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Title: Algorithms/Sorting and Searching - Common comparison sorts Explanation, algorithm analysis, empirical data, and source code for the bubble, heap, insertion, merge, quick, selection, and shell sorts.
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Sorting Algorithms Knowledge Base >Algorithms & Data Structures >Sorting Algorithms Sorting Algorithms Adobe PDF Format One of the fundamental problems of computer science is ordering a list ofitems. There's a plethora of solutions to this problem, known as sortingalgorithms. Some sorting algorithms are simple and intuitive, such as thebubble sort. Others, such as thequick sort are extremelycomplicated, but produce lightening-fast results. Below are links to algorithms, analysis, and source code for seven of themost common sorting algorithms. Sorting AlgorithmsBubble sortHeap sortInsertion sortMerge sortQuick sortSelection sortShell sort 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 itto say that there's a direct correlation between the complexity of an algorithm and its relative efficiency. Algorithmic complexity is generallywritten in a form known as Big-O notation, where the O represents thecomplexity of the algorithm and a value n represents the size of theset the algorithm is run against. For example, O(n) means that an algorithm has a linearcomplexity. In other words, it takes ten times longer to operate on a setof 100 items than it does on a set of 10 items (10 * 10 = 100). If thecomplexity was O(n2) (quadratic complexity), then it would take 100 times longer to operate on a set of 100 items than it doeson a set of 10 items. The two classes of sorting algorithms are O(n2), whichincludes the bubble, insertion, selection, and shell sorts; and O(n log n) which includes the heap, merge, and quick sorts. In addition to algorithmic complexity, the speed of the various sorts can becompared with empirical data. Since the speed of a sort can vary greatlydepending on what data set it sorts, accurate empirical results requireseveral 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 randomdata sets on a single-user 250MHz UltraSPARC II. The run times on yoursystem will almost certainly vary from these results, but the relativespeeds should be the same - the selection sort runs in roughly half the timeof the bubble sort on the UltraSPARC II, and it should run in roughly half the time on whatever system you use as well. These empirical efficiency graphs are kind of like golf - the lowest line is the"best". Keep in mind that "best" depends on your situation - thequick sort may look like the fastestsort, but using it to sort a list of 20 items is kind of like going after a flywith a sledgehammer. O(n2) Sorts O(n squared) Sorts As the graph pretty plainly shows, the bubble sort is grossly inefficient, and theshell sort blows it out of thewater. 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 aninteractive application. Even using the shell sort, users are going to betwiddling their thumbs if you try to sort much more than 10,000 data items. On the bright side, all of these algorithms are incredibly simple (with thepossible exception of the shell sort). For quick test programs, rapidprototypes, or internal-use software they're not bad choices unless you reallythink you need split-second efficiency. O(n log n) Sorts O(n log n) Sorts Speaking of split-second efficiency, the O(n log n) sortsare where it's at. Notice that the time on this graph is measured in tenths ofseconds, instead hundreds of seconds like the O(n2)graph. But as with everything else in the real world, there are trade-offs. Thesealgorithms are blazingly fast, but that speed comes at the cost of complexity.Recursion, advanced data structures, multiple arrays - these algorithms makeextensive use of those nasty things. In the end, the important thing is to pick the sorting algorithm that you thinkis appropriate for the task at hand. You should be able to use the source codeon this site as a "black box" if you need to - you can just use it, withoutunderstanding how it works. Obviously taking the time to understand how thealgorithm you choose works is preferable, but time constraints are a fact oflife. Michael's Homepage      WKU-Linux
 

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http://linux.wku.edu/~lamonml/algor/sort/sort.html

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Explanation, algorithm analysis, empirical data, and source code for the bubble, heap, insertion, merge, quick, selection, and shell sorts.

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