Data Structures and Algorithms

# What is Randomized Select Algorithm?

In this article I will explain What is Randomized Select Algorithm and how does it work.

The Randomized Select algorithm is a variation of the QuickSelect algorithm for finding the kth smallest element in an unsorted array. Like QuickSelect, the Randomized Select algorithm has an average time complexity of O(n), where n is the size of the array.

The algorithm works as follows:

1. Choose a pivot element at random from the array.
2. Partition the array into two sub-arrays: one containing elements smaller than the pivot and the other containing elements larger than the pivot.
3. Determine the rank (position) of the pivot element in the array. If the rank is equal to k, then we have found the kth smallest element and we can return it. If the rank is greater than k, then we recurse on the sub-array containing the smaller elements. If the rank is less than k, then we recurse on the sub-array containing the larger elements, but we look for the (k-rank)th smallest element in that sub-array.
4. Repeat the process until we find the kth smallest element.

The randomized selection of the pivot ensures that the algorithm has a good average-case performance, even if the input array is already partially sorted or contains repeated elements. The worst-case time complexity is still O(n^2), but this occurs with a very low probability.

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