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<title>Issue 787: complexity of binary_search</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="787"><a href="lwg-defects.html#787">787</a>. complexity of <code>binary_search</code></h3>
<p><b>Section:</b> 26.8.4.5 <a href="https://wg21.link/binary.search">[binary.search]</a> <b>Status:</b> <a href="lwg-active.html#CD1">CD1</a>
 <b>Submitter:</b> Daniel Kr&uuml;gler <b>Opened:</b> 2007-09-08 <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>
In 26.8.4.5 <a href="https://wg21.link/binary.search">[binary.search]</a> p. 3 the complexity of <code>binary_search</code> is described as
</p>

<blockquote><p>
At most <code>log(last - first) + 2</code> comparisons.
</p></blockquote>

<p>
This should be precised and brought in line with the nomenclature used for
<code>lower_bound</code>, <code>upper_bound</code>, and <code>equal_range</code>.
</p>

<p>
All existing libraries I'm aware of, delegate to
<code>lower_bound</code> (+ one further comparison). Since
issue <a href="lwg-defects.html#384" title="equal_range has unimplementable runtime complexity (Status: CD1)">384</a><sup><a href="https://cplusplus.github.io/LWG/issue384" title="Latest snapshot">(i)</a></sup> has now WP status, the resolution of #787 should
be brought in-line with <a href="lwg-defects.html#384" title="equal_range has unimplementable runtime complexity (Status: CD1)">384</a><sup><a href="https://cplusplus.github.io/LWG/issue384" title="Latest snapshot">(i)</a></sup> by changing the <code>+ 2</code>
to <code>+ O(1)</code>.
</p>

<p><i>[
Sophia Antipolis:
]</i></p>


<blockquote><p>
Alisdair prefers to apply an upper bound instead of O(1), but that would
require fixing for <code>lower_bound</code>, <code>upper_bound</code> etc. as well. If he really
cares about it, he'll send an issue to Howard.
</p></blockquote>



<p id="res-787"><b>Proposed resolution:</b></p>
<p>
Change 26.8.4.5 <a href="https://wg21.link/binary.search">[binary.search]</a>/3
</p>

<blockquote><p>
<i>Complexity:</i> At most <code>log<ins><sub>2</sub></ins>(last - first) + <del>2</del> <ins><i>O</i>(1)</ins></code> comparisons.
</p></blockquote>





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