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<H1>divide and conquer</H1>
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(algorithmic technique)
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<strong>Definition:</strong>
An algorithmic technique. To solve a problem on an instance of size <em>n</em>, a solution is found either directly because solving that instance is easy (typically, because the instance is small) or the instance is <em>divided</em> into two or more smaller instances. Each of these smaller instances is <a href="recursion.html" tppabs="http://hissa.nist.gov/dads/HTML/recursion.html"><em>recursively</em></a> solved, and the solutions are combined to produce a solution for the original instance.
<P><em>Note:
The name <em>divide and conquer</em> is because the problem is conquered by dividing it into several smaller problems. <P> This technique yields elegant, simple and quite often very efficient algorithms. Well-known examples include <a href="binarysrch.html" tppabs="http://hissa.nist.gov/dads/HTML/binarysrch.html"><em>binary search</em></a>, <a href="mergesort.html" tppabs="http://hissa.nist.gov/dads/HTML/mergesort.html"><em>merge sort</em></a>, <a href="quicksort.html" tppabs="http://hissa.nist.gov/dads/HTML/quicksort.html"><em>quicksort</em></a>, Strassen's fast matrix multiplication, and the Fast Fourier Transform (FFT). Similar principles are at the heart of several important data structures as <a href="binarysrchtr.html" tppabs="http://hissa.nist.gov/dads/HTML/binarysrchtr.html"><em>binary</em></a> and <a href="multisrchtre.html" tppabs="http://hissa.nist.gov/dads/HTML/multisrchtre.html"><em>multiway search trees</em></a>, <a href="trie.html" tppabs="http://hissa.nist.gov/dads/HTML/trie.html"><em>tries</em></a>, <a href="skiplist.html" tppabs="http://hissa.nist.gov/dads/HTML/skiplist.html"><em>skip lists</em></a>, multidimensional search trees (<a href="kdtree.html" tppabs="http://hissa.nist.gov/dads/HTML/kdtree.html"><em>k-d trees</em></a>, <a href="quadtree.html" tppabs="http://hissa.nist.gov/dads/HTML/quadtree.html"><em>quadtrees</em></a>), etc.</em>
<P>Author: <a href="terms.html#authorCM" tppabs="http://hissa.nist.gov/dads/terms.html#authorCM">CM</a>
<H2>Implementation</H2>
<A HREF="javascript:if(confirm('http://www.nist.gov/cgi-bin/exit_nist.cgi?url=http://www.geocities.com/Vienna/7079/src/addodd.txt \n\nThis file was not retrieved by Teleport Pro, because it is addressed on a domain or path outside the boundaries set for its Starting Address. \n\nDo you want to open it from the server?'))window.location='http://www.nist.gov/cgi-bin/exit_nist.cgi?url=http://www.geocities.com/Vienna/7079/src/addodd.txt'" tppabs="http://www.nist.gov/cgi-bin/exit_nist.cgi?url=http://www.geocities.com/Vienna/7079/src/addodd.txt">how many odd numbers in an array? (C)</A>
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<a href="javascript:if(confirm('http://hissa.nist.gov/~black/black.html \n\nThis file was not retrieved by Teleport Pro, because it is addressed on a domain or path outside the boundaries set for its Starting Address. \n\nDo you want to open it from the server?'))window.location='http://hissa.nist.gov/~black/black.html'" tppabs="http://hissa.nist.gov/~black/black.html">Paul E. Black</a>
(<a href="mailto:paul.black@nist.gov">paul.black@nist.gov</a>).
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Entry modified Wed Nov 24 13:32:41 1999.<BR>
HTML page formatted Wed Dec 22 09:35:10 1999.
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