Min Heap vs Max Heap When to Use Which in DSA Typescript - Interactive Comparison Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to create a Min Heap by choosing the correct comparison operator.

DSA Typescript

class MinHeap {
  heap: number[] = [];

  insert(value: number) {
    this.heap.push(value);
    this.bubbleUp(this.heap.length - 1);
  }

  bubbleUp(index: number) {
    while (index > 0) {
      const parentIndex = Math.floor((index - 1) / 2);
      if (this.heap[index] [1] this.heap[parentIndex]) {
        [this.heap[index], this.heap[parentIndex]] = [this.heap[parentIndex], this.heap[index]];
        index = parentIndex;
      } else {
        break;
      }
    }
  }
}

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

A>

B===

C<

D>=

Attempts:

3 left

💡 Hint

Common Mistakes

Using '>' instead of '<' causes a Max Heap behavior.

Using '===' does not maintain heap property.

In a Min Heap, the child node should be smaller than the parent node to maintain the heap property. So, we swap when the child is less than the parent.

2fill in blank

medium

Complete the code to create a Max Heap by choosing the correct comparison operator.

DSA Typescript

class MaxHeap {
  heap: number[] = [];

  insert(value: number) {
    this.heap.push(value);
    this.bubbleUp(this.heap.length - 1);
  }

  bubbleUp(index: number) {
    while (index > 0) {
      const parentIndex = Math.floor((index - 1) / 2);
      if (this.heap[index] [1] this.heap[parentIndex]) {
        [this.heap[index], this.heap[parentIndex]] = [this.heap[parentIndex], this.heap[index]];
        index = parentIndex;
      } else {
        break;
      }
    }
  }
}

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

A>

B<

C<=

D===

Attempts:

3 left

💡 Hint

Common Mistakes

Using '<' instead of '>' causes a Min Heap behavior.

Using '===' does not maintain heap property.

In a Max Heap, the child node should be greater than the parent node to maintain the heap property. So, we swap when the child is greater than the parent.

3fill in blank

hard

Fix the error in the code that removes the root from a Min Heap by choosing the correct method to restore heap property.

DSA Typescript

class MinHeap {
  heap: number[] = [];

  removeRoot() {
    if (this.heap.length === 0) return null;
    const root = this.heap[0];
    this.heap[0] = this.heap.pop()!;
    this.[1](0);
    return root;
  }

  bubbleDown(index: number) {
    // Implementation omitted
  }
}

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

AbubbleDown

Bheapify

CbubbleUp

Dsort

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'bubbleUp' after removing root causes incorrect heap structure.

Using 'sort' is inefficient and not specific to heap.

After removing the root, we need to restore the heap property by moving the new root down if needed. This is done by 'bubbleDown'.

4fill in blank

hard

Fill both blanks to complete the condition that decides when to swap nodes during bubbleDown in a Max Heap.

DSA Typescript

bubbleDown(index: number) {
  const left = 2 * index + 1;
  const right = 2 * index + 2;
  let largest = index;

  if (left < this.heap.length && this.heap[left] [1] this.heap[largest]) {
    largest = left;
  }

  if (right < this.heap.length && this.heap[right] [2] this.heap[largest]) {
    largest = right;
  }

  if (largest !== index) {
    [this.heap[index], this.heap[largest]] = [this.heap[largest], this.heap[index]];
    this.bubbleDown(largest);
  }
}

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

A>

B<

C>=

D<=

Attempts:

3 left

💡 Hint

Common Mistakes

Using '<' causes Min Heap behavior.

Using '>=' or '<=' may cause unnecessary swaps.

In a Max Heap, during bubbleDown, we swap with the child that is greater than the current node to maintain the heap property.

5fill in blank

hard

Fill all three blanks to create a function that returns the root element of a Min Heap without removing it.

DSA Typescript

peek(): number | null {
  if (this.heap.length === 0) {
    return [1];
  }
  return this.heap[[2]];
  // The root is at index [3]
}

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

Aundefined

B0

Dnull

Attempts:

3 left

💡 Hint

Common Mistakes

Returning undefined instead of null for empty heap.

Using wrong index for root element.

If the heap is empty, we return null. The root element is always at index 0 in a heap.

Practice

1. What is the main difference between a Min Heap and a Max Heap?

easy

A. Min Heap stores elements in ascending order, Max Heap stores elements in descending order.

B. Min Heap always has the smallest element at the root, Max Heap has the largest at the root.

C. Min Heap is used only for numbers, Max Heap only for strings.

D. Min Heap and Max Heap are the same data structure with different names.

Solution

1. Step 1: Understand heap root property

   A Min Heap keeps the smallest element at the root, while a Max Heap keeps the largest element at the root.

