Heap Extract Min or Max Bubble Down in DSA Go - Execution Trace

Concept Flow - Heap Extract Min or Max Bubble Down

Start: Extract root (min or max)

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Replace root with last element

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Remove last element from heap

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Set current index = 0

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Compare current with children

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Swap with smaller/larger child

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Update current index to child's index

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Repeat until heap property restored

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Done

Extract the root element, replace it with the last element, then bubble down by swapping with the smaller (min-heap) or larger (max-heap) child until heap property is restored.

Execution Sample

DSA Go

heap := []int{10, 15, 30, 40, 50, 100, 40}
extractMin(heap)
// Extract root 10 and bubble down

Extract the minimum element (root) from a min-heap and restore heap property by bubbling down.

Execution Table

Step	Operation	Heap Array State	Pointer Changes	Visual State
1	Extract root (10)	[10, 15, 30, 40, 50, 100, 40]	root = 10	Tree: 10 / \ 15 30 / \ / \ 40 50 100 40
2	Replace root with last element (40)	[40, 15, 30, 40, 50, 100, 40]	root replaced by last element 40	Tree: 40 / \ 15 30 / \ / \ 40 50 100 40
3	Remove last element (index 6)	[40, 15, 30, 40, 50, 100]	last element removed	Tree: 40 / \ 15 30 / \ / 40 50 100
4	Compare root (40) with children (15, 30)	[40, 15, 30, 40, 50, 100]	current=0, left=1(15), right=2(30)	40 > 15 and 40 > 30, swap with smaller child 15
5	Swap root with left child (15)	[15, 40, 30, 40, 50, 100]	swap indices 0 and 1	Tree after swap: 15 / \ 40 30 / \ / 40 50 100
6	Update current index to 1	[15, 40, 30, 40, 50, 100]	current=1	Focus on node with value 40 at index 1
7	Compare current (40) with children (40, 50)	[15, 40, 30, 40, 50, 100]	left=3(40), right=4(50)	40 <= 40 and 40 <= 50, no swap needed
8	Heap property restored, stop	[15, 40, 30, 40, 50, 100]	no pointer changes	Final heap: 15 / \ 40 30 / \ / 40 50 100

💡 Heap property restored at step 7, no further swaps needed.

Variable Tracker

Variable	Start	After Step 2	After Step 3	After Step 5	After Step 6	Final
heap	[10, 15, 30, 40, 50, 100, 40]	[40, 15, 30, 40, 50, 100, 40]	[40, 15, 30, 40, 50, 100]	[15, 40, 30, 40, 50, 100]	[15, 40, 30, 40, 50, 100]	[15, 40, 30, 40, 50, 100]
current	N/A	0	0	0	1	1
left child index	N/A	1	1	1	3	3
right child index	N/A	2	2	2	4	4

Key Moments - 3 Insights

Why do we replace the root with the last element before bubbling down?

Replacing the root with the last element keeps the heap complete (no gaps). Then bubbling down restores the heap order. See execution_table step 2 and 3.

Why do we swap with the smaller child in a min-heap during bubble down?

Swapping with the smaller child ensures the smallest element moves up, maintaining min-heap property. See step 4 and 5 where 40 swaps with 15.

When do we stop bubbling down?

We stop when the current node is smaller or equal to both children (min-heap), meaning heap property is restored. See step 7 where no swap occurs.

Visual Quiz - 3 Questions

Look at the execution_table at step 5, what is the heap array state after the swap?

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

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

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

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

💡 Hint

Refer to the 'Heap Array State' column at step 5 in execution_table.

At which step does the current index update to 1 during bubble down?

A Step 6

B Step 5

C Step 4

D Step 7

💡 Hint

Check the 'Pointer Changes' column for current index updates.

If the last element was larger than the root, how would the heap array change after step 2?

A Root replaced by larger last element, likely no swaps needed

B Root remains unchanged

C Root replaced by larger last element, immediate swap with smaller child

D Heap size increases

💡 Hint

Think about bubble down logic when root is replaced by a larger value.

Concept Snapshot

Heap Extract Min or Max Bubble Down:
- Remove root (min or max element)
- Replace root with last element
- Remove last element from heap
- Bubble down: swap with smaller (min-heap) or larger (max-heap) child
- Repeat until heap property restored
- Maintains complete binary tree and heap order

Full Transcript

This visualization shows how to extract the root element from a heap and restore the heap property by bubbling down. First, the root is removed and replaced by the last element in the heap array to keep the tree complete. Then the last element is removed from the array. Starting at the root, we compare it with its children and swap with the smaller child in a min-heap if the root is larger. We update the current index to the swapped child's position and repeat this process until the heap property is restored, meaning the current node is smaller or equal to its children. The execution table tracks each step, showing the heap array state, pointer changes, and the visual tree structure. Key moments clarify why we replace the root with the last element, why we swap with the smaller child, and when to stop bubbling down. The visual quiz tests understanding of the heap array state after swaps, pointer updates, and the effect of replacing the root with a larger last element.