Heap Concept Structure and Properties in DSA C# - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to declare a max heap using a list in C#.

DSA C#

List<int> maxHeap = new List<int>[1];

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

A()

B{}

C[]

D<>

Attempts:

3 left

💡 Hint

Common Mistakes

Using curly braces {} which are for collection initializers, not constructor call.

Using square brackets [] which are for arrays.

In C#, to create a new list, you use parentheses () after the type.

2fill in blank

medium

Complete the code to get the index of the left child of a node at index i in a heap.

DSA C#

int leftChildIndex = [1];

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

A2 * i

Bi + 1

C2 * i + 1

D2 * i - 1

Attempts:

3 left

💡 Hint

Common Mistakes

Using 2 * i which is the formula for 1-based indexing.

Using i + 1 which is just the next element.

In a heap stored as an array or list, the left child of node at index i is at 2 * i + 1.

3fill in blank

hard

Fix the error in the code to get the parent index of a node at index i in a heap.

DSA C#

int parentIndex = (i - 1) [1] 2;

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

A-

B*

C+

D/

Attempts:

3 left

💡 Hint

Common Mistakes

Using multiplication instead of division.

Using addition or subtraction which do not give correct parent index.

The parent of a node at index i is at index (i - 1) / 2 in zero-based indexing.

4fill in blank

hard

Fill both blanks to complete the condition that checks if a node at index i has a right child in the heap.

DSA C#

bool hasRightChild = (rightChildIndex < [1]) && (rightChildIndex == i [2] 1);

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

Aheap.Count

Bheap.Length

C+

D-

Attempts:

3 left

💡 Hint

Common Mistakes

Using heap.Length which is for arrays, not lists.

Using subtraction instead of addition for right child index.

To check if right child exists, its index must be less than the heap size (heap.Count in C# List). The right child index is 2 * i + 2, which is i + 1 more than left child index 2 * i + 1.

5fill in blank

hard

Fill all three blanks to complete the code that swaps two elements at indices i and j in the heap list.

DSA C#

int temp = heap[[1]];
heap[[2]] = heap[[3]];
heap[[1]] = temp;

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

Ai

Bj

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Mixing up indices i and j in assignments.

Using a fixed index like 0 instead of i or j.

To swap elements at indices i and j, store heap[i] in temp, assign heap[j] to heap[i], then assign temp to heap[j].

Practice

1. What is a key property of a max-heap data structure?

easy

A. Every parent node is greater than or equal to its children

B. Every parent node is less than or equal to its children

C. All leaf nodes have the same value

D. The tree is always a complete binary tree with sorted leaves

Solution

1. Step 1: Understand max-heap property

   A max-heap requires that each parent node's value is greater than or equal to the values of its children.

2. Step 2: Compare options with definition

   Every parent node is greater than or equal to its children matches the max-heap property exactly. Every parent node is less than or equal to its children describes a min-heap. Options A and C are incorrect properties.

3. Final Answer:

   Every parent node is greater than or equal to its children -> Option A

4. Quick Check:

   Max-heap = parent ≥ children [OK]

Hint: Max-heap means parent ≥ children values [OK]

Common Mistakes:

• Confusing max-heap with min-heap property
• Thinking leaves must be sorted
• Assuming all nodes have equal values

2. Which of the following is the correct way to declare a min-heap using C#'s PriorityQueue?

easy

A. var minHeap = new PriorityQueue();

B. var minHeap = new PriorityQueue(Comparer<int>.Default);

C. var minHeap = new PriorityQueue(Comparer<int>.Create((x, y) => y - x));

D. var minHeap = new PriorityQueue(Comparer<int>.Create((x, y) => x + y));

Solution

1. Step 1: Recall default behavior of PriorityQueue

   In C#, PriorityQueue by default acts as a min-heap using the natural order of TPriority.

2. Step 2: Analyze options

   var minHeap = new PriorityQueue(); uses default constructor, creating a min-heap. var minHeap = new PriorityQueue(Comparer<int>.Default); incorrectly tries to pass a comparer to constructor which does not exist. var minHeap = new PriorityQueue(Comparer<int>.Create((x, y) => y - x)); reverses order for max-heap. var minHeap = new PriorityQueue(Comparer<int>.Create((x, y) => x + y)); uses invalid comparer logic.