2. Step 2: Compare heap ordering

   Min Heap ensures parent nodes are smaller than children; Max Heap ensures parent nodes are larger than children.

3. Final Answer:

   Min Heap always has the smallest element at the root, Max Heap has the largest at the root. -> Option B

4. Quick Check:

   Heap root property = Min smallest, Max largest [OK]

Hint: Min root is smallest, Max root is largest [OK]

Common Mistakes:

• Confusing heap ordering with sorted arrays
• Thinking Min Heap stores ascending order fully
• Assuming heaps only store numbers

2. Which of the following is the correct TypeScript syntax to create a Min Heap using a priority queue library?

easy

A. const minHeap = new PriorityQueue((a, b) => a > b);

B. const minHeap = new PriorityQueue((a, b) => b < a);

C. const minHeap = new PriorityQueue((a, b) => a === b);

D. const minHeap = new PriorityQueue((a, b) => a < b);

Solution

1. Step 1: Understand comparator for Min Heap

   Min Heap comparator returns true if first element is less than second to keep smallest on top.

2. Step 2: Match comparator syntax

   The comparator (a, b) => a < b correctly orders elements for a Min Heap.

3. Final Answer:

   const minHeap = new PriorityQueue((a, b) => a < b); -> Option D

4. Quick Check:

   Min Heap comparator uses < for ordering [OK]

Hint: Min Heap comparator uses less than operator [OK]

Common Mistakes:

• Using greater than comparator for Min Heap
• Using equality comparator which breaks ordering
• Reversing comparator logic

3. Given the following TypeScript code using a Max Heap, what will be the output after inserting elements 3, 10, 5, 1?

medium

A. [10, 5, 3, 1]

B. [1, 3, 5, 10]

C. [3, 1, 5, 10]

D. [5, 10, 3, 1]

Solution

1. Step 1: Insert elements into Max Heap

   Insert 3, then 10 (bubbles up to root), then 5, then 1. Max Heap root is largest element.

2. Step 2: Visualize heap array after insertions

   Heap array after insertions: root 10, children 5 and 3, last element 1.

3. Final Answer:

   [10, 5, 3, 1] -> Option A

4. Quick Check:

   Max Heap root largest = 10 [OK]

Hint: Max Heap root is largest inserted element [OK]

Common Mistakes:

• Assuming insertion order equals array order
• Confusing Min Heap output with Max Heap
• Ignoring heap property after insertions

4. You wrote this TypeScript code to create a Min Heap but it behaves like a Max Heap. What is the bug?

const heap = new PriorityQueue((a, b) => a > b);
heap.insert(4);
heap.insert(2);
heap.insert(7);
console.log(heap.peek());

medium

A. peek() returns wrong element, use pop() instead.

B. Insert method is incorrect, should be insertMin.

C. Comparator should use < instead of > for Min Heap.

D. PriorityQueue class does not support comparator functions.

Solution

1. Step 1: Analyze comparator function

   The comparator (a, b) => a > b causes Max Heap behavior because it prioritizes larger elements.

2. Step 2: Correct comparator for Min Heap

   To get Min Heap behavior, comparator must be (a, b) => a < b so smaller elements rise to top.

3. Final Answer:

   Comparator should use < instead of > for Min Heap. -> Option C

4. Quick Check:

   Min Heap comparator uses < operator [OK]

Hint: Min Heap comparator must use less than [OK]

Common Mistakes:

• Using wrong comparator sign
• Confusing peek() with pop()
• Assuming insert method name affects heap type

5. You need to efficiently find the top 3 smallest numbers from a large stream of data. Which heap type and approach is best?

hard

A. Use a Max Heap of size 3 to keep track of smallest numbers seen so far.

B. Use a Min Heap of size 3 to keep track of smallest numbers seen so far.

C. Use a Max Heap of full data to sort all numbers then pick top 3.

D. Use a Min Heap of full data to sort all numbers then pick top 3.

Solution

1. Step 1: Understand problem requirement

   We want top 3 smallest numbers from a large stream without storing all data.

2. Step 2: Choose heap type and size

   Use a Max Heap of size 3 to keep the current smallest 3 numbers. If new number is smaller than heap root, replace root.

3. Step 3: Why Max Heap?

   Max Heap root is largest among the 3 smallest, so it is easy to discard larger numbers efficiently.

4. Final Answer:

   Use a Max Heap of size 3 to keep track of smallest numbers seen so far. -> Option A

5. Quick Check:

   Top k smallest = Max Heap size k [OK]

Hint: Use max heap size k to track k smallest [OK]

Common Mistakes:

• Using Min Heap size k which grows too large
• Sorting full data which is inefficient
• Using wrong heap type for top k smallest