Heap Extract Min or Max Bubble Down in DSA Javascript - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the purpose of the 'bubble down' operation in a heap after extracting the min or max?

The 'bubble down' operation restores the heap property by moving the root element down the tree to its correct position after extraction, ensuring the heap remains a valid min-heap or max-heap.

beginner

In a min-heap, after extracting the minimum element, which element replaces the root before bubbling down?

The last element in the heap replaces the root before the bubble down process starts.

intermediate

What condition determines when to stop the bubble down process in a heap?

Bubble down stops when the current node is smaller (min-heap) or larger (max-heap) than both its children or when it has no children.

intermediate

Why do we swap the current node with the smaller (min-heap) or larger (max-heap) child during bubble down?

Swapping with the smaller or larger child maintains the heap property by ensuring the parent node is always less than (min-heap) or greater than (max-heap) its children.

advanced

Show the bubble down steps after extracting the max from this max-heap: [50, 30, 40, 10, 20]

1. Remove max (50), replace root with last element (20): [20, 30, 40, 10] 2. Compare 20 with children 30 and 40; swap with 40 (largest child): [40, 30, 20, 10] 3. Now 20 has no children, so stop. Final heap: [40, 30, 20, 10]

What element replaces the root in a heap after extracting the min or max?

A The second last element

B The first child of the root

C A new random element

D The last element in the heap

After extraction, the last element moves to the root before bubble down.

In a min-heap, bubble down swaps the current node with which child?

A The larger child

B The smaller child

C The left child always

D The right child always

Swapping with the smaller child maintains the min-heap property.

When does the bubble down process stop?

A When the node is in correct order with children or has no children

B When the node is smaller than its children in a max-heap

C When the node is larger than its children in a min-heap

D After a fixed number of swaps

Bubble down stops when the heap property is restored or no children exist.

What is the time complexity of bubble down in a heap of size n?

A O(n)

B O(1)

C O(log n)

D O(n log n)

Bubble down moves down the height of the heap, which is log n.

Which of these is NOT true about bubble down?

A It always swaps with the left child

B It restores heap property after extraction

C It swaps with the child violating heap property

D It stops when heap property is satisfied

Bubble down swaps with the smaller or larger child depending on heap type, not always left child.

Explain the bubble down process after extracting the root from a min-heap.

Think about how to keep the smallest element at the root.

Describe why bubble down is necessary after extracting the max from a max-heap.

Consider what happens to the heap structure after removal.

Practice

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

easy

A. To remove the largest element from the heap

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

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

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

Solution

1. Step 1: Understand extract-min in a min-heap

   Extracting the minimum removes the root, which breaks the heap property.

2. Step 2: Role of bubble down

   Bubble down moves the new root element down 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 C

4. Quick Check:

   Bubble down fixes heap after extract-min [OK]

Hint: Bubble down fixes heap by pushing root down after extract [OK]

Common Mistakes:

• Thinking bubble down inserts new elements
• Confusing bubble down with bubble up
• Assuming bubble down removes largest element

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

easy

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

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

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

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

Solution

1. Step 1: Identify JavaScript swap syntax

   ES6 allows swapping with destructuring: [a, b] = [b, a].

2. Step 2: Check each option

   [arr[i], arr[j]] = [arr[j], arr[i]]; uses correct destructuring syntax. temp = arr[i]; arr[i] = arr[j]; arr[j] = temp; is valid but missing var or let for temp, so incomplete. Options A and C are incorrect syntax or logic.

3. Final Answer:

   [arr[i], arr[j]] = [arr[j], arr[i]]; -> Option A

4. Quick Check:

   Use destructuring swap in JS [OK]

Hint: Use ES6 destructuring for swap: [a,b]=[b,a] [OK]

Common Mistakes:

• Using undefined swap function
• Overwriting values without temp variable
• Incorrect assignment order causing same values

3. Given the min-heap array [2, 5, 3, 8, 10], after extracting the minimum and performing bubble down, what is the resulting heap array?

medium

A. [3, 5, 8, 10]

B. [5, 3, 8, 10]

C. [5, 8, 3, 10]

D. [3, 5, 10, 8]

Solution

1. Step 1: Extract min and replace root

   Remove 2 (root), move last element 10 to root: [10, 5, 3, 8]

2. Step 2: Bubble down 10

   Compare 10 with children 5 and 3. Smallest child is 3 at index 2. Swap 10 and 3: [3, 5, 10, 8]. Now 10 at index 2 has no children (indices 5 and 6 out of bounds), so stop.

3. Final Answer:

   [3, 5, 10, 8] -> Option D

4. Quick Check:

   Bubble down restores min-heap [OK]

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

Common Mistakes:

• Not swapping with smallest child
• Forgetting to remove last element
• Swapping with larger child

4. Consider this bubble down code snippet for a max-heap extract operation:

function bubbleDown(arr, index) {
  let left = 2 * index + 1;
  let right = 2 * index + 2;
  let largest = index;
  if (left < arr.length && arr[left] > arr[largest]) {
    largest = left;
  }
  if (right < arr.length && arr[right] > arr[largest]) {
    largest = right;
  }
  if (largest !== index) {
    [arr[index], arr[largest]] = [arr[largest], arr[index]];
    bubbleDown(arr, largest);
  }
}

What is the bug if the heap array is empty after extract and bubbleDown is called with index 0?

medium

A. Infinite recursion because largest never equals index

B. No bug; function handles empty array correctly

C. Accessing arr[0] causes undefined behavior on empty array

D. Swapping elements without checking array length

Solution

1. Step 1: Analyze empty array case

   If arr is empty, arr.length = 0, left and right indices are 1 and 2, both >= length, so no swaps.

2. Step 2: Check access at arr[index]

   No accesses occur because child indices out of bounds and && short-circuits prevent evaluating arr[largest]. Function handles empty array safely.

3. Final Answer:

   No bug; function handles empty array correctly -> Option B

4. Quick Check:

   Check array length before accessing index [OK]

Hint: Always check array length before accessing indices [OK]

Common Mistakes:

• Assuming recursion stops automatically
• Ignoring empty array edge case
• Not validating index bounds

5. You have a max-heap represented as [50, 30, 40, 10, 20, 35]. After extracting the maximum and performing bubble down, what is the final heap array?

hard

A. [40, 30, 35, 10, 20]

B. [40, 30, 35, 20, 10]

C. [40, 35, 30, 10, 20]

D. [35, 30, 40, 10, 20]

Solution

1. Step 1: Extract max and replace root

   Remove 50 (root), move last element 35 to root: [35, 30, 40, 10, 20]

2. Step 2: Bubble down 35

   Compare 35 with children 30 and 40. Largest child is 40 at index 2. Swap 35 and 40: [40, 30, 35, 10, 20]. Now 35 at index 2 has children beyond array length, so stop.

3. Final Answer:

   [40, 30, 35, 10, 20] -> Option A

4. Quick Check:

   Bubble down swaps with largest child in max-heap [OK]

Hint: Swap root with largest child until heap property restored [OK]

Common Mistakes:

• Swapping with smaller child
• Not moving last element to root
• Stopping bubble down too early