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<HTML><HEAD>  <TITLE>Complexity</TITLE></HEAD><BODY BGCOLOR="FFFFFF"><TABLE WIDTH="100%" BGCOLOR="EEEEFF"><TR><TD>  <A HREF="index.html">cppreference.com</A> -&gt; Complexity</TD></TR></TABLE><H3>Complexity</H3><P>There are different measurements of the speed of any given algorithm.  Given aninput size of <strong>N</strong>, they can be described as follows:</P><TABLE>  <TR>     <TH>Name</TH>    <TH>Speed</TH>    <TH>Description</TH>  <TR>  <TR BGCOLOR="EEEEFF">    <TD>exponential time</TD>    <TD>slow</TD>    <TD>takes an amount of time proportional to a constant raised to the       <STRONG>N</STRONG>th power (K^<STRONG>N</STRONG>)</TD>  <TR>  <TR>     <TD>polynomial time</TD>    <TD>fast</TD>    <TD>takes an amount of time proportional to <STRONG>N</STRONG> raised       to some constant power (<STRONG>N</STRONG>^K)</TD>  <TR>  <TR BGCOLOR="EEEEFF">     <TD>linear time</TD>    <TD>faster</TD>    <TD>takes an amount of time directly proportional to <STRONG>N</STRONG>       (K * <STRONG>N</STRONG>)</TD>  <TR>  <TR>     <TD>logarithmic time</TD>    <TD>much faster</TD>    <TD>takes an amount of time proportional to the logarithm of      <STRONG>N</STRONG> (log(<STRONG>N</STRONG>))</TD>  <TR>  <TR BGCOLOR="EEEEFF">     <TD>constant time</TD>    <TD>fastest</TD>    <TD>takes a fixed amount of time, no matter how large the input is (K)</TD>  <TR></TABLE></BODY></HTML><br><html>
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