the execution table steps.

Concept Snapshot

BST Property:
- Left subtree nodes < parent node
- Right subtree nodes > parent node
- Used to find/insert efficiently
- Insert by comparing and moving left/right
- Stop at null child to insert new node

Full Transcript

The Binary Search Tree (BST) property means every node's left child has a smaller value and right child has a larger value. When inserting a new value, start at the root and compare. If smaller, go left; if larger, go right. Repeat until you find a null child pointer, then insert the new node there. This keeps the tree ordered and allows fast searching and insertion. The execution table shows inserting 5, 15, and 12 into a BST with root 10, moving left or right based on comparisons, and placing nodes at the correct null child pointers.