Problem Statement
Element Rank Finder
You're analyzing a dataset and need to find the kth largest value without fully sorting the data.
Given an integer array nums and an integer k, return the kth largest element in the array.
Note that it is the kth largest element in the sorted order, not the kth distinct element.
Can you solve it without sorting the entire array?
Examples
Example 1:
Input: nums = [3,2,1,5,6,4], k = 2
Output: 5
Explanation: The elements in descending order are [6,5,4,3,2,1]. The 2nd largest element is 5.
Example 2:
Input: nums = [3,2,3,1,2,4,5,5,6], k = 4
Output: 4
Explanation: The elements in descending order are [6,5,5,4,3,3,2,2,1]. The 4th largest element is 4.
Constraints
- 1 <= k <= nums.length <= 10^5
- -10^4 <= nums[i] <= 10^4
Problem Breakdown
To solve this problem, we need to:
- The kth largest element is the element that would be at index k-1 in the array sorted in descending order
- We don't need to sort the entire array to find the kth largest element
- A min heap of size k can efficiently maintain the k largest elements
- The QuickSelect algorithm can find the kth largest element in O(n) average time
- Duplicate elements count as separate elements for ranking purposes
- This problem is a classic application of selection algorithms
String Problems
Learning Objective
Apply string manipulation concepts to solve a real-world problem.
Element Rank Finder
You're analyzing a dataset and need to find the kth largest value without fully sorting the data.
Given an integer array nums and an integer k, return the kth largest element in the array.
Note that it is the kth largest element in the sorted order, not the kth distinct element.
Can you solve it without sorting the entire array?
Examples
Example 1:
The elements in descending order are [6,5,4,3,2,1]. The 2nd largest element is 5.
Example 2:
The elements in descending order are [6,5,5,4,3,3,2,2,1]. The 4th largest element is 4.
Problem Breakdown
Constraints:
- 1 <= k <= nums.length <= 10^5
- -10^4 <= nums[i] <= 10^4
Key Insights:
The kth largest element is the element that would be at index k-1 in the array sorted in descending order
We don't need to sort the entire array to find the kth largest element
A min heap of size k can efficiently maintain the k largest elements
The QuickSelect algorithm can find the kth largest element in O(n) average time
Duplicate elements count as separate elements for ranking purposes
This problem is a classic application of selection algorithms
Real-World Application
This problem has several practical applications:
Data Analysis
Finding top-k elements in datasets without sorting the entire dataset.
Search Algorithms
Implementing efficient search algorithms that don't require complete sorting.
Database Systems
Optimizing top-k queries in database management systems.
Randomized Algorithms
Applying randomized selection techniques in various computational problems.