Heap Sort Algorithm in DSA Javascript - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to swap two elements in the array.

DSA Javascript

function swap(arr, i, j) {
  let temp = arr[i];
  arr[i] = arr[1]j;
  arr[j] = temp;
}

Drag options to blanks, or click blank then click option'

A+

B-

C[

D.

Attempts:

3 left

💡 Hint

Common Mistakes

Using dot notation instead of square brackets to access array elements.

Using plus or minus signs which are arithmetic operators, not for indexing.

We use square brackets to access array elements by index in JavaScript.

2fill in blank

medium

Complete the code to heapify a subtree rooted at index i.

DSA Javascript

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

  if (left < n && arr[left] > arr[largest]) {
    largest = left;
  }

  if (right < n && arr[right] > arr[largest]) {
    largest = right;
  }

  if (largest !== i) {
    swap(arr, i, largest);
    heapify(arr, n, largest);
  }
}

Drag options to blanks, or click blank then click option'

A0

B3

C1

D2

Attempts:

3 left

💡 Hint

Common Mistakes

Using 1 instead of 2 for the right child index.

Using 3 or 0 which are incorrect for child indexing.

The right child index in a heap is calculated as 2 * i + 2, so the blank should be 2.

3fill in blank

hard

Fix the error in the loop that builds the max heap.

DSA Javascript

for (let i = Math.floor(n / 2) - 1; i [1] 0; i--) {
  heapify(arr, n, i);
}

Drag options to blanks, or click blank then click option'

A>=

B<=

C<

D>

Attempts:

3 left

💡 Hint

Common Mistakes

Using '<' or '<=' which causes the loop to skip the root node.

Using '>' which causes an infinite loop.

The loop should run while i is greater than or equal to 0 to cover all parent nodes.

4fill in blank

hard

Fill both blanks to complete the heap sort main loop.

DSA Javascript

for (let i = n - 1; i > [1]; i--) {
  swap(arr, 0, i);
  heapify(arr, i, [2]);
}

Drag options to blanks, or click blank then click option'

A0

B1

Ci

Dn

Attempts:

3 left

💡 Hint

Common Mistakes

Using 1 or n instead of 0 for heapify starting index.

Using i instead of 0 for heapify starting index.

We swap the root (index 0) with the last element and then heapify from the root (index 0).

5fill in blank

hard

Fill all three blanks to complete the heap sort function.

DSA Javascript

function heapSort(arr) {
  let n = arr.length;

  for (let i = Math.floor(n / 2) - 1; i [1] 0; i--) {
    heapify(arr, n, i);
  }

  for (let i = n - 1; i > [2]; i--) {
    swap(arr, 0, i);
    heapify(arr, i, [3]);
  }
}

Drag options to blanks, or click blank then click option'

A>=

B>

C0

D1

Attempts:

3 left

💡 Hint

Common Mistakes

Using '<' or '<=' in the first loop condition.

Using 1 instead of 0 for heapify starting index.

Using '>=' instead of '>' in the second loop condition.

The first loop runs while i >= 0, the second while i > 0, and heapify starts at index 0.

Practice

1. What is the main purpose of the heap in the Heap Sort algorithm?

easy

A. To reverse the array elements

B. To store elements in sorted order permanently

C. To count the number of elements in the array

D. To efficiently find and remove the largest (or smallest) element

Solution

1. Step 1: Understand heap property

   A heap is a special tree-based structure that allows quick access to the largest (max-heap) or smallest (min-heap) element.

2. Step 2: Role in Heap Sort

   Heap Sort uses the heap to repeatedly extract the largest element and place it at the end, sorting the array.

3. Final Answer:

   To efficiently find and remove the largest (or smallest) element -> Option D

4. Quick Check:

   Heap = fast max/min access [OK]

Hint: Heap helps quickly get max or min element [OK]

Common Mistakes:

• Thinking heap stores sorted elements permanently
• Confusing heap with simple array storage
• Assuming heap reverses the array

2. Which of the following is the correct way to swap two elements arr[i] and arr[j] in JavaScript during Heap Sort?

easy

A. let temp = arr[i]; arr[i] = arr[j]; arr[j] = temp;

B. arr[i], arr[j] = arr[j], arr[i];

C. swap(arr[i], arr[j]);

D. arr[i] = arr[j]; arr[j] = arr[i];

Solution

1. Step 1: Understand JavaScript swap syntax

   JavaScript does not support tuple unpacking like Python, so swapping requires a temporary variable.

