Heap Sort Algorithm in DSA C# - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to swap two elements in the array.

DSA C#

void Swap(int[] arr, int i, int j) {
    int temp = arr[i];
    arr[i] = arr[[1]];
    arr[j] = temp;
}

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

Aarr[j]

Bi

C0

Dj

Attempts:

3 left

💡 Hint

Common Mistakes

Using arr[i] instead of arr[j] for the swap.

Assigning arr[j] before saving temp.

We swap arr[i] with arr[j], so arr[i] should get arr[j].

2fill in blank

medium

Complete the code to find the left child index in the heap.

DSA C#

int LeftChild(int i) {
    return 2 * i [1] 1;
}

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

A+

B-

C*

D/

Attempts:

3 left

💡 Hint

Common Mistakes

Using subtraction instead of addition.

Using multiplication twice.

Left child index in heap is 2*i + 1.

3fill in blank

hard

Fix the error in the heapify function to maintain max heap property.

DSA C#

void Heapify(int[] arr, int n, int i) {
    int largest = i;
    int left = 2 * i + 1;
    int right = 2 * i + 2;

    if (left < n && arr[left] [1] arr[largest])
        largest = left;

    if (right < n && arr[right] [1] 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'

A==

B<

C>

D!=

Attempts:

3 left

💡 Hint

Common Mistakes

Using < instead of > in comparisons.

Using equality operators instead of comparison.

To maintain max heap, we check if child is greater than current largest.

4fill in blank

hard

Fill both blanks to build the max heap from the array.

DSA C#

void BuildMaxHeap(int[] arr, int n) {
    for (int i = n / 2 - 1; i [1] -1; i[2]) {
        Heapify(arr, n, i);
    }
}

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A>

B<

C--

D++

Attempts:

3 left

💡 Hint

Common Mistakes

Using i++ instead of i-- in the loop.

Using less than instead of greater than in condition.

We start from the last parent and move backwards, so i >= 0 and i--.

5fill in blank

hard

Complete the code to complete the heap sort main loop.

DSA C#

void HeapSort(int[] arr) {
    int n = arr.Length;
    BuildMaxHeap(arr, n);

    for (int i = n - 1; i > 0; i[1]) {
        Swap(arr, 0, i);
        Heapify(arr, i, 0);
    }
}

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

A--

B,

C)

D+

Attempts:

3 left

💡 Hint

Common Mistakes

Using i++ instead of i-- in loop.

Missing comma between arguments in Heapify.

Missing closing parenthesis in Heapify call.

We decrement i in loop, pass i as size to Heapify, and close the argument list with ).

Practice

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

easy

A. To build a max heap from an unordered array

B. To swap the first and last elements of the array

C. To reverse the array after sorting

D. To count the number of elements in the array

Solution

1. Step 1: Understand heapify's role

   The heapify function rearranges elements to satisfy the max heap property, where each parent node is greater than its children.

2. Step 2: Connect heapify to building max heap

   Heapify is called repeatedly to build a max heap from an unordered array before sorting begins.

3. Final Answer:

   To build a max heap from an unordered array -> Option A

4. Quick Check:

   heapify builds max heap = A [OK]

Hint: Heapify creates max heap structure before sorting [OK]

Common Mistakes:

• Confusing heapify with swapping elements
• Thinking heapify reverses the array
• Assuming heapify counts elements

2. Which of the following is the correct way to swap two elements arr[i] and arr[j] in C# during heap sort?

easy

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

B. int temp = arr[i]; arr[i] = arr[j]; arr[j] = temp;

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

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

Solution

1. Step 1: Identify correct C# swap syntax

   In C#, swapping requires a temporary variable to hold one value during exchange.

2. Step 2: Check each option

   int 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 invalid without a swap method. arr[i] = arr[j]; arr[j] = arr[i]; overwrites values incorrectly.

