Heap Concept Structure and Properties in DSA Typescript - Execution Trace

Concept Flow - Heap Concept Structure and Properties

Start with empty heap

↓

Insert element at end of array

↓

Compare element with parent

Yes / No↓

Swap with parent

↓

Repeat compare with new parent

↓

Heap property maintained

↓

Heap ready for next operation

This flow shows how elements are added to a heap and moved up to maintain the heap property.

Execution Sample

DSA Typescript

Insert 10
Insert 15
Insert 30
Insert 40
Insert 50
Insert 100

Inserting elements one by one into a min-heap and adjusting to maintain heap property.

Execution Table

Step	Operation	Nodes in Heap (Array)	Pointer Changes	Visual State (Tree)
1	Insert 10	[10]	head=0	10
2	Insert 15	[10, 15]	Compare 15 with parent 10: 15 > 10, no swap	10 / 15
3	Insert 30	[10, 15, 30]	Compare 30 with parent 10: 30 > 10, no swap	10 / \ 15 30
4	Insert 40	[10, 15, 30, 40]	Compare 40 with parent 15: 40 > 15, no swap	10 / \ 15 30 / 40
5	Insert 50	[10, 15, 30, 40, 50]	Compare 50 with parent 15: 50 > 15, no swap	10 / \ 15 30 / \ 40 50
6	Insert 100	[10, 15, 30, 40, 50, 100]	Compare 100 with parent 30: 100 > 30, no swap	10 / \ 15 30 / \ / 40 50 100
7	End	[10, 15, 30, 40, 50, 100]	Heap property maintained, no more swaps	Final heap as above

💡 All elements inserted and heap property maintained after each insertion.

Variable Tracker

Variable	Start	After 1	After 2	After 3	After 4	After 5	After 6	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]
Last Inserted Index	N/A	0	1	2	3	4	5	5
Parent Index	N/A	N/A	0	0	1	1	2	N/A
Swaps Made	0	0	0	0	0	0	0	0

Key Moments - 3 Insights

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

Because the heap is a complete binary tree, new elements are always added at the next available leaf position, which corresponds to the end of the array (see execution_table steps 1 to 6).

Why do we compare the inserted element with its parent?

To maintain the heap property (min-heap here), the inserted element must be smaller than or equal to its parent. If not, we swap and continue up (execution_table shows no swaps because all inserted elements are larger).

What happens if the inserted element is larger than its parent?

No swap is needed and the heap property is maintained immediately (see steps 2 to 6 in execution_table where no swaps occur).

Visual Quiz - 3 Questions

Look at the execution_table at step 4, what is the parent index of the newly inserted element?

A 0

B 1

C 3

D 2

💡 Hint

Check the 'Parent Index' column in variable_tracker after step 4.

At which step does the heap first have 5 elements?

A Step 3

B Step 4

C Step 5

D Step 6

💡 Hint

Look at the 'Nodes in Heap (Array)' column in execution_table to count elements.

If we inserted 5 instead of 50 at step 5, what would happen?

A Swap with parent 15, then swap with 10

B No swap, 5 stays at the end

C Swap with 30 only

D Heap property breaks

💡 Hint

Recall heap property and bubbling up process from concept_flow and execution_table.

Concept Snapshot

Heap is a complete binary tree stored as an array.
Insertions add element at array end.
Compare inserted element with parent.
Swap if smaller (min-heap) to maintain heap property.
Repeat until heap property holds.
No swaps if inserted element is larger than parent.

Full Transcript

A heap is a special tree structure where every parent node is smaller than its children in a min-heap. We add new elements at the end of the array to keep the tree complete. Then we compare the new element with its parent. If the new element is smaller, we swap and continue moving up until the heap property is restored. If the new element is larger, no swaps are needed. This process keeps the heap balanced and ordered for efficient access.