HEAP11 - Editorial

editorial
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Problem Link - Find Kth Largest element

Problem Statement:

You are given an array A of n integers and an integer k. The task is to find and print the k-th largest element in the array using a Max Heap. A Max Heap has already been implemented to help you solve this problem.

Approach:

The key idea of this solution is to use a Max Heap to efficiently find the k-th largest element in the array. A Max Heap always has the largest element at the top, which helps us extract the largest elements in descending order.

Here’s how the approach works:

  1. Heap Insertion: Insert each element from the array into the heap using the insert() function, maintaining the heap property where the parent is greater than its children.

  2. Remove Largest Elements: Remove the largest element from the heap k-1 times using the delete_from_heap() function. This ensures that the root of the heap now holds the k-th largest element.

  3. Heapify: After removing an element, Heapify() restores the heap property by pushing down the swapped element to its correct position.

  4. Final Output: The root of the heap now holds the k-th largest element, which is printed.

This approach leverages heap properties for efficient extraction of the largest elements.

Time Complexity:

  • Heap Insertion: Each insertion takes O(log n) time due to bubbling up, so inserting n elements takes O(n log n).

  • Deleting from Heap: Each deletion also takes O(log n) due to bubbling down, so deleting k-1 elements takes O(k log n).

Space Complexity:

  • O(n) since we use a heap to store all n elements from the array.