Quickselect Algorithm

Quickselect is a selection algorithm to find the k-th smallest element in an unordered list. It is related to the quick sort sorting algorithm.
Examples:

Input: arr[] = {7, 10, 4, 3, 20, 15}
k = 3
Output: 7

Input: arr[] = {7, 10, 4, 3, 20, 15}
k = 4
Output: 10

The algorithm is similar to QuickSort. The difference is, instead of recurring for both sides (after finding pivot), it recurs only for the part that contains the k-th smallest element. The logic is simple, if index of the partitioned element is more than k, then we recur for the left part. If index is the same as k, we have found the k-th smallest element and we return. If index is less than k, then we recur for the right part. This reduces the expected complexity from O(n log n) to O(n), with a worst-case of O(n^2).

function quickSelect(list, left, right, k)

 if left = right
 return list[left]

 Select a pivotIndex between left and right

 pivotIndex := partition(list, left, right, 
 pivotIndex)
 if k = pivotIndex
 return list[k]
 else if k < pivotIndex
 right := pivotIndex - 1
 else
 left := pivotIndex + 1 

Output:

K-th smallest element is 6

Important Points: 

1. Like quicksort, it is fast in practice, but has poor worst-case performance. It is used in
2. The partition process is same as QuickSort, only recursive code differs.
3. There exists an algorithm that finds k-th smallest element in O(n) in worst case, but QuickSelect performs better on average.  

Time Complexity : O(n^2) in the worst case, but on average works in O(n Log n) time and performs better than priority queue based algorithm.
Auxiliary Space : O(n) for recursion call stack in worst case. On average : O(Log n)

Related C++ function : std::nth_element in C++