Build Heap from Array Heapify in DSA Javascript

Mental Model

We turn an unordered list into a heap by fixing each parent node from the bottom up so the heap property holds everywhere.

Analogy: Imagine stacking boxes so that bigger boxes are always below smaller boxes. We start fixing from the bottom shelves up to the top to make sure the stack is stable.

Array: [4, 10, 3, 5, 1]
Heap tree:
       4
     /   \
   10     3
  /  \
 5    1

Dry Run Walkthrough

Input: array: [4, 10, 3, 5, 1]

Goal: Convert the array into a max heap where every parent is bigger than its children

Step 1: Start heapify from last parent index (1), fix subtree rooted at index 1

[4, 10, 3, 5, 1]

Why: We start from last parent because leaves are already heaps

Step 2: Compare node 10 with children 5 and 1, no swap needed

[4, 10, 3, 5, 1]

Why: Parent 10 is already bigger than children, subtree is heap

Step 3: Move to parent index 0, fix subtree rooted at 4

[4, 10, 3, 5, 1]

Why: We fix from bottom up to ensure heap property

Step 4: Compare 4 with children 10 and 3, swap 4 with 10

[10, 4, 3, 5, 1]

Why: Parent must be bigger, so swap with largest child

Step 5: Fix subtree rooted at index 1 (value 4), compare with children 5 and 1, swap 4 with 5

[10, 5, 3, 4, 1]

Why: After swap, subtree might break heap, so fix recursively

Step 6: Fix subtree rooted at index 3 (value 4), no children to compare

[10, 5, 3, 4, 1]

Why: Leaf node reached, heap property holds

Result:

Final heap array: [10, 5, 3, 4, 1]

Annotated Code

DSA Javascript

class MaxHeap {
  constructor(array) {
    this.heap = array;
    this.buildHeap();
  }

  buildHeap() {
    const n = this.heap.length;
    // Start from last parent node and heapify down to root
    for (let i = Math.floor(n / 2) - 1; i >= 0; i--) {
      this.heapify(i);
    }
  }

  heapify(i) {
    const n = this.heap.length;
    let largest = i;
    const left = 2 * i + 1;
    const right = 2 * i + 2;

    // Check if left child is larger
    if (left < n && this.heap[left] > this.heap[largest]) {
      largest = left;
    }

    // Check if right child is larger
    if (right < n && this.heap[right] > this.heap[largest]) {
      largest = right;
    }

    // If largest is not parent, swap and heapify subtree
    if (largest !== i) {
      [this.heap[i], this.heap[largest]] = [this.heap[largest], this.heap[i]];
      this.heapify(largest);
    }
  }

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

// Driver code
const array = [4, 10, 3, 5, 1];
const maxHeap = new MaxHeap(array);
maxHeap.printHeap();

for (let i = Math.floor(n / 2) - 1; i >= 0; i--) {

start heapify from last parent to root

this.heapify(i);

fix subtree rooted at i to maintain heap property

if (left < n && this.heap[left] > this.heap[largest]) {

check if left child is bigger than current largest

if (right < n && this.heap[right] > this.heap[largest]) {

check if right child is bigger than current largest

if (largest !== i) {

if parent is not largest, swap and heapify child subtree

this.heapify(largest);

recursively fix subtree after swap

Output

10, 5, 3, 4, 1

Complexity Analysis

Time: O(n) because heapify is called on n/2 nodes and each call takes O(log n) worst but overall sums to O(n)

Space: O(1) because heapify is done in place without extra arrays

vs Alternative: Naive approach inserting elements one by one into heap is O(n log n), so this bottom-up heapify is faster

Edge Cases

empty array

buildHeap does nothing and heap remains empty

DSA Javascript

for (let i = Math.floor(n / 2) - 1; i >= 0; i--) {

array with one element

heapify runs once but no swaps needed, heap is the same

DSA Javascript

for (let i = Math.floor(n / 2) - 1; i >= 0; i--) {

array with all equal elements

no swaps happen, heap property holds trivially

DSA Javascript

if (largest !== i) {

When to Use This Pattern

When you need to build a heap quickly from an unordered array, use bottom-up heapify starting from last parent to root to efficiently enforce heap property.

Common Mistakes

Mistake: Starting heapify from index 0 instead of last parent causes unnecessary work and incorrect heap
Fix: Start heapify from Math.floor(n/2) - 1 down to 0 to only fix parents

Mistake: Not recursively heapifying after swap breaks heap property in subtrees
Fix: Call heapify recursively on the swapped child's index

Summary

Builds a max heap from an unordered array by fixing heap property from bottom up.

Use when you want to convert an array into a heap efficiently before heap operations.

Start heapify from last parent node down to root, recursively fixing subtrees after swaps.