2. Step 2: Check each option

   let temp = arr[i]; arr[i] = arr[j]; arr[j] = temp; uses a temporary variable correctly. arr[i], arr[j] = arr[j], arr[i]; is Python syntax, swap(arr[i], arr[j]); is undefined function, arr[i] = arr[j]; arr[j] = arr[i]; overwrites values incorrectly.

3. Final Answer:

   let temp = arr[i]; arr[i] = arr[j]; arr[j] = temp; -> Option A

4. Quick Check:

   Use temp variable to swap [OK]

Hint: Use temp variable to swap in JS [OK]

Common Mistakes:

• Using Python-style tuple swap in JS
• Calling undefined swap function
• Overwriting values without temp variable

3. What will be the output array after applying Heap Sort on [4, 10, 3, 5, 1]?

medium

A. [1, 3, 4, 5, 10]

B. [10, 5, 4, 3, 1]

C. [1, 4, 3, 5, 10]

D. [5, 10, 4, 3, 1]

Solution

1. Step 1: Understand Heap Sort output

   Heap Sort sorts the array in ascending order by default.

2. Step 2: Sort the array

   Sorting [4, 10, 3, 5, 1] gives [1, 3, 4, 5, 10].

3. Final Answer:

   [1, 3, 4, 5, 10] -> Option A

4. Quick Check:

   Sorted ascending = [1, 3, 4, 5, 10] [OK]

Hint: Heap Sort outputs sorted ascending array [OK]

Common Mistakes:

• Confusing heap structure with final sorted array
• Thinking output is descending by default
• Mixing up original and sorted arrays

4. Identify the error in this Heap Sort snippet:

function heapSort(arr) {
  let n = arr.length;
  for (let i = Math.floor(n / 2); i >= 0; i--) {
    heapify(arr, n, i);
  }
  for (let i = n - 1; i > 0; i--) {
    let temp = arr[0];
    arr[0] = arr[i];
    arr[i] = temp;
    heapify(arr, i, 0);
  }
}

medium

A. Swapping elements is done incorrectly

B. The first for loop should start from Math.floor(n / 2) - 1

C. The second for loop should start from i = 0

D. heapify function is called with wrong parameters

Solution

1. Step 1: Check heap building loop

   The first loop builds the heap and should start from the last non-leaf node at index Math.floor(n / 2) - 1, not Math.floor(n / 2).

2. Step 2: Verify other parts

   The second loop and swapping are correct. heapify parameters are also correct.

3. Final Answer:

   The first for loop should start from Math.floor(n / 2) - 1 -> Option B

4. Quick Check:

   Heap build starts at last non-leaf node [OK]

Hint: Heap build starts at floor(n/2)-1 [OK]

Common Mistakes:

• Starting heap build loop at wrong index
• Incorrect swap logic
• Wrong heapify parameters

5. Given an array [12, 11, 13, 5, 6, 7], how many times will the heapify function be called during the entire Heap Sort process?

hard

A. 6 times

B. 10 times

C. 13 times

D. 15 times

Solution

1. Step 1: Count heapify calls during heap build

   Heap build calls heapify top-level from index floor(n/2)-1=2 down to 0 (3 top-level). For this array, heapify(6,0) recurses once to heapify(6,2), total 4 calls.

2. Step 2: Count heapify calls during sorting

   After building heap, heapify called top-level 5 times (i=5 to 1). Tracing: i=5:2 calls, i=4:2, i=3:2, i=2:2, i=1:1, total 9 calls.

3. Step 3: Total calls

   Total heapify calls = 4 (build) + 9 (sort) = 13.

4. Final Answer:

   13 times -> Option C

5. Quick Check:

   Heapify calls = build + sort + recursive calls = 13 [OK]

Hint: Count build + sort + recursive heapify calls =13 [OK]

Common Mistakes:

• Counting only build or only sort calls
• Ignoring recursive heapify calls
• Assuming heapify called once per element