How do you solve Kth Largest Element in an Array on LeetCode?

Kth Largest Element in an Array (LeetCode #215) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n log k) time complexity and O(k) space complexity. Key insight: Using a heap allows us to efficiently track the largest elements without sorting the entire array.

What is the time complexity of Kth Largest Element in an Array?

The optimal solution for Kth Largest Element in an Array runs in O(n log k) time and uses O(k) space. Maintaining a heap of size k takes O(log k) time for each of the n elements, resulting in O(n log k) overall. We use O(k) space for the heap.

What is the brute force solution for Kth Largest Element in an Array?

The brute force approach for Kth Largest Element in an Array is Brute Force, with O(n log n) time complexity and O(1) space complexity. The simplest way to find the k-th largest element is to sort the array and then access the element at the appropriate index. This is straightforward but not efficient for large arrays. The optimal Optimal Solution approach improves this to O(n log k).

What are the interview tips for Kth Largest Element in an Array?

Always clarify the problem statement to ensure you understand the requirements. Discuss your thought process and potential approaches before diving into coding. Consider edge cases and test your solution with different inputs.

What are common mistakes when solving Kth Largest Element in an Array?

Confusing k-th largest with k-th distinct element. Not handling edge cases where k equals the length of the array.

#215

Kth Largest Element in an Array

Medium

ArrayDivide and ConquerSortingHeap (Priority Queue)QuickselectHeapSortingQuickselect

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Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n log n)	O(n log k)
Space	O(1)	O(k)

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Intuition

Time O(n log k)Space O(k)

We can find the k-th largest element without fully sorting the array using a min-heap. By maintaining a heap of size k, we can efficiently track the largest k elements.

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Algorithm

4 steps

1Step 1: Create a min-heap of size k.
2Step 2: Iterate through the array, adding elements to the heap.
3Step 3: If the heap exceeds size k, remove the smallest element (the root of the heap).
4Step 4: After processing all elements, the root of the heap is the k-th largest element.

solution.py5 lines

1# Full working Python code
2import heapq
3
4def findKthLargest(nums, k):
5    return heapq.nlargest(k, nums)[-1]

ℹ

Complexity note: Maintaining a heap of size k takes O(log k) time for each of the n elements, resulting in O(n log k) overall. We use O(k) space for the heap.

1Using a heap allows us to efficiently track the largest elements without sorting the entire array.
2The k-th largest element can be found in linear time using Quickselect, which is another optimal approach.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.