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<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"><html> <head> <meta name="generator" content="HTML Tidy for Linux/x86 (vers 1st October 2002), see www.w3.org"> <title>Complexity</title> </head> <body bgcolor="#ffffff"> <table width="100%" bgcolor="#eeeeff"> <tr> <td><a href="index.html">cppreference.com</a> -> Complexity</td> </tr> </table> <h3>Complexity</h3> <p>There are different measurements of the speed of any given algorithm. Given an input 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> <td> </td> </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> </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> <td> </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> </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> <td> </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>
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