Heap Insert Operation Bubble Up in DSA C# - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to calculate the parent index in a binary heap.

DSA C#

int parentIndex = (childIndex [1] 1) / 2;

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

A+

B-

C*

D/

Attempts:

3 left

💡 Hint

Common Mistakes

Using + instead of -

Using * or / incorrectly

The parent index in a binary heap is calculated by subtracting 1 from the child index, then dividing by 2.

2fill in blank

medium

Complete the condition to check if the child node is greater than the parent node in a max heap.

DSA C#

if (heap[childIndex] [1] heap[parentIndex])

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

A<

B==

C<=

D>

Attempts:

3 left

💡 Hint

Common Mistakes

Using < instead of >

Using == which doesn't trigger swap

In a max heap, the child node should be greater than the parent node to bubble up.

3fill in blank

hard

Fix the error in swapping the parent and child nodes during bubble up.

DSA C#

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

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

AparentIndex

BchildIndex

C0

Dheap.Length

Attempts:

3 left

💡 Hint

Common Mistakes

Swapping with wrong indices

Using fixed indices like 0 or heap.Length

To swap, use parentIndex and childIndex to access the correct elements.

4fill in blank

hard

Fill both blanks to correctly update the child and parent indices after swapping during bubble up.

DSA C#

childIndex = [1];
parentIndex = (childIndex [2] 1) / 2;

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

AparentIndex

BchildIndex

C-

D+

Attempts:

3 left

💡 Hint

Common Mistakes

Using childIndex instead of parentIndex for update

Using + instead of - in parent index calculation

After swapping, childIndex becomes parentIndex, and parentIndex is recalculated by subtracting 1 from childIndex then dividing by 2.

5fill in blank

hard

Fill all three blanks to complete the bubble up loop condition and update indices correctly.

DSA C#

while (childIndex > 0 && heap[childIndex] [1] heap[[2]]) {
    int temp = heap[childIndex];
    heap[childIndex] = heap[[3]];
    heap[[3]] = temp;
    childIndex = [3];
    parentIndex = (childIndex - 1) / 2;
}

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

A>

BparentIndex

D<

Attempts:

3 left

💡 Hint

Common Mistakes

Using < instead of > in condition

Mixing up parentIndex and childIndex in swap

The loop continues while childIndex is greater than 0 and the child node is greater than the parent node. Swap uses parentIndex, and childIndex updates to parentIndex.

Practice

1. What is the main purpose of the bubble up operation during a heap insert?

easy

A. To restore the heap property by moving the new element up if it is smaller than its parent

B. To move the new element to the bottom of the heap

C. To remove the smallest element from the heap

D. To sort all elements in the heap

Solution

1. Step 1: Understand heap property

   In a min-heap, every parent node is smaller than its children. When inserting, this property might break.

2. Step 2: Purpose of bubble up

   The bubble up operation moves the newly inserted element up the tree if it is smaller than its parent, restoring the heap property.

3. Final Answer:

   To restore the heap property by moving the new element up if it is smaller than its parent -> Option A

4. Quick Check:

   Bubble up fixes heap order by moving smaller elements up [OK]

Hint: Bubble up moves smaller inserted element up to fix heap [OK]

Common Mistakes:

• Thinking bubble up moves element down
• Confusing bubble up with removing elements
• Assuming bubble up sorts the entire heap

2. Which of the following C# code snippets correctly swaps two elements in an array during bubble up?

easy

A. int temp = heap[parent]; heap[parent] = heap[i]; heap[i] = temp;

B. heap[i] = heap[parent]; heap[parent] = heap[i];

C. heap[i] = heap[parent]; heap[parent] = heap[parent];

D. int temp = heap[i]; heap[i] = heap[parent]; heap[parent] = heap[i];

Solution

1. Step 1: Understand swapping logic

   To swap two elements, store one in a temporary variable, assign the second to the first, then assign temp to the second.

2. Step 2: Check each option

   int temp = heap[parent]; heap[parent] = heap[i]; heap[i] = temp; correctly stores heap[parent] in temp, then swaps heap[parent] and heap[i]. int temp = heap[i]; heap[i] = heap[parent]; heap[parent] = heap[i]; swaps incorrectly by storing heap[i] first.

