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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 1 September 2005), see www.w3.org">  <title>Complexity</title>  <link href="cppreference.css" rel="stylesheet" type="text/css"></head><body><table>  <tr>  <td>  <div class="body-content">  <div class="header-box">    <a href="index.html">cppreference.com</a> &gt; Complexity  </div>  <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 class="misc-table">    <tr>      <th>Name</th>      <th>Speed</th>      <th>Description</th>      <th>Formula</th>    </tr>    <tr class="misc-table-tr-2">      <td class="misc-table-td">exponential time</td>      <td class="misc-table-td">slow</td>      <td class="misc-table-td">takes an amount of time proportional to a constant raised to      the <strong>N</strong>th power</td>      <td class="misc-table-td">K^<strong>N</strong></td>    </tr>    <tr class="misc-table-tr-1">      <td class="misc-table-td">polynomial time</td>      <td class="misc-table-td">fast</td>      <td class="misc-table-td">takes an amount of time proportional to <strong>N</strong>      raised to some constant power</td>      <td class="misc-table-td"><strong>N</strong>^K</td>    </tr>    <tr class="misc-table-tr-2">      <td class="misc-table-td">linear time</td>      <td class="misc-table-td">faster</td>      <td class="misc-table-td">takes an amount of time directly proportional to      <strong>N</strong></td>      <td class="misc-table-td">K * <strong>N</strong></td>    </tr>    <tr class="misc-table-tr-1">      <td class="misc-table-td">logarithmic time</td>      <td class="misc-table-td">much faster</td>      <td class="misc-table-td">takes an amount of time proportional to the logarithm of      <strong>N</strong></td>      <td class="misc-table-td">K * log(<strong>N</strong>)</td>    </tr>    <tr class="misc-table-tr-2">      <td class="misc-table-td">constant time</td>      <td class="misc-table-td">fastest</td>      <td class="misc-table-td">takes a fixed amount of time, no matter how large the input      is</td>      <td class="misc-table-td">K</td>    </tr>  </table>  </div>  </td>    </tr>  </table></body></html>
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