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<title>Issue 715: minmax_element 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="715"><a href="lwg-defects.html#715">715</a>. <code>minmax_element</code> complexity is too lax</h3>
<p><b>Section:</b> 26.8.9 <a href="https://wg21.link/alg.min.max">[alg.min.max]</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 other</b> <a href="lwg-index-open.html#alg.min.max">active issues</a> in [alg.min.max].</p>
<p><b>View all other</b> <a href="lwg-index.html#alg.min.max">issues</a> in [alg.min.max].</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 for <code>minmax_element</code> (26.8.9 <a href="https://wg21.link/alg.min.max">[alg.min.max]</a> par 16) says "At most <code>max(2 *
(last - first ) - 2, 0)</code> applications of the corresponding comparisons",
i.e. the worst case complexity is no better than calling <code>min_element</code> and
<code>max_element</code> separately. This is gratuitously inefficient. There is a
well known technique that does better: see section 9.1 of CLRS
(Introduction to Algorithms, by Cormen, Leiserson, Rivest, and Stein).
</p>


<p id="res-715"><b>Proposed resolution:</b></p>
<p>
Change 26.8.9 <a href="https://wg21.link/alg.min.max">[alg.min.max]</a> to:
</p>

<blockquote>
<pre>
template&lt;class ForwardIterator&gt; 
  pair&lt;ForwardIterator, ForwardIterator&gt; 
    minmax_element(ForwardIterator first , ForwardIterator last); 
template&lt;class ForwardIterator, class Compare&gt; 
  pair&lt;ForwardIterator, ForwardIterator&gt; 
    minmax_element(ForwardIterator first , ForwardIterator last , Compare comp);
</pre>
<blockquote>
<p>
<i>Returns:</i> <code>make_pair(m, M)</code>, where <code>m</code> is
<del><code>min_element(first, last)</code> or <code>min_element(first, last,
comp)</code></del> <ins>the first iterator in <code>[first,
last)</code> such that no iterator in the range refers to a smaller element,</ins> and
<ins>where</ins> <code>M</code> is <del><code>max_element(first, last)</code> or
<code>max_element(first, last, comp)</code></del> <ins>the last iterator
in <code>[first, last)</code> such that no iterator in the range refers to a larger element</ins>.
</p>
<p>
<i>Complexity:</i> At most <del><code>max(2 * (last - first ) - 2, 0)</code></del>
<ins><code>max(&lfloor;(3/2) (N-1)&rfloor;, 0)</code></ins> applications of the
corresponding <del>comparisons</del> <ins>predicate, where <code>N</code> is <code>distance(first, last)</code></ins>.
</p>
</blockquote>
</blockquote>






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