3. Final Answer:

   var minHeap = new PriorityQueue<int, int>(); -> Option A

4. Quick Check:

   Default PriorityQueue is min-heap [OK]

Hint: Default PriorityQueue is min-heap without comparer [OK]

Common Mistakes:

• Trying to pass comparer to constructor (not supported)
• Using wrong comparer logic for min-heap
• Confusing min-heap and max-heap syntax

3. Consider the following C# code using a max-heap implemented as a binary heap array:

int[] heap = { 50, 30, 40, 10, 20 };
// Insert 60 and then heapify up
Insert(heap, 60);

What will be the heap array after insertion?

medium

A. [60, 50, 40, 10, 20, 60]

B. [60, 30, 50, 10, 20, 40]

C. [60, 50, 40, 30, 20, 10]

D. [50, 30, 40, 10, 20, 60]

Solution

1. Step 1: Insert 60 at the end of heap array

   Initial heap: [50, 30, 40, 10, 20]. Insert 60 at index 5: [50, 30, 40, 10, 20, 60]

2. Step 2: Heapify up to maintain max-heap

   Compare 60 with parent at index 2 (40). 60 > 40, swap. New array: [50, 30, 60, 10, 20, 40]. Compare 60 with parent at index 0 (50). 60 > 50, swap. Final array: [60, 30, 50, 10, 20, 40]

3. Final Answer:

   [60, 30, 50, 10, 20, 40] -> Option B

4. Quick Check:

   Insert + heapify up = [60,30,50,10,20,40] [OK]

Hint: Insert at end, swap up while parent smaller [OK]

Common Mistakes:

• Not swapping with parent correctly
• Placing new element at wrong index
• Confusing heapify up with heapify down

4. The following C# code attempts to remove the root from a max-heap stored in an array but has a bug:

void RemoveRoot(int[] heap, int size) {
    heap[0] = heap[size - 1];
    size--;
    HeapifyDown(heap, 0, size);
}

What is the main issue causing incorrect heap behavior?

medium

A. HeapifyDown is called with wrong starting index

B. The last element is not removed before assignment

C. The size variable is decremented locally but not updated outside

D. The root is not replaced with the maximum child

Solution

1. Step 1: Analyze size decrement scope

   The size variable is decremented inside the method but since it's passed by value, the caller's size remains unchanged.

2. Step 2: Effect on heap operations

   Because size outside is not updated, heap operations may access invalid elements or not reflect the reduced heap size, causing incorrect behavior.

3. Final Answer:

   Size variable is decremented locally but not updated outside -> Option C

4. Quick Check:

   Size must update outside method [OK]

Hint: Pass size by ref or return new size [OK]

Common Mistakes:

• Assuming size changes persist without ref
• Thinking heapify down index is wrong
• Ignoring size update importance

5. You have a min-heap represented as an array: [5, 10, 15, 20, 25, 30]. You want to replace the root with 22 and restore the min-heap property. Which sequence of array states correctly shows the heap after replacing and heapifying down?

hard

A. [22, 10, 15, 20, 25, 30] -> [10, 22, 15, 20, 25, 30]

B. [22, 10, 15, 20, 25, 30] -> [10, 15, 22, 20, 25, 30]

C. [22, 10, 15, 20, 25, 30] -> [15, 10, 22, 20, 25, 30]

D. [22, 10, 15, 20, 25, 30] -> [10, 20, 15, 22, 25, 30]

Solution

1. Step 1: Replace root with 22

   Initial heap: [5, 10, 15, 20, 25, 30]. Replace root 5 with 22: [22, 10, 15, 20, 25, 30]

2. Step 2: Heapify down to restore min-heap

   Compare 22 with children 10 and 15. Smallest child is 10. Swap 22 and 10: [10, 22, 15, 20, 25, 30]. Now 22 at index 1 has children at indices 3 (20) and 4 (25). Smallest is 20 < 22, swap 22 and 20: [10, 20, 15, 22, 25, 30]. 22 now at index 3 has no children, stop.

3. Final Answer:

   [22, 10, 15, 20, 25, 30] -> [10, 20, 15, 22, 25, 30] -> Option D

4. Quick Check:

   Replace root + heapify down = [22,10,15,20,25,30] -> [10,20,15,22,25,30] [OK]

Hint: Swap root down with smallest child until heap restored [OK]

Common Mistakes:

• Swapping with wrong child
• Stopping heapify too early
• Confusing min-heap with max-heap rules