📄 sorting algorithms.htm
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<META content="Michael Lamont" name=Author>
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content="Description, source code, algorithm analysis, and empirical results for bubble, heap, insertion, merge, quick, selection, and shell sorts."
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<BODY><A class=BlueLink href="http://linux.wku.edu/~lamonml/kb.html">Knowledge
Base</A> > <A class=BlueLink
href="http://linux.wku.edu/~lamonml/algor/">Algorithms & Data Structures</A>
> <A class=BlueLink
href="http://linux.wku.edu/~lamonml/algor/sort/index.html">Sorting
Algorithms</A>
<P><B class=TitleText>Sorting Algorithms</B>
<HR align=left noShade SIZE=1 width="40%">
<P><A class=BlueLink
href="http://linux.wku.edu/~lamonml/algor/sort/sort.pdf">Adobe PDF Format</A>
</P>
<P class=BodyText>One of the fundamental problems of computer science is
ordering a list of items. There's a plethora of solutions to this problem, known
as sorting algorithms. Some sorting algorithms are simple and intuitive, such as
the <A class=BlueLink
href="http://linux.wku.edu/~lamonml/algor/sort/bubble.html">bubble</A> sort.
Others, such as the <A class=BlueLink
href="http://linux.wku.edu/~lamonml/algor/sort/quick.html">quick</A> sort are
extremely complicated, but produce lightening-fast results.
<P class=BodyText>Below are links to algorithms, analysis, and source code for
seven of the most common sorting algorithms.
<P class=BodyText>
<HR align=center noShade SIZE=1 width="100%">
<B class=BodyText>Sorting Algorithms</B><BR><A class=BlueLink
href="http://linux.wku.edu/~lamonml/algor/sort/bubble.html">Bubble
sort</A><BR><A class=BlueLink
href="http://linux.wku.edu/~lamonml/algor/sort/heap.html">Heap sort</A><BR><A
class=BlueLink
href="http://linux.wku.edu/~lamonml/algor/sort/insertion.html">Insertion
sort</A><BR><A class=BlueLink
href="http://linux.wku.edu/~lamonml/algor/sort/merge.html">Merge sort</A><BR><A
class=BlueLink href="http://linux.wku.edu/~lamonml/algor/sort/quick.html">Quick
sort</A><BR><A class=BlueLink
href="http://linux.wku.edu/~lamonml/algor/sort/selection.html">Selection
sort</A><BR><A class=BlueLink
href="http://linux.wku.edu/~lamonml/algor/sort/shell.html">Shell sort</A><BR>
<HR align=center noShade SIZE=1 width="100%">
<P class=BodyText>The common sorting algorithms can be divided into two classes
by the complexity of their algorithms. Algorithmic complexity is a complex
subject (imagine that!) that would take too much time to explain here, but
suffice it to say that there's a direct correlation between the complexity of an
algorithm and its relative efficiency. Algorithmic complexity is generally
written in a form known as Big-O notation, where the <I>O</I> represents the
complexity of the algorithm and a value <I>n</I> represents the size of the set
the algorithm is run against.
<P class=BodyText>For example, <I>O</I>(<I>n</I>) means that an algorithm has a
linear complexity. In other words, it takes ten times longer to operate on a set
of 100 items than it does on a set of 10 items (10 * 10 = 100). If the
complexity was <I>O</I>(<I>n</I><SUP>2</SUP>) (quadratic complexity), then it
would take 100 times longer to operate on a set of 100 items than it does on a
set of 10 items.
