Selection Algorithm - Nonlinear General Selection Algorithm

Nonlinear General Selection Algorithm

Using the same ideas used in minimum/maximum algorithms, we can construct a simple, but inefficient general algorithm for finding the kth smallest or kth largest item in a list, requiring O(kn) time, which is effective when k is small. To accomplish this, we simply find the most extreme value and move it to the beginning until we reach our desired index. This can be seen as an incomplete selection sort. Here is the minimum-based algorithm:

function select(list, k) for i from 1 to k minIndex = i minValue = list for j from i+1 to n if list < minValue minIndex = j minValue = list swap list and list return list

Other advantages of this method are:

• After locating the jth smallest element, it requires only O(j + (k-j)2) time to find the kth smallest element, or only O(1) for k ≤ j.
• It can be done with linked list data structures, whereas the one based on partition requires random access.