Heap Insert Operation Bubble Up in DSA Go - Execution Trace

Concept Flow - Heap Insert Operation Bubble Up

Insert new element at end of array

↓

Compare new element with parent

↓

Swap with parent

↓

Move pointer to parent

↩Back to compare step

Insert new element at the end, then repeatedly swap it with its parent if smaller, moving up until heap property is restored.

Execution Sample

DSA Go

heap := []int{10, 15, 30, 40, 50, 100, 40}
heap = append(heap, 8)
// Bubble up 8 to restore min-heap

Insert 8 into min-heap and bubble it up to maintain heap order.

Execution Table

Step	Operation	Heap Array State	Pointer (Index)	Action	Visual State
1	Insert 8 at end	[10, 15, 30, 40, 50, 100, 40, 8]	7 (new element)	Start bubble up	Array: [10, 15, 30, 40, 50, 100, 40, 8]
2	Compare with parent (index 3)	[10, 15, 30, 40, 50, 100, 40, 8]	7 (8) vs 3 (40)	8 < 40 → Swap	Swap elements at 7 and 3
3	After swap	[10, 15, 30, 8, 50, 100, 40, 40]	3 (moved 8)	Move pointer to parent index 3	Array: [10, 15, 30, 8, 50, 100, 40, 40]
4	Compare with parent (index 1)	[10, 15, 30, 8, 50, 100, 40, 40]	3 (8) vs 1 (15)	8 < 15 → Swap	Swap elements at 3 and 1
5	After swap	[10, 8, 30, 15, 50, 100, 40, 40]	1 (moved 8)	Move pointer to parent index 1	Array: [10, 8, 30, 15, 50, 100, 40, 40]
6	Compare with parent (index 0)	[10, 8, 30, 15, 50, 100, 40, 40]	1 (8) vs 0 (10)	8 < 10 → Swap	Swap elements at 1 and 0
7	After swap	[8, 10, 30, 15, 50, 100, 40, 40]	0 (moved 8)	Pointer at root, stop bubble up	Array: [8, 10, 30, 15, 50, 100, 40, 40]
8	Bubble up complete	[8, 10, 30, 15, 50, 100, 40, 40]	N/A	Heap property restored	Final heap array

💡 Pointer reached root or no swap needed; heap property restored.

Variable Tracker

Variable	Start	After Step 1	After Step 2	After Step 4	After Step 6	Final
heap	[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]
pointer	N/A	7	3	1	0	N/A

Key Moments - 3 Insights

Why do we swap the new element with its parent only if it is smaller?

Because in a min-heap, parents must be smaller or equal to children. Swapping only when the child is smaller restores this property, as shown in steps 2, 4, and 6 in the execution_table.

What happens when the pointer reaches the root during bubble up?

When the pointer reaches index 0 (root), bubble up stops because the root has no parent to compare with. This is shown in step 7 where the pointer is at 0 and no further swaps occur.

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

Because the heap is a complete binary tree represented as an array, new elements are always added at the end to maintain completeness before restoring heap order by bubbling up, as shown in step 1.

Visual Quiz - 3 Questions

Look at the execution_table at step 4, what is the heap array state after the swap?

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

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

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

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

💡 Hint

Check the 'After swap' row after step 4 in the execution_table.

At which step does the pointer reach the root and bubble up stops?

A Step 7

B Step 5

C Step 6

D Step 8

💡 Hint

Look for the step where pointer is at index 0 and no further swaps occur.

If the inserted element was 35 instead of 8, how would the bubble up process change?

A No swaps would occur because 35 is not smaller than its parent 40.

B It would swap all the way to root like 8 did.

C It would swap only once with 40.

D It would be inserted at the root directly.

💡 Hint

Compare inserted value with parents as in execution_table steps 2, 4, 6.

Concept Snapshot

Heap Insert Bubble Up:
- Insert new element at array end
- Compare with parent: if smaller, swap
- Move pointer to parent
- Repeat until root or no swap needed
- Restores min-heap property
- Uses array index math: parent = (i-1)/2

Full Transcript

This visual trace shows how inserting a new element into a min-heap works by adding it at the end of the array and then bubbling it up. The bubble up compares the new element with its parent and swaps if the new element is smaller, moving the pointer up the tree until the heap property is restored or the root is reached. The execution table tracks each step, the heap array state, pointer position, and actions taken. Key moments clarify why swaps happen only when the child is smaller, why insertion is at the end, and when bubble up stops. The visual quiz tests understanding of heap states and pointer movements during bubble up.