Randomized selection

The randomized selection algorithm is used to obtain the k^th smallest number that is based on the quicksort algorithm; the randomized selection algorithm is also known as quickselect. In Chapter 11, Sorting, we discussed the quicksort algorithm. The quicksort algorithm is an efficient algorithm to sort an unordered list of items. To summarize, the quicksort algorithm works as follows:

1. It selects a pivot.
2. It partitions the unsorted list around the pivot.
3. It recursively sorts the two halves of the partitioned list using steps 1 and 2.

One important fact about quicksort is that after every partitioning step, the index of the pivot does not change, even after the list becomes sorted. This means that after each iteration, the selected pivot value will be placed in its correct position in the list. This property of quicksort enables us to obtain the k^th smallest number without sorting the complete list. Let’s discuss the randomized...