Heap Extract Min or Max Bubble Down in DSA Java - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to get the index of the left child in a heap array.

DSA Java

int leftChildIndex = 2 * parentIndex [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 or division instead of addition.

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

2fill in blank

medium

Complete the code to swap two elements in the heap array.

DSA Java

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

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

A0

BchildIndex

CparentIndex

Di

Attempts:

3 left

💡 Hint

Common Mistakes

Swapping with the wrong index.

Using an undefined variable.

To swap, we temporarily store the parent's value and then assign child's value to parent's position.

3fill in blank

hard

Fix the error in the condition to check if the child index is within heap size.

DSA Java

while (childIndex [1] heapSize) {

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

A>

B<=

C>=

D<

Attempts:

3 left

💡 Hint

Common Mistakes

Using '>=' or '>' which causes out of bounds errors.

Using '<=' which allows invalid index.

The child index must be less than heap size to be valid inside the array bounds.

4fill in blank

hard

Fill both blanks to correctly update the parent and child indices during bubble down.

DSA Java

parentIndex = [1];
childIndex = 2 * parentIndex [2] 1;

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

AchildIndex

BparentIndex

C+

D-

Attempts:

3 left

💡 Hint

Common Mistakes

Not updating indices correctly causing infinite loops.

Using wrong arithmetic operators.

After swapping, the parent moves to child's position, and child index is recalculated as left child of new parent.

5fill in blank

hard

Fill all three blanks to complete the bubble down logic comparing parent and child values.

DSA Java

if (heap[childIndex + 1] [1] heap[childIndex]) {
    childIndex = childIndex [2] 1;
}
if (heap[parentIndex] [3] heap[childIndex]) {
    break;
}

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

A>

B+

C<=

D-

Attempts:

3 left

💡 Hint

Common Mistakes

Using wrong comparison operators causing incorrect bubbling.

Not updating child index correctly.

We check if right child is smaller or equal to left child to pick the smaller child, then if parent is smaller or equal to child, we stop bubbling down.

Practice

1. What is the main purpose of the bubble down operation in a heap after extracting the min or max element?

easy

A. To remove all leaf nodes from the heap

B. To restore the heap property by moving the root element down to its correct position

C. To swap the last element with the root without any further changes

D. To insert a new element at the bottom of the heap

Solution

1. Step 1: Understand the extract operation

   When we remove the min or max element (usually the root), the heap may lose its order property.

2. Step 2: Purpose of bubble down

   Bubble down moves the new root element down the tree to restore the heap property by swapping it with the smaller (min-heap) or larger (max-heap) child.

3. Final Answer:

   To restore the heap property by moving the root element down to its correct position -> Option B

4. Quick Check:

   Bubble down fixes heap order after extraction [OK]

Hint: Bubble down fixes heap order after removing root [OK]

Common Mistakes:

• Thinking bubble down inserts new elements
• Assuming bubble down removes leaf nodes
• Believing bubble down only swaps root and last element

2. Which of the following Java method signatures correctly represents a bubble down operation for a min-heap stored in an array?

easy

A. void bubbleDown(int[] heap, int index, int size)

B. int bubbleDown(int[] heap, int size)

C. void bubbleDown(int index, int[] heap)

D. boolean bubbleDown(int[] heap, int index)

Solution

1. Step 1: Identify parameters needed for bubble down

   We need the heap array, the current index to bubble down from, and the size of the heap to avoid out-of-bounds.

2. Step 2: Match method signature

   void bubbleDown(int[] heap, int index, int size) has all parameters in correct order and returns void as bubble down modifies the heap in place.

3. Final Answer:

   void bubbleDown(int[] heap, int index, int size) -> Option A

4. Quick Check:

   Correct parameters and void return for bubble down [OK]

Hint: Bubble down needs array, index, and size parameters [OK]

Common Mistakes:

• Missing size parameter causing index errors
• Wrong return type expecting a value
• Incorrect parameter order

3. Given the min-heap array [2, 5, 3, 10, 7], after extracting the min element and performing bubble down, what will be the resulting heap array?

medium

A. [3, 5, 7, 10]

B. [5, 7, 3, 10]

C. [3, 7, 5, 10]

D. [5, 3, 7, 10]

Solution

1. Step 1: Remove min and replace root

   Remove 2 (min), replace root with last element 7: [7, 5, 3, 10]

2. Step 2: Bubble down from root

   Compare 7 with children 5 and 3; smallest is 3. Swap 7 and 3: [3, 5, 7, 10]. Now 7 has children 10 only, 7 < 10, so stop.

3. Final Answer:

   [3, 5, 7, 10] -> Option A

4. Quick Check:

   Bubble down restores min-heap order [OK]

Hint: Replace root with last, then swap down with smaller child [OK]

Common Mistakes:

• Not replacing root with last element before bubble down
• Swapping with wrong child (larger instead of smaller)
• Stopping bubble down too early

4. Consider this bubble down code snippet for a max-heap. Identify the bug:

void bubbleDown(int[] heap, int index, int size) {
  int largest = index;
  int left = 2 * index + 1;
  int right = 2 * index + 2;
  if (left < size && heap[left] > heap[largest]) {
    largest = left;
  }
  if (right < size && heap[right] > heap[largest]) {
    largest = right;
  }
  if (largest != index) {
    int temp = heap[index];
    heap[index] = heap[largest];
    heap[largest] = temp;
    bubbleDown(heap, largest, size);
  }
}

medium

A. The comparison operators should be < instead of > for max-heap

B. The left and right child indices calculation is incorrect

C. The recursive call should be bubbleDown(heap, index, size) instead of bubbleDown(heap, largest, size)

D. There is no bug; the code correctly performs bubble down

Solution

1. Step 1: Check child index calculations

   Left = 2*index+1 and right = 2*index+2 are correct for binary heap stored in array.

2. Step 2: Verify comparisons and recursion

   Comparisons use > for max-heap to find largest child. Recursive call uses largest index to continue bubbling down correctly.

3. Final Answer:

   There is no bug; the code correctly performs bubble down -> Option D

4. Quick Check:

   Child indices and recursion are correct [OK]

Hint: Check indices and recursion carefully; they are often correct [OK]

Common Mistakes:

• Confusing child index formulas
• Wrong comparison operators for max-heap
• Incorrect recursive call index

5. You have a max-heap represented by the array [20, 18, 15, 10, 12, 9, 8]. After extracting the max element and performing bubble down, what is the resulting heap array?

hard

A. [18, 15, 12, 10, 9, 8]

B. [18, 12, 15, 10, 9, 8]

C. [18, 12, 15, 10, 8, 9]

D. [18, 10, 15, 12, 9, 8]

Solution

1. Step 1: Extract max and replace root

   Remove 20, replace root with last element 8: [8, 18, 15, 10, 12, 9]

2. Step 2: Bubble down from root

   Compare 8 with children 18 and 15; largest is 18. Swap 8 and 18: [18, 8, 15, 10, 12, 9]. Now bubble down at index 1.

3. Step 3: Continue bubble down

   At index 1, children are 10 and 12; largest is 12. Swap 8 and 12: [18, 12, 15, 10, 8, 9]. At index 4, children do not exist, stop.

4. Final Answer:

   [18, 12, 15, 10, 8, 9] -> Option C

5. Quick Check:

   Bubble down swaps with largest child until heap restored [OK]

Hint: Replace root with last, swap down with largest child repeatedly [OK]

Common Mistakes:

• Not continuing bubble down after first swap
• Swapping with smaller child by mistake
• Forgetting to update heap size after extraction