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<H1>memoization</H1>
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(algorithmic technique)

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<strong>Definition:</strong>
An algorithmic technique which saves (memoizes) a computed answer for later reuse, rather than recomputing the answer.
<P><em>Note:
The term comes from "memo": "A short note written as a reminder." [The American Heritage Dictionary of the English Language, &copy; 1970, American Heritage Publishing] <P> A naive program to compute <a href="fibonacnmbrs.html" tppabs="http://hissa.nist.gov/dads/HTML/fibonacnmbrs.html"><em>Fibonacci numbers</em></a> is <pre> fib(n) {<br> &nbsp;&nbsp;&nbsp;if n is 1 or 2, return 1;<br> &nbsp;&nbsp;&nbsp;return fib(n-1) + fib(n-2);<br> } </pre> Because fib() is recomputed over and over for the same argument, run time for the above is <a href="omegaCapital.html" tppabs="http://hissa.nist.gov/dads/HTML/omegaCapital.html"><em> <img src="Omega-1.gif" tppabs="http://hissa.nist.gov/dads/HTML/Images/Omega.gif"  border=0 height=10 width=9  alt="Capital Omega"></em></a>(1.6<sup>n</sup>). If instead we memoize (save) the value of fib(n) the first time we compute it, the run time is <a href="theta.html" tppabs="http://hissa.nist.gov/dads/HTML/theta.html"><em> <img src="Theta-1.gif" tppabs="http://hissa.nist.gov/dads/HTML/Images/Theta.gif"  border=0 height=10 width=8  alt="Capital Theta"></em></a>(n). <pre> allocate array for memo;<br> initialize memo[1] and memo[2] to 1;<br> <br> fib(n) {<br> &nbsp;&nbsp;&nbsp;if memo[n] is not zero, return memo[n];<br> &nbsp;&nbsp;&nbsp;memo[n] = fib(n-1) + fib(n-2);<br> &nbsp;&nbsp;&nbsp;return memo[n];<br> } </pre> <P> Of course, computing Fibonacci numbers can be easily done in constant time (see <a href="fibonacnmbrs.html" tppabs="http://hissa.nist.gov/dads/HTML/fibonacnmbrs.html"><em>Fibonacci numbers</em></a>), but this illustrates the technique.</em>
<P>Author: <a href="terms.html#authorPEB" tppabs="http://hissa.nist.gov/dads/terms.html#authorPEB">PEB</a>

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Entry modified Fri Jan  7 09:28:38 2000.<BR>
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