Search
⌘K
Get Premium
Heap
Kth Largest Element in an Array
medium
Count: 10
DESCRIPTION (inspired by Leetcode.com)
Write a function that takes an array of unsorted integers nums and an integer k, and returns the kth largest element in the array. This function should run in O(n log k) time, where n is the length of the array.
Example 1:
Inputs:
nums = [5, 3, 2, 1, 4] k = 2
Output:
4
Explanation
Approach 1: Sorting
The simplest approach is to sort the array in descending order and return the kth element. This approach has a time complexity of O(n log n) where n is the number of elements in the array, and a space complexity of O(1).
Approach 2: Min Heap
By using a min-heap, we can reduce the time complexity to O(n log k), where n is the number of elements in the array and k is the value of k.
The idea behind this solution is to iterate over the elements in the array while storing the k largest elements we've seen so far in a min-heap. At each element, we check if it is greater than the smallest element (the root) of the heap. If it is, we pop the smallest element from the heap and push the current element into the heap. This way, the heap will always contain the k largest elements we've seen so far.
After iterating over all the elements, the root of the heap will be the kth largest element in the array.
Solution
Try these examples:
Visualization
Python
def kth_largest(nums, k):if not nums:returnheap = []for num in nums:if len(heap) < k:heapq.heappush(heap, num)elif num > heap[0]:heapq.heappushpop(heap, num)return heap[0]
kth largest element in an array
0 / 10
Test Your Knowledge
Login to take the complexity quiz and track your progress
Complexity Analysis
Time Complexity: O(n log k) where n is the number of elements in the array and k is the input parameter. We iterate over all elements, and in the worst case, we both push and pop each element from the heap, which takes O(log k) time per element.
Space Complexity: O(k) where k is the input parameter. The space is used by the heap to store the k largest elements.
Mark as read
Unlock Premium Coding Content
Reading Progress
On This Page
Your account is free and you can post anonymously if you choose.