Heap Insert Operation Bubble Up in DSA Typescript

Mental Model

When adding a new number to a heap, we put it at the end and then move it up to keep the heap rules.

Analogy: Imagine adding a new card to a pile where bigger cards must be on top. You place the card at the bottom and then swap it up until it fits the order.

       10
      /  \
     5    3
    / 
   2  
  ↑ (new value here at the end)

Dry Run Walkthrough

Input: heap: [10, 5, 3, 2], insert value 6

Goal: Add 6 to the heap and move it up until the heap property is restored

Step 1: Insert 6 at the end of the array

[10, 5, 3, 2, 6 ↑]

Why: New value must start at the end before moving up

Step 2: Compare 6 with its parent 5, swap because 6 > 5

[10, 6 ↑, 3, 2, 5]

Why: 6 is bigger than parent, so swap to keep max-heap order

Step 3: Compare 6 with new parent 10, no swap because 6 < 10

[10, 6 ↑, 3, 2, 5]

Why: 6 is smaller than parent, so stop bubbling up

Result:

[10, 6, 3, 2, 5] with heap property restored

Annotated Code

DSA Typescript

class MaxHeap {
  heap: number[] = [];

  insert(value: number) {
    this.heap.push(value); // add at end
    this.bubbleUp(); // fix heap
  }

  bubbleUp() {
    let index = this.heap.length - 1;
    while (index > 0) {
      const parentIndex = Math.floor((index - 1) / 2);
      if (this.heap[index] <= this.heap[parentIndex]) break; // stop if heap property ok
      [this.heap[index], this.heap[parentIndex]] = [this.heap[parentIndex], this.heap[index]]; // swap
      index = parentIndex; // move up
    }
  }

  printHeap() {
    console.log(this.heap.join(', '));
  }
}

// Driver code
const heap = new MaxHeap();
heap.heap = [10, 5, 3, 2];
heap.insert(6);
heap.printHeap();

this.heap.push(value); // add at end

Add new value at the end of the heap array

while (index > 0) {

Keep bubbling up until we reach the root

const parentIndex = Math.floor((index - 1) / 2);

Find parent index to compare

if (this.heap[index] <= this.heap[parentIndex]) break;

Stop if current value is not bigger than parent

[this.heap[index], this.heap[parentIndex]] = [this.heap[parentIndex], this.heap[index]];

Swap current value with parent to move up

index = parentIndex;

Update index to parent's position for next iteration

Output

10, 6, 3, 2, 5

Complexity Analysis

Time: O(log n) because the new value moves up at most the height of the heap

Space: O(1) because we only use a few variables and swap in place

vs Alternative: Compared to rebuilding the heap from scratch (O(n)), bubbling up is faster for single insertions

Edge Cases

Insert into empty heap

Value is added as root without bubbling

DSA Typescript

while (index > 0) {

Insert value smaller than all existing values

Value stays at the end, no swaps

DSA Typescript

if (this.heap[index] <= this.heap[parentIndex]) break;

Insert value larger than root

Value bubbles all the way to root

DSA Typescript

index = parentIndex;

When to Use This Pattern

When you need to add a new element to a heap and keep it ordered, use bubble up to restore heap order efficiently.

Common Mistakes

Mistake: Not updating the index after swapping, causing infinite loop
Fix: Set index = parentIndex after swap to continue bubbling up

Mistake: Swapping even when the child is smaller or equal to parent
Fix: Add condition to break loop if child <= parent

Summary

It adds a new value to the heap and moves it up to keep the heap order.

Use it when inserting elements into a heap to maintain the max-heap property.

The key is to swap the new value with its parent until it fits the heap rules.

Practice

1. What is the main purpose of the bubble up operation during a heap insert?

easy

A. To swap all elements randomly in the heap

B. To remove the root element from the heap

C. To sort all elements in the heap in ascending order

D. To restore the heap property by moving the new element up if it is smaller (min-heap) or larger (max-heap) than its parent

Solution

1. Step 1: Understand the heap property

   In a min-heap, each parent node must be smaller than its children. In a max-heap, each parent must be larger.

2. Step 2: Purpose of bubble up

   When inserting a new element, it is placed at the end. Bubble up moves it up the tree to restore the heap property if violated.

3. Final Answer:

   To restore the heap property by moving the new element up if it is smaller (min-heap) or larger (max-heap) than its parent -> Option D

4. Quick Check:

   Bubble up fixes heap order after insert [OK]

Hint: Bubble up fixes heap order by moving new element up [OK]

Common Mistakes:

• Confusing bubble up with removing elements
• Thinking bubble up sorts the entire heap
• Assuming bubble up swaps elements randomly

2. Which of the following TypeScript code snippets correctly performs the bubble up step in a min-heap after inserting a new element at the end?

easy

A. while (index > 0 && heap[index] < heap[parentIndex]) { swap(heap, index, parentIndex); index = parentIndex; }

B. while (index > 0 && heap[index] > heap[parentIndex]) { swap(heap, index, parentIndex); index = parentIndex; }

C. for (let i = 0; i < heap.length; i++) { if (heap[i] < heap[i+1]) swap(heap, i, i+1); }

D. if (heap[index] > heap[parentIndex]) { swap(heap, index, parentIndex); }

Solution

1. Step 1: Identify min-heap bubble up condition

   In a min-heap, bubble up swaps while the child is smaller than the parent.

