Kth Largest Element Using Max Heap in DSA C++ - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to push elements into the max heap.

DSA C++

std::priority_queue<int> maxHeap;
for (int num : nums) {
    maxHeap.[1](num);
}

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

Atop

Bpop

Cpush

Dempty

Attempts:

3 left

💡 Hint

Common Mistakes

Using pop() instead of push() to add elements.

Trying to access top() to add elements.

Checking empty() instead of adding elements.

We use push() to add elements to the max heap.

2fill in blank

medium

Complete the code to remove the largest element from the max heap.

DSA C++

if (!maxHeap.empty()) {
    maxHeap.[1]();
}

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

Apush

Bempty

Ctop

Dpop

Attempts:

3 left

💡 Hint

Common Mistakes

Using push() instead of pop() to remove elements.

Trying to access top() to remove elements.

Calling empty() which only checks if heap is empty.

pop() removes the largest element from the max heap.

3fill in blank

hard

Fix the error in accessing the largest element from the max heap.

DSA C++

int largest = maxHeap.[1]();

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

Apop

Btop

Cpush

Dempty

Attempts:

3 left

💡 Hint

Common Mistakes

Using pop() which removes the element instead of accessing it.

Using push() which adds elements.

Using empty() which returns a boolean.

top() returns the largest element without removing it.

4fill in blank

hard

Fill both blanks to extract the kth largest element using the max heap.

DSA C++

for (int i = 1; i < [1]; ++i) {
    maxHeap.[2]();
}

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

Ak

Bpop

Cpush

Dsize

Attempts:

3 left

💡 Hint

Common Mistakes

Using push() instead of pop() inside the loop.

Looping up to size instead of k.

Using wrong variable names.

We pop the largest element k-1 times to reach the kth largest.

5fill in blank

hard

Fill all three blanks to complete the function that returns the kth largest element.

DSA C++

int findKthLargest(std::vector<int>& nums, int [1]) {
    std::priority_queue<int> maxHeap;
    for (int num : nums) {
        maxHeap.[2](num);
    }
    for (int i = 1; i < [3]; ++i) {
        maxHeap.pop();
    }
    return maxHeap.top();
}

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

Ak

Bpush

Dsize

Attempts:

3 left

💡 Hint

Common Mistakes

Using size instead of k for the loop.

Using pop() instead of push() to add elements.

Incorrect parameter name.

Parameter k is used to control the loop and push adds elements to the heap.

Practice

1. What is the main idea behind finding the kth largest element using a max heap?

easy

A. Use a hash map to count frequencies and find the kth largest

B. Build a max heap from the array and extract the maximum element k times

C. Sort the array and pick the kth element from the start

D. Build a min heap and extract the minimum element k times

Solution

1. Step 1: Understand max heap property

   A max heap always keeps the largest element at the root, so extracting the root gives the current largest element.

2. Step 2: Extract max k times

   By removing the root k times, the last extracted element is the kth largest.

3. Final Answer:

   Build max heap and extract max k times -> Option B

4. Quick Check:

   Max heap extraction = kth largest element [OK]

Hint: Extract max from max heap k times to get kth largest [OK]

Common Mistakes:

• Using min heap instead of max heap
• Sorting and picking wrong index
• Confusing kth largest with kth smallest

2. Which of the following is the correct C++ syntax to create a max heap from a vector nums in-place?

easy

A. std::priority_queue maxHeap(nums.begin(), nums.end());

B. std::make_heap(nums.begin(), nums.end(), std::greater<int>());

C. std::priority_queue<int> maxHeap(nums.begin(), nums.end());

D. std::make_heap(nums.begin(), nums.end());

Solution

1. Step 1: Understand std::make_heap default behavior

   By default, std::make_heap creates a max heap using operator<.

2. Step 2: Check syntax correctness

   std::make_heap(nums.begin(), nums.end()); correctly calls std::make_heap on the vector range without extra comparators, making a max heap in-place.

3. Final Answer:

   std::make_heap(nums.begin(), nums.end()); -> Option D

4. Quick Check:

   Default make_heap = max heap [OK]

Hint: Use std::make_heap without comparator for max heap [OK]

Common Mistakes:

• Using std::greater<int>() creates min heap
• Incorrect priority_queue constructor usage
• Confusing comparator direction

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

std::vector<int> nums = {3, 2, 1, 5, 6, 4};
std::make_heap(nums.begin(), nums.end());
for (int i = 0; i < 2; ++i) {
  std::pop_heap(nums.begin(), nums.end() - i);
}
int kthLargest = nums[0];
std::cout << kthLargest << std::endl;

medium

A. 4

B. 6

C. 5

D. 3

Solution

1. Step 1: Build max heap from nums

   Heap after make_heap is [6, 5, 4, 2, 3, 1] (largest at front).

2. Step 2: Perform two pop_heap operations

   First pop_heap moves 6 to end, second pop_heap moves 5 next to end. Now, nums[0] is 5.

3. Final Answer:

   5 -> Option C

4. Quick Check:

   After 2 pops, root = 5 [OK]

Hint: After popping max twice, root is 3rd largest [OK]

Common Mistakes:

• Assuming root stays 6 after pops
• Confusing pop_heap with pop_back
• Not adjusting heap size correctly

4. Identify the error in the following code to find the 3rd largest element using a max heap:

std::vector<int> nums = {7, 10, 4, 3, 20, 15};
std::priority_queue<int> maxHeap(nums.begin(), nums.end());
int kthLargest;
for (int i = 0; i < 3; ++i) {
  kthLargest = maxHeap.top();
  maxHeap.pop();
}
std::cout << kthLargest << std::endl;

medium

A. No error, code works correctly

B. Priority queue constructor syntax is incorrect

C. Loop should run k-1 times, not k

D. Must use std::make_heap instead of priority queue

Solution

1. Step 1: Check priority_queue construction

   Constructing maxHeap from vector range is valid and creates max heap.

2. Step 2: Verify loop logic for kth largest

   Loop extracts top element 3 times; last extracted is 3rd largest.

3. Final Answer:

   No error, code works correctly -> Option A

4. Quick Check:

   Priority queue pop k times = kth largest [OK]

Hint: Pop max k times from priority queue to get kth largest [OK]

Common Mistakes:

• Thinking priority_queue constructor is invalid
• Off-by-one error in loop count
• Confusing make_heap and priority_queue usage

5. Given a large array with many duplicate elements, which approach is most efficient to find the 5th largest unique element using a max heap?

hard

A. Use a min heap of size 5 to track unique elements while iterating

B. Sort the array and pick the 5th element from the end

C. Insert all elements into a set, then build a max heap from the set and pop 5 times

D. Build a max heap from the array and pop elements until 5 unique elements are found

Solution

1. Step 1: Efficiency priority

   For large n, O(n log k) is best vs O(n log n); min-heap size k scans once.

2. Step 2: Track unique top-k largest

   Iterate array, maintain min-heap of top 5 uniques (with set for lookup); add if new and > root or size <5, evict root otherwise.

3. Final Answer:

   Use a min heap of size 5 to track unique elements while iterating -> Option A

4. Quick Check:

   Min-heap size k + set = O(n log k) kth unique largest [OK]

Hint: Min heap size k + seen set for kth distinct largest O(n log k) [OK]

Common Mistakes:

• Full max heap pop until k unique (worst O(n log n) with dup leaders)
• Set first: O(n log n) time/space
• Sorting without explicit dedup logic