Build Heap from Array Heapify in DSA Javascript - Build from Scratch

Build Heap from Array Heapify

📖 Scenario: Imagine you have a list of numbers representing tasks with different priorities. You want to organize them so the highest priority task is always easy to find. This is like arranging a pile of books so the biggest book is always on top.

🎯 Goal: You will build a max heap from an unsorted array using the heapify process. This means rearranging the array so each parent number is bigger than its children, making it easy to get the largest number quickly.

📋 What You'll Learn

Create an array called tasks with the exact numbers: [4, 10, 3, 5, 1]

Create a variable called n that stores the length of the tasks array

Write a function called heapify that takes tasks, n, and i as parameters and rearranges the array to maintain max heap property

Use a for loop to call heapify starting from the last parent node down to the root

Print the tasks array after building the max heap

💡 Why This Matters

🌍 Real World

Heaps are used in task scheduling, priority queues, and sorting algorithms like heapsort.

💼 Career

Understanding heap data structures helps in software engineering roles involving efficient data processing and algorithm optimization.

1

Create the initial array

Create an array called tasks with these exact numbers: [4, 10, 3, 5, 1]

DSA Javascript

// Create the array tasks with the numbers [4, 10, 3, 5, 1]
// Your code here

Hint

Use const tasks = [4, 10, 3, 5, 1]; to create the array.

2

Set the length variable

Create a variable called n that stores the length of the tasks array

DSA Javascript

const tasks = [4, 10, 3, 5, 1];
// Create a variable n that stores the length of tasks
// Your code here

Hint

Use const n = tasks.length; to get the array length.

3

Write the heapify function

Write a function called heapify that takes tasks, n, and i as parameters and rearranges the array to maintain max heap property. Use variables largest, left, and right inside the function.

DSA Javascript

const tasks = [4, 10, 3, 5, 1];
const n = tasks.length;
// Write the heapify function below
// Your code here

Hint

Use the heapify logic to compare parent and children and swap if needed, then call heapify recursively.

4

Build the heap and print the result

Use a for loop starting from Math.floor(n / 2) - 1 down to 0 to call heapify(tasks, n, i). Then print the tasks array using console.log(tasks).

DSA Javascript

const tasks = [4, 10, 3, 5, 1];
const n = tasks.length;

function heapify(tasks, n, i) {
    let largest = i;
    let left = 2 * i + 1;
    let right = 2 * i + 2;

    if (left  tasks[largest]) {
        largest = left;
    }

    if (right  tasks[largest]) {
        largest = right;
    }

    if (largest !== i) {
        let temp = tasks[i];
        tasks[i] = tasks[largest];
        tasks[largest] = temp;

        heapify(tasks, n, largest);
    }
}

// Use a for loop to build the heap and then print tasks
// Your code here

Hint

Start from the last parent node and call heapify down to the root. Then print the array.

Practice

1. What is the main purpose of the heapify process when building a heap from an array?

easy

A. To reverse the array elements

B. To sort the array in ascending order

C. To find the maximum element in the array

D. To rearrange the array elements to satisfy the heap property

Solution

1. Step 1: Understand heap property

   A heap is a special tree where each parent node is greater (max-heap) or smaller (min-heap) than its children.

2. Step 2: Role of heapify

   Heapify rearranges elements so the heap property holds for every subtree, starting from a node downwards.

3. Final Answer:

   To rearrange the array elements to satisfy the heap property -> Option D

4. Quick Check:

   Heapify = Rearrange for heap property [OK]

Hint: Heapify fixes subtree to maintain heap order [OK]

Common Mistakes:

• Thinking heapify sorts the array
• Confusing heapify with finding max element
• Assuming heapify reverses the array

2. Which of the following is the correct way to start heapifying an array arr of length n in JavaScript to build a max heap?

easy

A. for(let i = 0; i < n; i++) heapify(arr, i, n);

B. for(let i = 1; i < n; i++) heapify(arr, i, n);

C. for(let i = Math.floor(n/2) - 1; i >= 0; i--) heapify(arr, i, n);

D. for(let i = n - 1; i >= 0; i--) heapify(arr, i, n);

Solution

1. Step 1: Identify heapify start index

   Heapify starts from the last non-leaf node, which is at index Math.floor(n/2) - 1.