2. Step 2: Check code correctness

   while (index > 0 && heap[index] < heap[parentIndex]) { swap(heap, index, parentIndex); index = parentIndex; } uses a while loop with condition heap[index] < heap[parentIndex], correctly swapping and updating index.

3. Final Answer:

   while (index > 0 && heap[index] < heap[parentIndex]) { swap(heap, index, parentIndex); index = parentIndex; } -> Option A

4. Quick Check:

   Min-heap bubble up swaps smaller child up [OK]

Hint: Bubble up swaps while child < parent in min-heap [OK]

Common Mistakes:

• Using > instead of < for min-heap
• Using for loop instead of while
• Not updating index after swap

3. Given a max-heap represented as an array: [50, 30, 40, 10, 20], what will be the heap array after inserting 45 and performing bubble up?

medium

A. [50, 45, 40, 10, 20, 30]

B. [50, 30, 45, 10, 20, 40]

C. [50, 30, 40, 10, 20, 45]

D. [45, 30, 50, 10, 20, 40]

Solution

1. Step 1: Insert 45 at the end

   Array becomes [50, 30, 40, 10, 20, 45]

2. Step 2: Bubble up 45 in max-heap

   Parent index of 45 (index 5) is 2 (value 40). Since 45 > 40, swap. New array: [50, 30, 45, 10, 20, 40]. Now index 2's parent is 0 (value 50). 45 < 50, stop bubbling up.

3. Final Answer:

   [50, 30, 45, 10, 20, 40] -> Option B

4. Quick Check:

   Bubble up swaps 45 with 40 only [OK]

Hint: Insert at end, swap up while child > parent in max-heap [OK]

Common Mistakes:

• Not swapping 45 with 40
• Swapping 45 with 30 instead of 40
• Stopping bubble up too early

4. Consider this bubble up code snippet for a min-heap insert:

while (index > 0 && heap[index] > heap[parentIndex]) {
  swap(heap, index, parentIndex);
  index = parentIndex;
}

What is the error in this code?

medium

A. The parentIndex is not updated inside the loop

B. The swap function is called incorrectly

C. The comparison operator should be '<' to maintain min-heap property

D. The loop should run while index < 0

Solution

1. Step 1: Check comparison for min-heap bubble up

   In a min-heap, bubble up swaps when child is smaller than parent, so condition should be heap[index] < heap[parentIndex].

2. Step 2: Identify error in code

   The code uses '>' which is incorrect for min-heap bubble up, causing wrong swaps.

3. Final Answer:

   The comparison operator should be '<' to maintain min-heap property -> Option C

4. Quick Check:

   Min-heap bubble up uses < comparison [OK]

Hint: Min-heap bubble up swaps when child < parent [OK]

Common Mistakes:

• Using > instead of < in condition
• Not updating parentIndex after swap
• Loop condition index > 0 is correct, not < 0

5. You have a min-heap represented as [5, 10, 15, 20, 25, 30]. You insert 12 and perform bubble up. After that, you insert 3 and perform bubble up again. What is the final heap array?

hard

A. [3, 5, 12, 10, 25, 30, 15, 20]

B. [3, 5, 15, 10, 25, 30, 12, 20]

C. [3, 5, 12, 20, 25, 30, 15, 10]

D. [3, 5, 15, 20, 25, 30, 12, 10]

Solution

1. Step 1: Insert 12 and bubble up

   Insert 12 at index 6: [5,10,15,20,25,30,12]. Parent of index 6 is 2 (value 15). Since 12 < 15, swap: [5,10,12,20,25,30,15]. Parent of index 2 is 0 (value 5). 12 > 5, stop.

2. Step 2: Insert 3 and bubble up

   Insert 3 at index 7: [5,10,12,20,25,30,15,3]. Parent of index 7 is 3 (value 20). 3 < 20, swap: [5,10,12,3,25,30,15,20]. Parent of index 3 is 1 (value 10). 3 < 10, swap: [5,3,12,10,25,30,15,20]. Parent of index 1 is 0 (value 5). 3 < 5, swap: [3,5,12,10,25,30,15,20]. Now at root, stop.

3. Final Answer:

   [3, 5, 12, 10, 25, 30, 15, 20] -> Option A

4. Quick Check:

   Bubble up swaps until heap property restored [OK]

Hint: Bubble up each insert until parent smaller in min-heap [OK]

Common Mistakes:

• Not swapping 3 all the way to root
• Incorrect parent index calculation
• Stopping bubble up too early