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Insertion sort

Tradionally, an in-place insertion sort is performed by starting from one end of the arry, say the left end, and performing an in-order insertion of an element into the sub-array to its left. The next element to the right is then chosen and the insertion process repeated. At each insertion, the sorted sub-array on the left grows until encompasses the entire array. An insertion sort is a very typical way in which people will order a set of playing cards in their hand.

Below is an animation of a traditional insertion sort algorithm:

Traditional insertion sort algorithm

Starting from the left, elements from the immediate right are inserted into a growing sub-array to the left.

In the Merrit paradigm, the insertion sort first splits the array or sub-array into two pieces simply by separating the right-most element. Recursively, the splitting process proceeds to from the right to the left until a single element is left in the sub-array. Sorting a one element array is a no-op, so then the recursion unwinds with the join process. The join process combines each single split-off element with its sorted sub-array partner to its left by performing an in-order insertion. This proceeds as the recusion unwinds until the entire array is fully sorted. In contrast to the selection sort, the bulk of the work is being done in the join method, hence classifying insertion sort as an "easy split, hard join" sorting process.

Below is an animation of a Merritt insertion sort algorithm:

Merritt insertion sort process

The right-most elements are first split-off one by one, starting at the right and moving left. The split-off elements are then joined by performing an in-order insertion to the left, starting at the left.

In the Java implementation of the selection sorter below, the split method simply splits off the right-most element of the sub-array. The join method performs an in-order insertion of the single split-off element into the larger sub-array to its left.

Insertionsorter class

package sorter; /*** A concrete sorter that uses the Insertion Sort technique. */public class InsertionSorter extends ASorter {/** * The constructor for this class.* @param iCompareOp The comparison strategy to use in the sorting. */public InsertionSorter(AOrder iCompareOp) {super(iCompareOp); }/** * Splits A[lo:hi]into A[lo:s-1] and A[s:hi]where s is the returned value of this function. * This simply splits off the element at index hi.* @param A the array A[lo:hi] to be sorted.* @param lo the low index of A. * @param hi the high index of A.* @return hi always. */protected int split(Object[] A, int lo, int hi){ return (hi);} /*** Joins sorted A[lo:s-1] and sorted A[s:hi]into A[lo:hi]. (s = hi)* The method performs an in-order insertion of A[hi] into the A[lo, hi-1]* @param A A[lo:s-1] and A[s:hi]are sorted. * @param lo the low index of A.* @param s * @param hi the high index of A.*/ protected void join(Object[]A, int lo, int s, int hi) {int j = hi; // remember s == hi. Object key = A[hi]; // Invariant: A[lo:j-1]and A[j+1:hi] are sorted and key<all elements of A[j+1:hi].// Shifts elements of A[lo:j-1] that are greater than key to the "right" to make room// for key. while (lo<j&&aOrder.lt(key, A[j-1])){ A[j]= A[j-1];A[j-1] = key;j = j - 1; // invariant is maintained. } // On loop exit: j = lo or A[j-1]<= key. Also invariant is still true. // A[j]= key; }}

The authors were once challenged that the Merritt template-based sorting paradigm could not be used to describe the Shaker Sort process (a bidirectional Bubble or Selection sort). See for instance, (External Link) . However, it can be done is a very straightforward manner. There are a number of viable solutions. Hint: think about the State Design Pattern .

The solution is left to the student but is available from the authors if proof of non-student status is provided.

Got questions? Get instant answers now!

For more examples, please see download the demo code . Please note that the ShakerSort code is disabled due to its use as a student exercise.

Questions & Answers

what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
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Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
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.
what is the actual application of fullerenes nowadays?
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.
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.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
so some one know about replacing silicon atom with phosphorous in semiconductors device?
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.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
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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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