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Selection sort can be implemented as a stable sort . If, rather than swapping in step 2, the minimum value is inserted into the first position (that is, all intervening items moved down), the algorithm is stable. However, this modification leads to Θ(n2 ) writes, eliminating the main advantage of selection sort over insertion sort, which is always stable.

6.1.3. bubble sort

(From Wikipedia, the free encyclopedia)

Bubble sort is a simple sorting algorithm . It works by repeatedly stepping through the list to be sorted, comparing two items at a time and swapping them if they are in the wrong order. The pass through the list is repeated until no swaps are needed, which means the list is sorted. The algorithm gets its name from the way smaller elements "bubble" to the top (i.e. the beginning) of the list via the swaps. (Another opinion: it gets its name from the way greater elements "bubble" to the end.) Because it only uses comparisons to operate on elements, it is a comparison sort . This is the easiest comparison sort to implement.

A simple way to express bubble sort in pseudocode is as follows:

procedure bubbleSort( A : list of sortable items ) defined as:

do

swapped := false

for each i in 0 to length( A ) - 2 do:

if A[ i ]>A[ i + 1 ] then

swap( A[ i ], A[ i + 1 ])

swapped := true

end if

end for

while swapped

end procedure

The algorithm can also be expressed as:

procedure bubbleSort( A : list of sortable items ) defined as:

for each i in 1 to length(A) do:

for each j in length(A) downto i + 1 do:

if A[ j ]<A[ j - 1 ] then

swap( A[ j ], A[ j - 1 ])

end if

end for

end for

end procedure

This difference between this and the first pseudocode implementation is discussed later in the article .

Analysis

Best-case performance

Bubble sort has best-case complexity Ω (n). When a list is already sorted, bubblesort will pass through the list once, and find that it does not need to swap any elements. Thus bubble sort will make only n comparisons and determine that list is completely sorted. It will also use considerably less time than О(n²) if the elements in the unsorted list are not too far from their sorted places. MKH...

Rabbits and turtles

The positions of the elements in bubble sort will play a large part in determining its performance. Large elements at the top of the list do not pose a problem, as they are quickly swapped downwards. Small elements at the bottom, however, as mentioned earlier, move to the top extremely slowly. This has led to these types of elements being named rabbits and turtles, respectively.

Various efforts have been made to eliminate turtles to improve upon the speed of bubble sort. Cocktail sort does pretty well, but it still retains O(n2) worst-case complexity. Comb sort compares elements large gaps apart and can move turtles extremely quickly, before proceeding to smaller and smaller gaps to smooth out the list. Its average speed is comparable to faster algorithms like Quicksort .

Alternative implementations

One way to optimize bubble sort is to note that, after each pass, the largest element will always move down to the bottom. During each comparison, it is clear that the largest element will move downwards. Given a list of size n, the nth element will be guaranteed to be in its proper place. Thus it suffices to sort the remaining n - 1 elements. Again, after this pass, the n - 1th element will be in its final place.

Questions & Answers

Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
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.
Harper
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
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Cied
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
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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
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Data structures and algorithms. OpenStax CNX. Jul 29, 2009 Download for free at http://cnx.org/content/col10765/1.1
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