2. Step 2: Loop backwards to root

   We heapify each node from this index down to 0 to ensure the entire tree satisfies heap property.

3. Final Answer:

   for(let i = Math.floor(n/2) - 1; i >= 0; i--) heapify(arr, i, n); -> Option C

4. Quick Check:

   Start heapify at last non-leaf node [OK]

Hint: Start heapify from last parent node backwards [OK]

Common Mistakes:

• Starting heapify from index 0 forwards
• Heapifying leaf nodes unnecessarily
• Using incorrect loop boundaries

3. Given the array [3, 9, 2, 1, 4, 5], what is the array after building a max heap using heapify?

medium

A. [9, 4, 5, 1, 3, 2]

B. [9, 4, 5, 3, 1, 2]

C. [5, 4, 9, 1, 3, 2]

D. [9, 3, 5, 1, 4, 2]

Solution

1. Step 1: Start heapify from index 2 (Math.floor(6/2)-1)

   Heapify at index 2: children are indices 5 (5) and no right child. 2 < 5, swap to get [3,9,5,1,4,2].

2. Step 2: Heapify at index 1

   Children at indices 3 (1) and 4 (4). 9 > 4 and 1, no swap needed.

3. Step 3: Heapify at index 0

   Children at indices 1 (9) and 2 (5). 3 < 9, swap 3 and 9: [9,3,5,1,4,2]. Heapify at index 1 again: children 3 (1) and 4 (4). 3 < 4, swap: [9,4,5,1,3,2].

4. Final Answer:

   [9, 4, 5, 1, 3, 2] -> Option A

5. Quick Check:

   Max heap root is 9, children smaller [OK]

Hint: Heapify bottom-up swaps to fix heap [OK]

Common Mistakes:

• Not heapifying children after swap
• Swapping with wrong child
• Stopping heapify too early

4. Consider this heapify function snippet in JavaScript:

function heapify(arr, i, n) {
  let largest = i;
  let left = 2 * i + 1;
  let right = 2 * i + 2;
  if (left < n && arr[left] > arr[largest]) largest = left;
  if (right < n && arr[right] > arr[largest]) largest = right;
  if (largest !== i) {
    [arr[i], arr[largest]] = [arr[largest], arr[i]];
    heapify(arr, largest, n);
  }
}

What is the bug if the function is called with heapify(arr, 0, arr.length - 1) instead of heapify(arr, 0, arr.length)?

medium

A. It will ignore the last element of the array during heapify

B. It will cause an infinite recursion

C. It will throw a syntax error

D. It will heapify the entire array correctly

Solution

1. Step 1: Understand parameter n meaning

   Parameter n is the array length limit for heapify to avoid out-of-bound access.

2. Step 2: Effect of passing arr.length - 1

   Passing arr.length - 1 excludes the last element index (n-1) from heapify checks, so last element is ignored.

3. Final Answer:

   It will ignore the last element of the array during heapify -> Option A

4. Quick Check:

   n must be array length, not length-1 [OK]

Hint: Use full array length as heapify limit [OK]

Common Mistakes:

• Confusing length and last index
• Expecting syntax error instead of logic error
• Ignoring off-by-one errors

5. You have an array [4, 10, 3, 5, 1] and want to build a min heap using heapify. Which of the following changes is necessary in the heapify function to build a min heap instead of a max heap?

hard

A. Swap the left and right child indices calculations

B. Change comparisons from '>' to '<' when comparing children with parent

C. Change comparisons from '<' to '>' when comparing children with parent

D. No change needed; heapify works for both min and max heaps

Solution

1. Step 1: Understand max vs min heap comparison

   Max heap keeps parent >= children; min heap keeps parent <= children.

2. Step 2: Adjust comparison operators

   To build min heap, change '>' to '<' so parent is smaller than children.

3. Final Answer:

   Change comparisons from '>' to '<' when comparing children with parent -> Option B

4. Quick Check:

   Min heap uses less-than comparisons [OK]

Hint: Flip comparison signs for min heap [OK]

Common Mistakes:

• Swapping child indices instead of comparisons
• Leaving comparisons unchanged
• Assuming heapify auto-detects heap type