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Template design pattern

The invariant sorting process as described by Merritt is an example of the Template Method Design Pattern.

Template method design pattern

Template Method Design Pattern
The Template Method Design Pattern describes an invariant concrete process in terms of variant, abstract methods.
Here, the invariant process is represented by a concrete method of an abstract superclass. This concrete method's implementation is in terms of abstract methods of the same class. These abstract methods represent the variant processes and are implemented in the sub-classes. This type of class organization where the variant processes are relegated to sub-classes is also known as a white box framework .

Concrete sorters

In order to create a sorter that can actually perform a sorting operation, we need to subclass the above ASorter class and implement the abstract split and join methods. It should be noted that in general, the split and join methods form a matched pair. One can argue that it is possible to write a universal join methods (a merge operation) but it would be highly inefficent in most cases.

Selection sort

Tradionally, an in-place selection sort is performed by selecting the smallest (or largest) value in the array and placing it in the right-most location by either swapping it with the right-most element or by shifting all the in-between elements to the left. The selection and swapping/shifting process then repeated with the sub-array to the left of the newly placed element. This continues until only one element remains in the array. A selection sort is commonly used to do something like a sort group of people into ascending height.

Below is an animation of a traditional selection sort algorithm:

Traditional selection sort algorithm

The extrema values are removed from an ever-shrinking unordered set and placed into the resulting sorted array. Here, the smallest values are removed from the left and placed to the right in the array.

In terms of the Merritt sorting paradigm, a selection sort can be broken down into a splitting process that is the same as the above selection process and a trivial join process. Looking at the above selection and swap/shift process, we see that it is describing a the splitting off of a single element, the smallest, from an array. The process repeats recursively until there is nothing more to split off. The sorting of a single element is a no-op, so after that the recursion rolls back out though the joining process. But the joining process is trivial, a no-op, because the elements are already in their corret positions. The beauty of Merritt's insight is the realize that by considering a no-op as an operational part of a process, all the different types of binary comparison-based sorting could be unified under a common framework.

Below is an animation of a Merritt selection sort algorithm:

Merritt selection sort process

The splitting process splits off one element at a time, the smallest element, from the left and placed to the right in the array. The join process is a no-op because the elements are already in their correct places.

Questions & Answers

find the 15th term of the geometric sequince whose first is 18 and last term of 387
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Commplementary angles
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or infinite solutions?
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Embra Reply
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Differences Between Laspeyres and Paasche Indices
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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
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I'm interested in Nanotube
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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?
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Source:  OpenStax, My first collection. OpenStax CNX. Aug 03, 2009 Download for free at http://cnx.org/content/col10870/1.1
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