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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

Is there any normative that regulates the use of silver nanoparticles?
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research.net
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Introduction about quantum dots in nanotechnology
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nano basically means 10^(-9). nanometer is a unit to measure length.
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characteristics of micro business
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Do somebody tell me a best nano engineering book for beginners?
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there is no specific books for beginners but there is book called principle of nanotechnology
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Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
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CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
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s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
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s.
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for screen printed electrodes ?
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Source:  OpenStax, Principles of object-oriented programming. OpenStax CNX. May 10, 2013 Download for free at http://legacy.cnx.org/content/col10213/1.37
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