Heap Extract Min or Max Bubble Down in DSA C - 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 C

int leftChild(int i) {
    return [1];
}

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Ai + 1

B2 * i - 1

Ci / 2

D2 * i + 1

Attempts:

3 left

💡 Hint

Common Mistakes

Using 2 * i - 1 instead of 2 * i + 1.

Confusing left child with parent index.

The left child of a node at index i in a heap is at 2 * i + 1.

2fill in blank

medium

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

DSA C

void swap(int *a, int *b) {
    int temp = *a;
    *a = [1];
    *b = temp;
}

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A*a

B*b

Ctemp

Da

Attempts:

3 left

💡 Hint

Common Mistakes

Assigning *a = temp which causes no change.

Using pointer variable names instead of dereferenced values.

To swap, assign *a the value of *b.

3fill in blank

hard

Fix the error in the bubble down loop condition to avoid infinite loop.

DSA C

while (smallest != i && smallest < [1]) {
    swap(&heap[i], &heap[smallest]);
    i = smallest;
    smallest = leftChild(i);
    if (rightChild(i) < size && heap[rightChild(i)] < heap[smallest]) {
        smallest = rightChild(i);
    }
}

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Asize

Bheap_size

Ccapacity

Dlength

Attempts:

3 left

💡 Hint

Common Mistakes

Using capacity instead of current size causes out-of-bound errors.

Not checking bounds leads to infinite loops.

The loop must check that smallest is less than the heap size to stay within bounds.

4fill in blank

hard

Fill both blanks to correctly update the smallest child index during bubble down.

DSA C

int smallest = [1](i);
if ([2](i) < size && heap[rightChild(i)] < heap[smallest]) {
    smallest = rightChild(i);
}

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AleftChild

BrightChild

Cparent

Dswap

Attempts:

3 left

💡 Hint

Common Mistakes

Using parent instead of child functions.

Swapping function names causes logic errors.

Start with left child index, then check right child to find the smallest.

5fill in blank

hard

Fill all three blanks to complete the extract min function with bubble down.

DSA C

int extractMin(int heap[], int *size) {
    if (*size <= 0) return -1;
    int root = heap[0];
    heap[0] = heap[[1]];
    (*size)--;
    int i = 0;
    int smallest = [2](i);
    while (smallest < *size && heap[smallest] < heap[i]) {
        swap(&heap[i], &heap[smallest]);
        i = smallest;
        smallest = [3](i);
    }
    return root;
}

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A*size

BleftChild

CrightChild

Dsize

Attempts:

3 left

💡 Hint

Common Mistakes

Using size instead of *size causes wrong indexing.

Using rightChild first breaks the min-heap property.

Replace last element at index *size, then bubble down starting from left child.

Practice

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

easy

A. To insert a new element at the bottom of 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 remove all elements smaller than the root

Solution

1. Step 1: Understand extract-min operation

   When the minimum element (root) is removed, the last element is moved to the root position.

2. Step 2: Apply bubble down to restore heap

   The bubble down operation moves this element down the tree to restore the min-heap property by swapping with smaller children.

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 after extract-min [OK]

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

Common Mistakes:

• Thinking bubble down inserts new elements
• Assuming bubble down only swaps root with last element
• Confusing bubble down with bubble up

2. Which of the following is the correct syntax to swap two elements heap[i] and heap[j] in C during bubble down?

easy

A. temp = heap[i]; heap[i] = heap[j]; heap[j] = temp;

B. swap(heap[i], heap[j]);

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

D. heap[i] <-> heap[j];

Solution

1. Step 1: Recognize C swap syntax

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

2. Step 2: Verify temp = heap[i]; heap[i] = heap[j]; heap[j] = temp; uses temp variable correctly

   temp = heap[i]; heap[i] = heap[j]; heap[j] = temp; uses a temporary variable to swap values correctly, while others use invalid or non-C syntax.

3. Final Answer:

   temp = heap[i]; heap[i] = heap[j]; heap[j] = temp; -> Option A

4. Quick Check:

   C swap needs temp variable [OK]

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

Common Mistakes:

• Using Python or pseudocode swap syntax in C
• Trying to swap without temp variable
• Using invalid operators like <->

3. Given the min-heap array [2, 4, 5, 10, 7, 6], after extracting the minimum and performing bubble down, what is the resulting heap array?

medium

A. [4, 7, 5, 10, 6]

B. [5, 4, 6, 10, 7]

C. [6, 4, 5, 10, 7]

D. [4, 6, 5, 10, 7]

Solution

1. Step 1: Remove root and replace with last element

   Remove 2, move last element 6 to root: [6, 4, 5, 10, 7]

2. Step 2: Bubble down 6 to restore min-heap

   Compare 6 with children 4 and 5; swap with smallest child 4: [4, 6, 5, 10, 7]. Next, 6's children are 10 and 7, both larger, so stop.

3. Final Answer:

   [4, 6, 5, 10, 7] -> Option D

4. Quick Check:

   Bubble down swaps with smaller child [OK]

Hint: Replace root with last, then bubble down [OK]

Common Mistakes:

• Not swapping with the smallest child
• Stopping bubble down too early
• Replacing root incorrectly

4. Consider this bubble down code snippet for a max-heap in C. What is the bug?

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

medium

A. No bug, code correctly bubbles down in max-heap

B. Left and right child indices calculation is wrong

C. Recursive call should be bubbleDown(heap, size, i) instead of largest

D. Swapping should happen only if heap[i] < heap[largest]

Solution

1. Step 1: Check child index calculations

   Left = 2*i+1 and right = 2*i+2 are correct for zero-based heap arrays.

2. Step 2: Verify bubble down logic

   Code finds largest among node and children, swaps if needed, then recurses on swapped child. This matches max-heap bubble down logic.

3. Final Answer:

   No bug, code correctly bubbles down in max-heap -> Option A

4. Quick Check:

   Correct child indices and recursion [OK]

Hint: Check child indices and recursion carefully [OK]

Common Mistakes:

• Confusing left/right child index formulas
• Wrong recursive call index
• Swapping condition misunderstanding

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

hard

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

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

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

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

Solution

1. Step 1: Remove root and replace with last element

   Remove 20, move last element 8 to root: [8, 18, 15, 10, 12, 9]

2. Step 2: Bubble down 8 to restore max-heap

   Compare 8 with children 18 and 15; swap with largest child 18: [18, 8, 15, 10, 12, 9]. Next, 8's children are 10 and 12; swap with largest child 12: [18, 12, 15, 10, 8, 9]. Now 8's children are out of range, stop.

3. Final Answer:

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

4. Quick Check:

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

Hint: Replace root with last, bubble down swapping largest child [OK]

Common Mistakes:

• Swapping with smaller child instead of largest
• Stopping bubble down too early
• Incorrectly replacing root element