3. Final Answer:

   int temp = arr[i]; arr[i] = arr[j]; arr[j] = temp; -> Option B

4. Quick Check:

   Use temp variable to swap in C# = C [OK]

Hint: Use temp variable to swap in C# [OK]

Common Mistakes:

• Using Python tuple swap syntax in C#
• Calling undefined swap function
• Overwriting values without temp variable

3. What will be the output array after applying heap sort on int[] arr = {4, 10, 3, 5, 1};?

medium

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

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

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

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

Solution

1. Step 1: Build max heap from array

   Starting array: [4, 10, 3, 5, 1]. Max heap after heapify: [10, 5, 3, 4, 1].

2. Step 2: Extract max and sort

   Swap 10 with last element, heapify reduced heap: [5, 4, 3, 1, 10]. Repeat until sorted: final sorted array is [1, 3, 4, 5, 10].

3. Final Answer:

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

4. Quick Check:

   Heap sort sorts ascending = [1, 3, 4, 5, 10] [OK]

Hint: Heap sort outputs sorted ascending array [OK]

Common Mistakes:

• Confusing max heap with sorted array
• Forgetting to heapify after swaps
• Assuming heap sort outputs descending order

4. Identify the error in this heap sort snippet:

void HeapSort(int[] arr) {
  int n = arr.Length;
  for (int i = n / 2 - 1; i >= 0; i--) {
    Heapify(arr, n, i);
  }
  for (int i = n - 1; i > 0; i--) {
    int temp = arr[0];
    arr[0] = arr[i];
    arr[i] = temp;
    Heapify(arr, n, 0);
  }
}

void Heapify(int[] arr, int n, int i) {
  int largest = i;
  int left = 2 * i + 1;
  int 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) {
    int swap = arr[i];
    arr[i] = arr[largest];
    arr[largest] = swap;
    Heapify(arr, n, largest);
  }
}

medium

A. Heapify call inside second loop uses wrong size parameter

B. The first for loop should start from n/2, not n/2 - 1

C. The second for loop condition should be i >= 0, not i > 0

D. Swap logic inside Heapify is incorrect

Solution

1. Step 1: Examine the second loop's Heapify call

   After swapping arr[0] and arr[i], the effective heap size is i. However, the code calls Heapify(arr, n, 0), using the original full size n instead of the reduced size i. This is the error.

2. Step 2: Confirm other options are not errors

   The first for loop should start from n/2, not n/2 - 1 is incorrect because it correctly starts at n/2 - 1. The second for loop condition should be i >= 0, not i > 0 is wrong because i > 0 is appropriate. Swap logic inside Heapify is incorrect is false; the swap is correct.

3. Final Answer:

   Heapify call inside second loop uses wrong size parameter -> Option A

4. Quick Check:

   Heapify in extract phase uses reduced size i, not n = B [OK]

Hint: Check loop bounds and heapify size carefully [OK]

Common Mistakes:

• Changing loop start incorrectly
• Using wrong loop end condition
• Misunderstanding heap size in heapify

5. Given a large array with many duplicate values, which modification to the standard heap sort algorithm can improve its stability (preserving order of equal elements)?

hard

A. Use a min heap instead of a max heap

B. Sort the array twice with heap sort

C. Add an index field to elements and compare indices when values are equal

D. Skip heapify calls for duplicate values

Solution

1. Step 1: Understand stability in sorting

   Stability means equal elements keep their original order after sorting.

2. Step 2: Analyze heap sort stability

   Standard heap sort is not stable because heap operations can reorder equal elements arbitrarily.

3. Step 3: Find modification to improve stability

   Adding an index field and comparing indices when values are equal preserves original order, making heap sort stable.

4. Final Answer:

   Add an index field to elements and compare indices when values are equal -> Option C

5. Quick Check:

   Use index to preserve order for stability = D [OK]

Hint: Use original indices to maintain stability in heap sort [OK]

Common Mistakes:

• Thinking min heap makes sort stable
• Skipping heapify breaks heap property
• Sorting twice wastes time without stability