Heap Concept Structure and Properties in DSA Javascript - Execution Trace

Concept Flow - Heap Concept Structure and Properties

Start with empty heap

↓

Insert element at end of array

↓

Compare element with parent

↓

Swap with parent

↓

Repeat compare with new parent

↓

Stop when root reached or no swap needed

This flow shows how a heap maintains its structure by inserting elements at the end and bubbling them up by swapping with parents if needed.

Execution Sample

DSA Javascript

const heap = [];
heap.push(10);
heap.push(15);
heap.push(30);
heap.push(40);
heap.push(50);
heap.push(100);
heap.push(40);
heap.push(8);

This code inserts elements into a min-heap array and bubbles up the last inserted element to maintain heap property.

Execution Table

Step	Operation	Array State	Pointer Changes	Visual State
1	Insert 10	[10]	head=0	10
2	Insert 15	[10, 15]	head=0, new=1	10 \ 15
3	Insert 30	[10, 15, 30]	head=0, new=2	10 / \ 15 30
4	Insert 40	[10, 15, 30, 40]	new=3	10 / \ 15 30 / 40
5	Insert 50	[10, 15, 30, 40, 50]	new=4	10 / \ 15 30 / \ 40 50
6	Insert 100	[10, 15, 30, 40, 50, 100]	new=5	10 / \ 15 30 / \ / 40 50 100
7	Insert 40	[10, 15, 30, 40, 50, 100, 40]	new=6	10 / \ 15 30 / \ / \ 40 50 100 40
8	Insert 8	[10, 15, 30, 40, 50, 100, 40, 8]	new=7	10 / \ 15 30 / \ / \ 40 50 100 40 / 8
9	Bubble up 8 < 40? Swap	[10, 15, 30, 8, 50, 100, 40, 40]	swap indices 3 and 7	10 / \ 15 30 / \ / \ 8 50 100 40 / 40
10	Bubble up 8 < 15? Swap	[10, 8, 30, 15, 50, 100, 40, 40]	swap indices 1 and 3	10 / \ 8 30 / \ / \ 15 50 100 40 / 40
11	Bubble up 8 < 10? Swap	[8, 10, 30, 15, 50, 100, 40, 40]	swap indices 0 and 1	8 / \ 10 30 / \ / \ 15 50 100 40 / 40
12	Stop bubbling (root reached)	[8, 10, 30, 15, 50, 100, 40, 40]	no swap	8 / \ 10 30 / \ / \ 15 50 100 40 / 40

💡 Stop bubbling when inserted element reaches root or no parent is larger.

Variable Tracker

Variable	Start	After 1	After 2	After 3	After 4	After 5	After 6	After 7	After 8	After 9	After 10	After 11	Final
heap array	[]	[10]	[10,15]	[10,15,30]	[10,15,30,40]	[10,15,30,40,50]	[10,15,30,40,50,100]	[10,15,30,40,50,100,40]	[10,15,30,40,50,100,40,8]	[10,15,30,8,50,100,40,40]	[10,8,30,15,50,100,40,40]	[8,10,30,15,50,100,40,40]	[8,10,30,15,50,100,40,40]
new element index	N/A	0	1	2	3	4	5	6	7	7->3	3->1	1->0	0
bubble up active	No	No	No	No	No	No	No	No	Yes	Yes	Yes	No	No

Key Moments - 3 Insights

Why do we insert the new element at the end of the array?

In the execution_table rows 1 to 8, the new element is always added at the end to maintain the complete binary tree structure before bubbling up.

Why do we compare the new element with its parent and swap?

As shown in rows 9 to 11, swapping with the parent ensures the heap property (parent smaller than children) is maintained by moving the smaller element up.

When does the bubbling up stop?

Row 12 shows bubbling stops when the element reaches the root or no parent is larger, so no more swaps are needed.

Visual Quiz - 3 Questions

Look at the execution_table at step 9, what is the array state after swapping?

A [8, 15, 30, 40, 50, 100, 40, 10]

B [10, 15, 30, 40, 50, 100, 40, 8]

C [10, 15, 30, 8, 50, 100, 40, 40]

D [10, 8, 30, 15, 50, 100, 40, 40]

💡 Hint

Check execution_table row 9 under 'Array State' column.

At which step does the new element reach the root of the heap?

A Step 10

B Step 11

C Step 9

D Step 12

💡 Hint

Look at variable_tracker for 'new element index' and see when it becomes 0.

If the inserted element was larger than its parent, what would happen in the bubbling steps?

A It would stop bubbling immediately.

B It would swap with the parent anyway.

C It would bubble down instead.

D It would be removed from the heap.

💡 Hint

Refer to concept_flow where bubbling stops if no swap needed.

Concept Snapshot

Heap is a complete binary tree stored as an array.
Insert new element at array end.
Bubble up by swapping with parent if smaller.
Stop when root reached or no swap needed.
Maintains min-heap property: parent ≤ children.

Full Transcript

A heap is a special tree structure stored as an array. When we add a new element, we put it at the end of the array to keep the tree complete. Then we compare it with its parent. If the new element is smaller, we swap them. We keep swapping up until the new element is no longer smaller than its parent or it reaches the root. This process keeps the heap property intact, where every parent is smaller or equal to its children. The execution table shows each insertion and bubbling step with the array and tree shape. The variable tracker follows the new element's position and the heap array after each step. Key moments explain why we insert at the end, why we swap, and when bubbling stops. The quiz tests understanding of array states and bubbling behavior. This visual trace helps beginners see how heaps keep order while staying complete trees.