Dropsort

Introduction

Dropsort is a fast, one-pass sorting algorithm suitable for many applications.

Algorithm Description

Dropsort is run on an ordered list of numbers by examining the numbers in sequence, beginning with the second number in the list. If the number being examined is less than the number before it, drop it from the list. Otherwise, it is in sorted order, so keep it. Then move to the next number.

After a single pass of this algorithm, the list will only contain numbers that are at least as large as the previous number in the list. In other words, the list will be sorted!

Analysis

Dropsort requires exactly n-1 comparisons to sort a list of length n, making this an O(n) algorithm, superior to the typical O(n logn) algorithms commonly used in most applications.

Dropsort is what is known in the computer science field as a lossy algorithm. It produces a fast result that is correct, but at the cost of potentially losing some of the input data. Although to those not versed in the arts of computer science this may seem undesirable, lossy algorithms are actually a well-accepted part of computing. An example is the popular JPEG image compression format, which enjoys widespread use because of its versatility and usefulness. In similar fashion, dropsort promises to revolutionise the sorting of data in fields as diverse as commercial finance, government record-keeping, and space exploration.

Resources

Jeremy Kent has implemented Dropsort! Well, sort of. (Pun intended.) In his own words:

It's an implementation of a sorting algorithm with your DropSort at the core -- basically call dropsort, keeping the dropped items... then reverse that list and call dropsort again recursively. (Because obviously anything that wasn't in ascending order before must be in descending order now.)

Get the python code here!