Heap Insert Operation Bubble Up in DSA Typescript - Build from Scratch

Heap Insert Operation Bubble Up

📖 Scenario: You are managing a priority queue using a min-heap. A min-heap is a special tree where the smallest number is always at the top. When you add a new number, you need to place it correctly so the smallest number stays on top.Imagine you have a list of tasks with different priorities. You want to add a new task and keep the list ordered by priority.

🎯 Goal: Build a min-heap insert operation that adds a new number to the heap and moves it up (bubble up) to keep the smallest number at the top.

📋 What You'll Learn

Create an array called heap with initial values representing a min-heap

Create a variable called newValue to hold the number to insert

Write a function called bubbleUp that moves the last element up to keep the min-heap property

Print the heap array after insertion and bubbling up

💡 Why This Matters

🌍 Real World

Heaps are used in task scheduling, priority queues, and algorithms like Dijkstra's shortest path.

💼 Career

Understanding heap insertions is important for software engineers working with efficient data structures and algorithms.

1

Create the initial min-heap array

Create an array called heap with these exact numbers in order: [10, 15, 20, 17, 25]

DSA Typescript

# Create the initial heap array
# Your code here

Hint

Use const heap = [10, 15, 20, 17, 25]; to create the array.

2

Add the new value to insert

Create a variable called newValue and set it to 8. Then add newValue to the end of the heap array using push.

DSA Typescript

const heap = [10, 15, 20, 17, 25];
# Create newValue = 8 and push it to heap
# Your code here

Hint

Use const newValue = 8; and heap.push(newValue);.

3

Write the bubbleUp function to restore min-heap

Write a function called bubbleUp that takes no arguments. It should start from the last index of heap and swap the element with its parent while it is smaller than the parent. Use a while loop and calculate the parent index as Math.floor((index - 1) / 2). Stop when the element is not smaller than the parent or when it reaches the root (index 0).

DSA Typescript

const heap = [10, 15, 20, 17, 25];
const newValue = 8;
heap.push(newValue);

# Write bubbleUp function to move last element up
# Your code here

Hint

Use a while loop and swap elements if the child is smaller than the parent.

4

Call bubbleUp and print the heap

Call the bubbleUp() function. Then print the heap array using console.log(heap).

DSA Typescript

const heap = [10, 15, 20, 17, 25];
const newValue = 8;
heap.push(newValue);

function bubbleUp() {
    let index = heap.length - 1;
    while (index > 0) {
        let parentIndex = Math.floor((index - 1) / 2);
        if (heap[index] < heap[parentIndex]) {
            // Swap
            [heap[index], heap[parentIndex]] = [heap[parentIndex], heap[index]];
            index = parentIndex;
        } else {
            break;
        }
    }
}

# Call bubbleUp and print heap
# Your code here

Hint

Call bubbleUp() and then console.log(heap).

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