3. Final Answer:

   int temp = heap[parent]; heap[parent] = heap[i]; heap[i] = temp; -> Option A

4. Quick Check:

   Swap uses temp variable correctly [OK]

Hint: Use temp variable to swap two array elements safely [OK]

Common Mistakes:

• Overwriting one element before saving it
• Swapping without temp variable causing data loss
• Confusing indices in swap

3. Given a min-heap array: [2, 5, 8, 10, 15], what will be the heap array after inserting 1 and performing bubble up?

medium

A. [1, 2, 8, 10, 15, 5]

B. [1, 5, 2, 10, 15, 8]

C. [1, 2, 5, 10, 15, 8]

D. [2, 5, 8, 10, 15, 1]

Solution

1. Step 1: Insert 1 at the end

   Insert 1 at index 5: [2, 5, 8, 10, 15, 1]

2. Step 2: Bubble up 1

   Parent of index 5 is index 2 (value 8). Since 1 < 8, swap: [2, 5, 1, 10, 15, 8]. Now index 2's parent is index 0 (value 2). Since 1 < 2, swap again: [1, 5, 2, 10, 15, 8].

3. Final Answer:

   [1, 2, 5, 10, 15, 8] -> Option C

4. Quick Check:

   Bubble up swaps until heap property restored [OK]

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

Common Mistakes:

• Not swapping enough times to restore heap
• Swapping with wrong parent index
• Inserting element at wrong position

4. Consider this bubble up code snippet in C# for a min-heap insert:

while (i > 0 && heap[i] < heap[(i - 1) / 2]) {
    int temp = heap[i];
    heap[i] = heap[(i - 1) / 2];
    heap[(i - 1) / 2] = temp;
    i = (i - 1) / 2;
}

What is the bug in this code?

medium

A. The parent index calculation is incorrect; it should be (i / 2) instead of (i - 1) / 2

B. No bug; the code correctly performs bubble up

C. The swap uses wrong indices; should swap with i + 1

D. The loop condition should use > instead of < for a min-heap

Solution

1. Step 1: Check parent index formula

   Parent index in zero-based heap is (i - 1) / 2, which is correct.

2. Step 2: Check loop condition and swap

   Loop continues while current element is smaller than parent, swapping them correctly. Indices used in swap are correct.

3. Final Answer:

   No bug; the code correctly performs bubble up -> Option B

4. Quick Check:

   Parent index and swap logic are correct [OK]

Hint: Parent index = (i-1)/2; swap if child smaller [OK]

Common Mistakes:

• Using wrong parent index formula
• Reversing comparison operator in condition
• Swapping with wrong indices

5. You have a max-heap represented by the array [20, 15, 18, 8, 10, 5]. You insert 17 and perform bubble up. What is the final heap array?

hard

A. [20, 17, 18, 8, 10, 5, 15]

B. [20, 15, 17, 8, 10, 5, 18]

C. [20, 15, 18, 8, 10, 17, 5]

D. [20, 15, 18, 8, 10, 5, 17]

Solution

1. Step 1: Insert 17 at the end

   Insert 17 at index 6: [20, 15, 18, 8, 10, 5, 17]

2. Step 2: Bubble up 17 in max-heap

   Parent of index 6 is index 2 (value 18). Since 17 < 18, no swap needed. Heap remains [20, 15, 18, 8, 10, 5, 17].

3. Step 3: Verify parent index

   Parent of 6 is (6-1)/2 = 2 (18). 17 < 18, so no swap for max-heap bubble up.

4. Step 4: Re-examine options

   Options A and B show incorrect bubbling up (A swaps with wrong parent 15, B swaps with parent 18). Since 17 < 18, no swap. Heap stays [20, 15, 18, 8, 10, 5, 17] matching [20, 15, 18, 8, 10, 5, 17].

5. Final Answer:

   [20, 15, 18, 8, 10, 5, 17] -> Option D

6. Quick Check:

   Bubble up swaps only if child > parent in max-heap [OK]

Hint: In max-heap, bubble up if child > parent only [OK]

Common Mistakes:

• Swapping when child is smaller than parent
• Confusing max-heap with min-heap rules
• Incorrect parent index calculation