<< Chapter < Page Chapter >> Page >
In 1985, Susan Merritt proposed a new taxonomy for comparison-based sorting algorithms. At the heart of Merritt's thesis is the principle of divide and conquer. Merritt's thesis is potentially a very powerful method for studying and understanding sorting. However, the paper did not offer any concrete implementation of the proposed taxonomy. The following is our object-oriented formulation and implementation of Merritt's taxonomy.

The following discussion is based on the the SIGCSE 2001 paper by Nguyen and Wong, "Design Patterns for Sorting" D. Nguyen and S. Wong, “Design Patterns for Sorting,” SIGCSE Bulletin 33:1, March 2001, 263-267 .

Merritt's thesis

In 1985, Susan Merritt proposed that all comparison-based sorting could be viewed as “Divide and Conquer” algorithms. S. Merritt, "An Inverted Taxonomy of Sorting Algorithms," Comm. of the ACM, Jan. 1985, Volume 28, Number 1, pp. 96-99 That is, sorting could be thought of as a process wherein one first "divides" the unsorted pile of whatever needs to sorted into smaller piles and then "conquers" them by sorting those smaller piles. Finally, one has to take the the smaller, now sorted piles and recombines them into a single, now-sorted pile.

We thus end up with a recursive definition of sorting:

  • To sort a pile:
    • Split the pile into smaller piles
    • Sort the smaller piles
    • Join the sorted smaller piles into a single pile

We can see Merritt's recursive notion of sorting as a split-sort-join process in a pictoral manner by considering the general sorting process as a "black box" process that takes an unsorted set and returns a sorted set. Merritt's thesis thus contends that this sorting process can be described as a splitting followed by a sorting of the smaller pieces followed by a joining of the sorted pieces. The smaller sorting process can thus be similarly described. The base case of this recursive process is when the set has been reduced to a single element, upon which the sorting process cannot be broken down any more as it is a trivial no-op.

Animation of the merritt sorting thesis (click the "reveal more" button)

Sorting can be seen as a recursive process that splits the unsorted items into multiple unsorted sets, sorts them and then rejoins the now sorted sets. When a set is reduced to a single element (blank boxes above), sorting is a trivial no-op.

Merritt's thesis is potentially a very powerful method for studying and understanding sorting. In addition, Merritt's abstract characterization of sorting exhibits much object-oriented (OO) flavor and can be described in terms of OO concepts.

Capturing the abstraction

So, how do we capture the abstraction of sorting as described by Merritt? Fundamentally, we have to recognize that the above description of sorting contains two distinct parts: the invariant process of splitting into sub-piles, sorting the sub-piles and joining the sub-piles, and the variant processes of the actual splitting and joining algorithms used.

Here, we will restrict ourselves to the process of sorting an array of objects, in-place -- that is, the original array is mutated from unsorted to sorted (as opposed to returning a new array of sorted values and leaving the original untouched). The Comparator object used to compare objects will be given to the sorter's constructor.

Abstract sorter class

Invariant sorting process represented in an abstract class
The invariant sorting process is represented as an abstract class
Here, the invariant process is represented by the concrete sort method, which performs the split-sort-sort-join process as described by Merritt. The variant processes are represented by the abstract split and join methods, whose exact behaviors are indeterminate at this time.

Questions & Answers

how do you translate this in Algebraic Expressions
linda Reply
why surface tension is zero at critical temperature
Shanjida
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Good
Got questions? Join the online conversation and get instant answers!
QuizOver.com Reply

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Principles of object-oriented programming. OpenStax CNX. May 10, 2013 Download for free at http://legacy.cnx.org/content/col10213/1.37
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Principles of object-oriented programming' conversation and receive update notifications?

Ask