Heap Insert Operation Bubble Up in DSA Javascript - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the purpose of the bubble up operation in a heap insert?

The bubble up operation moves the newly inserted element up the heap to restore the heap property, ensuring the parent node is always greater (max-heap) or smaller (min-heap) than its children.

beginner

In a max-heap, when does the bubble up operation stop?

It stops when the inserted element is less than or equal to its parent or when it reaches the root of the heap.

beginner

How do you find the parent index of a node at index i in a heap array?

The parent index is calculated as Math.floor((i - 1) / 2).

intermediate

What happens if the newly inserted element is larger than its parent in a max-heap during bubble up?

They swap places, and the bubble up continues with the new parent index until the heap property is restored.

beginner

Why is bubble up important for heap insert operation?

Because it maintains the heap structure and order after adding a new element, ensuring efficient retrieval of the max or min element.

What is the first step after inserting a new element at the end of a heap array?

A Do nothing

B Remove the root element

C Sort the entire array

D Perform bubble up to restore heap property

After insertion at the end, bubble up moves the element up to maintain heap order.

In a max-heap, if the inserted element is smaller than its parent, what happens during bubble up?

A Stop bubbling up

B Swap with parent

C Swap with child

D Remove the element

Bubble up stops because the heap property is satisfied.

How do you calculate the parent index of a node at index 5 in a heap array?

A 2

B 3

C 4

D 1

Parent index = Math.floor((5 - 1) / 2) = 2.

What data structure property does bubble up help maintain?

A Stack order

B Queue order

C Heap property

D Linked list order

Bubble up restores the heap property after insertion.

Which of these is true about bubble up in a min-heap?

A It moves the element down

B It moves the element up if smaller than parent

C It swaps with the smaller parent

D It swaps with the larger parent

In a min-heap, bubble up moves the element up if it is smaller than its parent.

Explain the bubble up process during a heap insert operation.

Think about how the new element moves up to keep the heap order.

Describe how to find the parent of a node in a heap stored as an array and why this is important for bubble up.

Remember the formula for parent index and its role in bubble up.

Practice

1. What is the main purpose of the bubble up operation when inserting a new element into a max heap?

easy

A. To move the new element up until the heap property is restored

B. To move the new element down to the bottom of the heap

C. To remove the smallest element from the heap

D. To sort all elements in ascending order

Solution

1. Step 1: Understand heap property

   A max heap requires each parent to be greater than or equal to its children.

2. Step 2: Purpose of bubble up

   When a new element is added at the end, bubble up moves it up to restore the max heap property.

3. Final Answer:

   To move the new element up until the heap property is restored -> Option A

4. Quick Check:

   Bubble up fixes heap by moving element up [OK]

Hint: Bubble up moves new element up to fix heap [OK]

Common Mistakes:

• Thinking bubble up moves element down
• Confusing bubble up with removing elements
• Assuming bubble up sorts entire heap

2. Which of the following is the correct syntax to swap two elements at indices i and parentIndex in a JavaScript array heap during bubble up?

easy

A. [heap[i], heap[parentIndex]] = [heap[parentIndex], heap[i]];

B. heap.swap(i, parentIndex);

C. swap(heap[i], heap[parentIndex]);

D. heap[i], heap[parentIndex] = heap[parentIndex], heap[i];

Solution

1. Step 1: Identify JavaScript swap syntax

   JavaScript uses array destructuring to swap: [a, b] = [b, a];

2. Step 2: Apply to heap array

   Swapping heap[i] and heap[parentIndex] is done by [heap[i], heap[parentIndex]] = [heap[parentIndex], heap[i]];

3. Final Answer:

   [heap[i], heap[parentIndex]] = [heap[parentIndex], heap[i]]; -> Option A

4. Quick Check:

   Destructuring swap syntax = [heap[i], heap[parentIndex]] = [heap[parentIndex], heap[i]]; [OK]

Hint: Use array destructuring to swap in JS [OK]

Common Mistakes:

• Using Python-style swap syntax
• Calling undefined swap function
• Trying to use non-existent array method

3. Given the max heap 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, 40, 10, 20, 45]

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

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

Solution

1. Step 1: Insert 45 at the end

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

2. Step 2: Bubble up 45

   Parent index of 45 (index 5) is 2 (value 40). Since 45 > 40, swap them. New heap: [50, 30, 45, 10, 20, 40]

3. Final Answer:

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

4. Quick Check:

   Bubble up swaps 45 with 40 [OK]

Hint: Insert at end, then swap up if bigger than parent [OK]

Common Mistakes:

• Not swapping after insertion
• Swapping with wrong parent index
• Assuming insertion sorts entire heap

4. Consider this bubble up code snippet for a max heap insertion:

while (i > 0 && heap[i] > heap[parentIndex]) {
  [heap[i], heap[parentIndex]] = [heap[parentIndex], heap[i]];
  i = parentIndex;
  parentIndex = Math.floor((i - 1) / 2);
}

What is the bug if parentIndex is not updated inside the loop?

medium

A. Syntax error due to missing semicolon

B. Heap property is restored correctly

C. Loop terminates prematurely after one swap because parentIndex never changes

D. The loop never runs because i is never updated

Solution

1. Step 1: Understand loop variables

   Inside the loop, after swap i = parentIndex, but if parentIndex is not updated, i now equals the unchanged parentIndex.

2. Step 2: Consequence of not updating parentIndex

   The condition heap[i] > heap[parentIndex] becomes heap[pos] > heap[pos] which is false, causing premature loop termination without full restoration.

3. Final Answer:

   Loop terminates prematurely after one swap because parentIndex never changes -> Option C

4. Quick Check:

   Without parentIndex update, i == parentIndex stops loop early [OK]

Hint: Always update parentIndex after swapping [OK]

Common Mistakes:

• Forgetting to update parentIndex
• Assuming i update is enough
• Ignoring loop condition effects

5. You have a min heap represented as [5, 10, 15, 20, 25]. You want to insert 12 and maintain the min heap property using bubble up. Which of the following sequences correctly shows the heap array after each bubble up swap?

medium

A. [5, 10, 15, 20, 25, 12] -> [5, 10, 15, 20, 25, 12]

B. [5, 10, 15, 20, 25, 12] -> [5, 10, 12, 20, 25, 15]

C. [5, 10, 15, 20, 25, 12] -> [5, 12, 15, 20, 25, 10]

D. [5, 10, 15, 20, 25, 12] -> [12, 10, 15, 20, 25, 5]

Solution

1. Step 1: Insert 12 at the end

   Heap becomes [5, 10, 15, 20, 25, 12]

2. Step 2: Bubble up 12

   Parent index of 12 (index 5) is 2 (value 15). Since 12 < 15, swap them. New heap: [5, 10, 12, 20, 25, 15]

3. Final Answer:

   [5, 10, 15, 20, 25, 12] -> [5, 10, 12, 20, 25, 15] -> Option B

4. Quick Check:

   Bubble up swaps 12 with 15 in min heap [OK]

Hint: In min heap, bubble up swaps if child < parent [OK]

Common Mistakes:

• Swapping with wrong parent
• Not swapping when child is smaller
• Confusing min heap with max heap rules