<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8">
<title>Issue 4162: Worst time complexity of non-parallel versions of nth_element is underspecified</title>
<meta property="og:title" content="Issue 4162: Worst time complexity of non-parallel versions of nth_element is underspecified">
<meta property="og:description" content="C++ library issue. Status: New">
<meta property="og:url" content="https://cplusplus.github.io/LWG/issue4162.html">
<meta property="og:type" content="website">
<meta property="og:image" content="http://cplusplus.github.io/LWG/images/cpp_logo.png">
<meta property="og:image:alt" content="C++ logo">
<style>
  p {text-align:justify}
  li {text-align:justify}
  pre code.backtick::before { content: "`" }
  pre code.backtick::after { content: "`" }
  blockquote.note
  {
    background-color:#E0E0E0;
    padding-left: 15px;
    padding-right: 15px;
    padding-top: 1px;
    padding-bottom: 1px;
  }
  ins {background-color:#A0FFA0}
  del {background-color:#FFA0A0}
  table.issues-index { border: 1px solid; border-collapse: collapse; }
  table.issues-index th { text-align: center; padding: 4px; border: 1px solid; }
  table.issues-index td { padding: 4px; border: 1px solid; }
  table.issues-index td:nth-child(1) { text-align: right; }
  table.issues-index td:nth-child(2) { text-align: left; }
  table.issues-index td:nth-child(3) { text-align: left; }
  table.issues-index td:nth-child(4) { text-align: left; }
  table.issues-index td:nth-child(5) { text-align: center; }
  table.issues-index td:nth-child(6) { text-align: center; }
  table.issues-index td:nth-child(7) { text-align: left; }
  table.issues-index td:nth-child(5) span.no-pr { color: red; }
  @media (prefers-color-scheme: dark) {
     html {
        color: #ddd;
        background-color: black;
     }
     ins {
        background-color: #225522
     }
     del {
        background-color: #662222
     }
     a {
        color: #6af
     }
     a:visited {
        color: #6af
     }
     blockquote.note
     {
        background-color: rgba(255, 255, 255, .10)
     }
  }
</style>
</head>
<body>
<hr>
<p><em>This page is a snapshot from the LWG issues list, see the <a href="lwg-active.html">Library Active Issues List</a> for more information and the meaning of <a href="lwg-active.html#New">New</a> status.</em></p>
<h3 id="4162"><a href="lwg-active.html#4162">4162</a>. Worst time complexity of non-parallel versions of <code>nth_element</code> is underspecified</h3>
<p><b>Section:</b> 26.8.3 <a href="https://wg21.link/alg.nth.element">[alg.nth.element]</a> <b>Status:</b> <a href="lwg-active.html#New">New</a>
 <b>Submitter:</b> Jiang An <b>Opened:</b> 2024-09-29 <b>Last modified:</b> 2024-10-09</p>
<p><b>Priority: </b>3
</p>
<p><b>View all other</b> <a href="lwg-index.html#alg.nth.element">issues</a> in [alg.nth.element].</p>
<p><b>View all issues with</b> <a href="lwg-status.html#New">New</a> status.</p>
<p><b>Discussion:</b></p>
<p>
Currently, 26.8.3 <a href="https://wg21.link/alg.nth.element">[alg.nth.element]</a> doesn't specify the worst time complexity for <code>nth_element</code>
without <code>ExecutionPolicy</code> parameter, which seemingly allows a complexity that is
<code>&#x1d4aa;(<i>N</i><sup>2</sup>)</code> or even worse. Presumably we should make the worst time complexity
consistent between parallel and non-parallel versions. For <code>sort</code>, LWG <a href="lwg-defects.html#713" title="sort() complexity is too lax (Status: CD1)">713</a><sup><a href="https://cplusplus.github.io/LWG/issue713" title="Latest snapshot">(i)</a></sup> already
strengthened complexity requirements.
</p>

<p><i>[2024-10-09; Reflector poll]</i></p>

<p>
Set priority to 3 after reflector poll.
</p>
<p>
"This seems to require changes to implementations for them to meet this
complexity guarantee."
</p>



<p id="res-4162"><b>Proposed resolution:</b></p>
<p>
This wording is relative to <a href="https://wg21.link/N4988" title=" Working Draft, Programming Languages — C++">N4988</a>.
</p>

<ol>
<li><p>Modify 26.8.3 <a href="https://wg21.link/alg.nth.element">[alg.nth.element]</a> as indicated:</p>

<blockquote>
<pre>
template&lt;class RandomAccessIterator&gt;
  constexpr void nth_element(RandomAccessIterator first, RandomAccessIterator nth,
                             RandomAccessIterator last);
template&lt;class ExecutionPolicy, class RandomAccessIterator&gt;
  void nth_element(ExecutionPolicy&amp;&amp; exec,
                   RandomAccessIterator first, RandomAccessIterator nth,
                   RandomAccessIterator last);
template&lt;class RandomAccessIterator, class Compare&gt;
  constexpr void nth_element(RandomAccessIterator first, RandomAccessIterator nth,
                             RandomAccessIterator last, Compare comp);
template&lt;class ExecutionPolicy, class RandomAccessIterator, class Compare&gt;
  void nth_element(ExecutionPolicy&amp;&amp; exec,
                   RandomAccessIterator first, RandomAccessIterator nth,
                   RandomAccessIterator last, Compare comp);
template&lt;random_access_iterator I, sentinel_for&lt;I&gt; S, class Comp = ranges::less,
         class Proj = identity&gt;
  requires sortable&lt;I, Comp, Proj&gt;
  constexpr I
    ranges::nth_element(I first, I nth, S last, Comp comp = {}, Proj proj = {});
</pre>
<blockquote>
<p>
[&hellip;]
<p/>
-5- <i>Complexity</i>: <del>For the overloads with no <code>ExecutionPolicy</code>, linear on average.
For the overloads with an <code>ExecutionPolicy</code>,</del> <code>&#x1d4aa;(<i>N</i>)</code> applications
of the predicate<del>,</del> and <code>&#x1d4aa;(<i>N</i> log <i>N</i>)</code> swaps, where <code><i>N</i> =
last - first</code>. <ins>For the overloads with no <code>ExecutionPolicy</code>, <code>&#x1d4aa;(<i>N</i>)</code>
on average.</ins>
</p>
</blockquote>
</blockquote>
</li>
</ol>





</body>
</html>
