Kth Largest Element In An Array Leetcode Problem 215 [Python Solution]
In this blog post, we'll tackle the LeetCode problem 215: Kth Largest Element in an Array.
This problem falls under the category of heap and priority queue, and it's considered a medium difficulty problem.
The goal is to find the kth largest element in an integer array.
You might think that the most straightforward solution is to sort the array and then return the kth largest element.
While this is a valid approach, we'll explore more efficient methods to solve this problem.
We'll dive into the quick select algorithm, which provides an average time complexity of O(n)
, making it more efficient than sorting for large datasets.
Let's begin by understanding the problem and its constraints.
Problem Overview
You are given an integer array nums
and an integer k
.
Your task is to return the kth largest element in the array.
Note that "kth largest" refers to the kth largest element in sorted order, not necessarily the kth distinct element.
Example 1:
Input: nums = [3, 2, 1, 5, 6, 4], k = 2
Output: 5
Example 2:
Input: nums = [3, 2, 3, 1, 2, 4, 5, 5, 6], k = 4
Output: 4
Constraints:
- 1 <= k <=
nums.length
<= 105 - -104 <=
nums[i]
<= 104
Now, let's delve into the "Quick Select" algorithm, which offers a more efficient solution to this problem.
Understanding Quick Select Constraints
Quick Select is an algorithm that allows us to find the kth largest element in an unsorted array efficiently.
It has an average time complexity of O(n)
, making it a strong candidate for solving the problem.
Here are the key steps of Quick Select:
- Choose a pivot element (in this case, we'll choose the rightmost element).
- Partition the array into two halves: elements less than or equal to the pivot on the left and elements greater than the pivot on the right.
- Determine the position of the pivot in the sorted order.
- Recursively apply Quick Select to the left or right subarray based on the position of the pivot.
In this algorithm, the pivot's position is critical.
If we find that the pivot is at index k, we have found the kth largest element.
If k is smaller, we search in the left subarray; if k is larger, we search in the right subarray.
Let's implement this algorithm in Python and explore two efficient solutions: one using sorting and the other using Quick Select.
Kth Largest Element In An Array LeetCode Problem Solution
1. Bruteforce Approach
We will start with a straightforward approach: sorting the array and returning the kth largest element.
While this approach has a time complexity of O(n*log(n)
), it is a good baseline to compare the efficiency of our other solutions.
class Solution1:
def findKthLargest(self, nums, k):
nums.sort()
return nums[len(nums) - k]
The sorting approach is clear and simple, but it might not be optimal for large arrays.
Let's explore more efficient solutions.
2. Efficient Approach: Quick Select
Now, we'll implement the Quick Select algorithm, which allows us to find the kth largest element efficiently.
class Solution2:
def partition(self, nums, left, right):
pivot, p = nums[right], left
for i in range(left, right):
if nums[i] <= pivot:
nums[p], nums[i] = nums[i], nums[p]
p += 1
nums[p], nums[right] = nums[right], nums[p]
return p
def findKthLargest(self, nums, k):
k = len(nums) - k
left, right = 0, len(nums) - 1
while left < right:
pivot = self.partition(nums, left, right)
if pivot < k:
left = pivot + 1
elif pivot > k:
right = pivot - 1
else:
break
return nums[k]
The Solution2
class contains the efficient Quick Select algorithm.
Here's a breakdown of the code:
- The
partition
method is responsible for partitioning the array into two halves, just as we discussed earlier.
It takes three parameters: nums
, left
, and right
, and returns the position of the pivot.
- The
findKthLargest
method initiates the Quick Select process.
It sets k
to the index we're looking for in the sorted order (kth largest).
It maintains two pointers, left
and right
, which define the current subarray being processed.
- Inside the loop, the
partition
method is used to determine the position of the pivot element.
If the pivot's position is less than k
, we narrow the search to the right subarray by updating left
.
If the pivot's position is greater than k
, we narrow the search to the left subarray by updating right
.
If we find that the pivot's position is exactly k
, we've located the kth largest element.
This efficient approach uses the Quick Select algorithm, which provides an average time complexity of O(n)
.
It's a great alternative to sorting, especially for large datasets.
Time and Space Complexity
Let's analyze the time and space complexity of the two solutions:
Bruteforce Approach (Solution1):
- Time Complexity:
- Best Case:
O(n)
- Average Case:
O(n*log(n)
) - Worst Case:
O(n*log(n)
)
- Best Case:
- Space Complexity:
O(n)
for the sorted array
Efficient Approach (Quick Select – Solution2):
- Time Complexity:
- Best Case:
O(n)
- Average Case:
O(n)
- Worst Case:
O(n^2)
(uncommon, but it can happen)
- Best Case:
- Space Complexity:
O(1)
(in-place algorithm)
The efficient Quick Select algorithm provides an average time complexity of O(n)
, which is significantly faster than the sorting approach for large arrays.
While the worst-case time complexity of O(n^2)
is possible, it is rare in practice.
Quick Select is a powerful algorithm that balances efficiency and simplicity.
Reasoning Behind Our Approach
We've explored two different approaches to solve the Kth Largest Element in an Array problem.
The first approach uses sorting, which is a straightforward but not the most efficient method.
Sorting the array first takes O(n*log(n)
) time, and then we find the kth largest element, which is also O(n)
.
So, the overall time complexity is O(n*log(n)
).
The second approach, Quick Select, is a more efficient algorithm for this problem.
It has an average time complexity of O(n)
and works by selecting a pivot element and partitioning the array.
We recursively search in the left or right subarray based on the pivot's position.
Quick Select is a great choice when we need to find the kth largest or smallest element in an unsorted array.
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Conclusion
In this blog post, we've explored the LeetCode problem 215: Kth Largest Element in an Array.
We've discussed two different approaches to solving this problem: a sorting approach and the efficient Quick Select algorithm.
While sorting is a straightforward solution, Quick Select provides a more efficient way to find the kth largest element in an unsorted array.
Its average time complexity of O(n)
makes it a powerful choice, especially for large datasets.
Remember that understanding and implementing algorithms like Quick Select is crucial for solving a wide range of programming problems.
It's a valuable addition to your toolkit as a programmer.
Practice and explore more problems to sharpen your problem-solving skills.