<< Chapter < Page Chapter >> Page >

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

how can chip be made from sand
Eke Reply
is this allso about nanoscale material
Almas
are nano particles real
Missy Reply
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
Lale Reply
no can't
Lohitha
where is the latest information on a no technology how can I find it
William
currently
William
where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
has a lot of application modern world
Kamaluddeen
yes
narayan
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Data structures and algorithms. OpenStax CNX. Jul 29, 2009 Download for free at http://cnx.org/content/col10765/1.1
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Data structures and algorithms' conversation and receive update notifications?

Ask