<P class=BodyText>The two classes of sorting algorithms are
<I>O</I>(<I>n</I><SUP>2</SUP>), which includes the <A class=BlueLink
href="http://linux.wku.edu/~lamonml/algor/sort/bubble.html">bubble</A>, <A
class=BlueLink
href="http://linux.wku.edu/~lamonml/algor/sort/insertion.html">insertion</A>, <A
class=BlueLink
href="http://linux.wku.edu/~lamonml/algor/sort/selection.html">selection</A>,
and <A class=BlueLink
href="http://linux.wku.edu/~lamonml/algor/sort/shell.html">shell</A> sorts; and
<I>O</I>(<I>n</I> log </I>n</I>) which includes the <A class=BlueLink
href="http://linux.wku.edu/~lamonml/algor/sort/heap.html">heap</A>, <A
class=BlueLink
href="http://linux.wku.edu/~lamonml/algor/sort/merge.html">merge</A>, and <A
class=BlueLink
href="http://linux.wku.edu/~lamonml/algor/sort/quick.html">quick</A> sorts.
<P class=BodyText>In addition to algorithmic complexity, the speed of the
various sorts can be compared with empirical data. Since the speed of a sort can
vary greatly depending on what data set it sorts, accurate empirical results
require several runs of the sort be made and the results averaged together. The
empirical data on this site is the average of a hundred runs against random data
sets on a single-user 250MHz UltraSPARC II. The run times on your system will
almost certainly vary from these results, but the relative speeds should be the
same - the <A class=BlueLink
href="http://linux.wku.edu/~lamonml/algor/sort/selection.html">selection</A>
sort runs in roughly half the time of the <A class=BlueLink
href="http://linux.wku.edu/~lamonml/algor/sort/bubble.html">bubble</A> sort on
the UltraSPARC II, and it should run in roughly half the time on whatever system
you use as well.
<P class=BodyText>These empirical efficiency graphs are kind of like golf - the
lowest line is the "best". Keep in mind that "best" depends on your situation -
the <A class=BlueLink
href="http://linux.wku.edu/~lamonml/algor/sort/quick.html">quick</A> sort may
look like the fastest sort, but using it to sort a list of 20 items is kind of
like going after a fly with a sledgehammer.
<P>
<CENTER><I class=BodyText>O(n<SUP>2</SUP>) Sorts</I><BR><IMG
alt="O(n squared) Sorts" src="Sorting Algorithms_files/slow.jpg"> </CENTER>
<P class=BodyText>As the graph pretty plainly shows, the <A class=BlueLink
href="http://linux.wku.edu/~lamonml/algor/sort/bubble.html">bubble</A> sort is
grossly inefficient, and the <A class=BlueLink
href="http://linux.wku.edu/~lamonml/algor/sort/shell.html">shell</A> sort blows
it out of the water. Notice that the first horizontal line in the plot area is
100 seconds - these aren't sorts that you want to use for huge amounts of data
in an interactive application. Even using the shell sort, users are going to be
twiddling their thumbs if you try to sort much more than 10,000 data items.
<P class=BodyText>On the bright side, all of these algorithms are incredibly
simple (with the possible exception of the shell sort). For quick test programs,
rapid prototypes, or internal-use software they're not bad choices unless you
really think you need split-second efficiency.
<P>
<CENTER><I class=BodyText>O(n log n) Sorts</I><BR><IMG alt="O(n log n) Sorts"
src="Sorting Algorithms_files/fast.jpg"> </CENTER>
<P class=BodyText>Speaking of split-second efficiency, the <I>O</I>(<I>n</I> log
<I>n</I>) sorts are where it's at. Notice that the time on this graph is
measured in tenths of seconds, instead hundreds of seconds like the
<I>O</I>(<I>n</I><SUP>2</SUP>) graph.
<P class=BodyText>But as with everything else in the real world, there are
trade-offs. These algorithms are blazingly fast, but that speed comes at the
cost of complexity. Recursion, advanced data structures, multiple arrays - these
algorithms make extensive use of those nasty things.
<P class=BodyText>In the end, the important thing is to pick the sorting
algorithm that you think is appropriate for the task at hand. You should be able
to use the source code on this site as a "black box" if you need to - you can
just use it, without understanding how it works. Obviously taking the time to
understand how the algorithm you choose works is preferable, but time
constraints are a fact of life. </P>
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