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<title>Issue 713: sort() complexity is too lax</title>
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<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#CD1">CD1</a> status.</em></p>
<h3 id="713"><a href="lwg-defects.html#713">713</a>. <code>sort()</code> complexity is too lax</h3>
<p><b>Section:</b> 26.8.2.1 <a href="https://wg21.link/sort">[sort]</a> <b>Status:</b> <a href="lwg-active.html#CD1">CD1</a>
 <b>Submitter:</b> Matt Austern <b>Opened:</b> 2007-08-30 <b>Last modified:</b> 2016-01-28</p>
<p><b>Priority: </b>Not Prioritized
</p>
<p><b>View all issues with</b> <a href="lwg-status.html#CD1">CD1</a> status.</p>
<p><b>Discussion:</b></p>
<p>
The complexity of <code>sort()</code> is specified as "Approximately <code>N
log(N)</code> (where <code>N == last - first</code> ) comparisons on the
average", with no worst case complicity specified. The intention was to
allow a median-of-three quicksort implementation, which is usually <code>O(N
log N)</code> but can be quadratic for pathological inputs. However, there is
no longer any reason to allow implementers the freedom to have a
worst-cast-quadratic sort algorithm. Implementers who want to use
quicksort can use a variant like David Musser's "Introsort" (Software
Practice and Experience 27:983-993, 1997), which is guaranteed to be <code>O(N
log N)</code> in the worst case without incurring additional overhead in the
average case. Most C++ library implementers already do this, and there
is no reason not to guarantee it in the standard.
</p>


<p id="res-713"><b>Proposed resolution:</b></p>
<p>
In 26.8.2.1 <a href="https://wg21.link/sort">[sort]</a>, change the complexity to "O(N log N)", and remove footnote 266:
</p>

<blockquote>
<p>
<i>Complexity:</i> <del>Approximately</del> <ins>O(</ins><i>N</i> log(<i>N</i>)<ins>)</ins> (where <i>N</i> == <i>last</i> - <i>first</i> )
comparisons<del> on the average</del>.<del><sup>266)</sup></del>
</p>
<p>
<del><sup>266)</sup>
If the worst case behavior is important <code>stable_sort()</code> (25.3.1.2) or <code>partial_sort()</code>
(25.3.1.3) should be used.</del>
</p>
</blockquote>






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