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

Practice - 5 Tasks

1fill in blank

easy

Complete the code to insert an element into a min heap using C++ STL.

DSA C++

std::priority_queue<int, std::vector<int>, [1]> minHeap;
minHeap.push(10);

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

Astd::greater<int>

Bstd::less<int>

Cstd::equal_to<int>

Dstd::not_equal_to<int>

Attempts:

3 left

💡 Hint

Common Mistakes

Using std::less creates a max heap, not a min heap.

To create a min heap in C++, use std::greater<int> as the comparison function.

2fill in blank

medium

Complete the code to get the top element from a max heap.

DSA C++

std::priority_queue<int> maxHeap;
maxHeap.push(20);
int topElement = maxHeap.[1]();

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

Afront

Bpop

Ctop

Dpeek

Attempts:

3 left

💡 Hint

Common Mistakes

Using pop() instead of top() to access the element.

The top() function returns the highest priority element in the heap without removing it.

3fill in blank

hard

Fix the error in the code to create a max heap that stores pairs and sorts by the first element.

DSA C++

std::priority_queue<std::pair<int, int>, std::vector<std::pair<int, int>>, [1]> pq;
pq.push({2, 5});

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

Astd::greater<std::pair<int, int>>

Bstd::greater<int>

Cstd::less<int>

Dstd::less<std::pair<int, int>>

Attempts:

3 left

💡 Hint

Common Mistakes

Using comparators for int instead of pair.

For a max heap of pairs sorted by the first element, use std::less<std::pair<int, int>> which is the default comparator.

4fill in blank

hard

Fill both blanks to create a min heap that stores integers and check if the heap is empty.

DSA C++

std::priority_queue<int, std::vector<int>, [1]> minHeap;
if (minHeap.[2]()) {
    std::cout << "Heap is empty";
}

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

Astd::greater<int>

Bempty

Csize

Dstd::less<int>

Attempts:

3 left

💡 Hint

Common Mistakes

Using std::less for min heap or size() to check emptiness.

Use std::greater<int> for min heap and empty() to check if the heap has no elements.

5fill in blank

hard

Fill all three blanks to create a max heap of pairs, push a pair, and get the top pair's first element.

DSA C++

std::priority_queue<std::pair<int, int>, std::vector<std::pair<int, int>>, [1]> pq;
pq.push({3, 7});
int maxFirst = pq.[2]().[3];

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

Astd::less<std::pair<int, int>>

Btop

Cfirst

Dstd::greater<std::pair<int, int>>

Attempts:

3 left

💡 Hint

Common Mistakes

Using std::greater for max heap or pop() instead of top().

Use std::less<std::pair<int, int>> for max heap of pairs, top() to access the top element, and first to get the first value of the pair.

Practice

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

easy

A. Min Heap and Max Heap have the same structure but different sizes

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

C. Min Heap is used only for sorting, Max Heap is used only for searching

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

Solution

1. Step 1: Understand heap root property

   In a Min Heap, the root node is the smallest element. In a Max Heap, the root node is the largest element.

2. Step 2: Compare heap ordering

   Min Heap ensures the smallest element is always accessible at the top, Max Heap ensures the largest is accessible at the top.

3. Final Answer:

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

4. Quick Check:

   Root element defines Min or Max Heap [OK]

Hint: Root holds smallest in Min, largest in Max [OK]

Common Mistakes:

• Confusing heap order with sorted order
• Thinking heaps store elements fully sorted
• Assuming Min and Max Heaps differ in size

2. Which of the following is the correct way to declare a Max Heap using C++ STL?

easy

A. priority_queue maxHeap;

B. priority_queue maxHeap;

C. priority_queue<int> maxHeap;

D. priority_queue maxHeap;

Solution

1. Step 1: Recall default priority_queue behavior

   By default, C++ STL priority_queue is a Max Heap using less<int> comparator.

2. Step 2: Analyze options

   Options with greater<int> comparator create Min Heaps. Options with list<int> container do not work because priority_queue requires a random-access container like vector. The default priority_queue<int> maxHeap; creates a Max Heap.

3. Final Answer:

   priority_queue<int> maxHeap; -> Option C

4. Quick Check:

   Default priority_queue is Max Heap [OK]

Hint: Default priority_queue is Max Heap in C++ [OK]

Common Mistakes:

• Using greater<int> for Max Heap
• Confusing vector and list as container types
• Adding unnecessary comparator for Max Heap

3. What will be the output of the following C++ code snippet?

std::priority_queue minHeap;
minHeap.push(10);
minHeap.push(5);
minHeap.push(20);
std::cout << minHeap.top();

medium

A. 5

B. 20

C. 10

D. Compilation error

Solution

1. Step 1: Understand heap type from declaration

   The priority_queue uses std::greater<int>, so it behaves as a Min Heap.

2. Step 2: Insert elements and check top

   Elements inserted: 10, 5, 20. In Min Heap, top() returns smallest element, which is 5.

3. Final Answer:

   5 -> Option A

4. Quick Check:

   Min Heap top() = smallest element [OK]

Hint: greater<int> means Min Heap, top() returns smallest [OK]

Common Mistakes:

• Assuming top() returns largest always
• Confusing comparator direction
• Thinking output is insertion order

4. Identify the error in the following code that tries to create a Min Heap in C++ STL:

std::priority_queue<int> minHeap;
minHeap.push(3);
minHeap.push(1);
minHeap.push(2);
std::cout << minHeap.top();

medium

A. priority_queue default is Max Heap, so top() returns largest, not smallest

B. No error, code correctly creates a Min Heap

C. Missing include for vector container

D. Cannot push elements into priority_queue

Solution

1. Step 1: Check default behavior of priority_queue

   By default, priority_queue is a Max Heap, so top() returns the largest element.

2. Step 2: Analyze code output

   Elements pushed: 3, 1, 2. top() will return 3 (largest), not 1 (smallest). So it is not a Min Heap.

3. Final Answer:

   priority_queue default is Max Heap, so top() returns largest, not smallest -> Option A

4. Quick Check:

   Default priority_queue is Max Heap [OK]

Hint: Default priority_queue is Max Heap, needs comparator for Min Heap [OK]

Common Mistakes:

• Assuming default priority_queue is Min Heap
• Ignoring comparator requirement
• Thinking top() returns insertion order

5. You want to efficiently find the median of a stream of numbers using heaps. Which combination of heaps is best suited for this task?

hard

A. Use one Min Heap for smaller half and one Max Heap for larger half

B. Use one Max Heap for smaller half and one Min Heap for larger half

C. Use two Max Heaps to store all numbers

D. Use two Min Heaps to store all numbers

Solution

1. Step 1: Understand median finding with heaps

   To find median efficiently, split numbers into two halves: smaller and larger.

2. Step 2: Assign heaps to halves

   Use a Max Heap to store the smaller half (to get max of smaller half quickly) and a Min Heap to store the larger half (to get min of larger half quickly).

3. Step 3: Median calculation

   If sizes are equal, median is average of top elements of both heaps; else top of the heap with more elements.

4. Final Answer:

   Use one Max Heap for smaller half and one Min Heap for larger half -> Option B

5. Quick Check:

   Max Heap for smaller, Min Heap for larger half [OK]

Hint: Max Heap for smaller half, Min Heap for larger half [OK]

Common Mistakes:

• Using two Max Heaps or two Min Heaps
• Reversing heap roles for halves
• Not balancing heap sizes