> For the complete documentation index, see [llms.txt](https://liuzhenglaichn.gitbook.io/algorithm/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://liuzhenglaichn.gitbook.io/algorithm/array/quick-select.md).

# Quick Select

Quickselect is a selection algorithm to find the k-th smallest/largest element in an unordered list. It uses the `partition` method in Quick Sort. The difference is, instead of recurring for both sides (after finding pivot), it recurs only for the part that contains the k-th smallest/largest element.

The time complexity is `O(N)` on average, and `O(N^2)` in the worst case.

## Implementation

Quick select with elements sorted in ascending order.

```cpp
// OJ: https://leetcode.com/problems/kth-largest-element-in-an-array/
// Author: github.com/lzl124631x
// Time: O(N) on averge, O(N^2) in the worst case
// Space: O(1)
class Solution {
    int partition(vector<int> &A, int L, int R) {
        int i = L, pivotIndex = L + rand() % (R - L + 1), pivot = A[pivotIndex];
        swap(A[pivotIndex], A[R]);
        for (int j = L; j < R; ++j) {
            if (A[j] < pivot) swap(A[i++], A[j]);
        }
        swap(A[i], A[R]);
        return i;
    }
public:
    int findKthLargest(vector<int>& A, int k) {
        int L = 0, R = A.size() - 1;
        k = A.size() - k + 1;
        while (true) {
            int M = partition(A, L, R);
            if (M + 1 == k) return A[M];
            if (M + 1 > k) R = M - 1;
            else L = M + 1;
        }
    }
};
```

Quick select with elements sorted in descending order.

```cpp
// OJ: https://leetcode.com/problems/kth-largest-element-in-an-array/
// Author: github.com/lzl124631x
// Time: O(N) on averge, O(N^2) in the worst case
// Space: O(1)
class Solution {
    int partition(vector<int> &A, int L, int R) {
        int i = L, pivotIndex = L + rand() % (R - L + 1), pivot = A[pivotIndex];
        swap(A[pivotIndex], A[R]);
        for (int j = L; j < R; ++j) {
            if (A[j] > pivot) swap(A[i++], A[j]);
        }
        swap(A[i], A[R]);
        return i;
    }
public:
    int findKthLargest(vector<int>& A, int k) {
        int L = 0, R = A.size() - 1;
        while (true) {
            int M = partition(A, L, R);
            if (M + 1 == k) return A[M];
            if (M + 1 > k) R = M - 1;
            else L = M + 1;
        }
    }
};
```

Or STL

```cpp
// OJ: https://leetcode.com/problems/kth-largest-element-in-an-array/
// Author: github.com/lzl124631x
// Time: O(N) on average, O(N^2) in the worst case
// Space: O(1)
class Solution {
public:
    int findKthLargest(vector<int>& A, int k) {
        nth_element(begin(A), begin(A) + k - 1, end(A), greater<int>());
        return A[k - 1];
    }
};
```

## Reference

* [Quickselect Algorithm - GeeksforGeeks](https://www.geeksforgeeks.org/quickselect-algorithm/)

## Problems

* [215. Kth Largest Element in an Array (Medium)](https://leetcode.com/problems/kth-largest-element-in-an-array/)
* [973. K Closest Points to Origin (Medium)](https://leetcode.com/problems/k-closest-points-to-origin/)
* [1471. The k Strongest Values in an Array (Medium)](https://leetcode.com/problems/the-k-strongest-values-in-an-array/)


---

# Agent Instructions
This documentation is published with GitBook. GitBook is the documentation platform designed so that both humans and AI agents can read, navigate, and reason over technical content effectively. Learn more at gitbook.com.

## Querying This Documentation
If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter, and the optional `goal` query parameter:

```
GET https://liuzhenglaichn.gitbook.io/algorithm/array/quick-select.md?ask=<question>&goal=<endgoal>
```

`ask` is the immediate question: it should be specific, self-contained, and written in natural language.
`goal` is optional and describes the broader end goal you are ultimately trying to accomplish on behalf of the user. GitBook uses it to tailor the answer towards what is most useful for that goal.

The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.