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<title>Issue 2973: inplace_merge exact comparison count complexity prohibits useful real-world optimizations</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#LEWG">LEWG</a> status.</em></p>
<h3 id="2973"><a href="lwg-active.html#2973">2973</a>. <code>inplace_merge</code> exact comparison count complexity prohibits useful real-world optimizations</h3>
<p><b>Section:</b> 26.8.6 <a href="https://wg21.link/alg.merge">[alg.merge]</a> <b>Status:</b> <a href="lwg-active.html#LEWG">LEWG</a>
 <b>Submitter:</b> Billy Robert O'Neal III <b>Opened:</b> 2017-06-08 <b>Last modified:</b> 2020-09-06</p>
<p><b>Priority: </b>Not Prioritized
</p>
<p><b>View all other</b> <a href="lwg-index.html#alg.merge">issues</a> in [alg.merge].</p>
<p><b>View all issues with</b> <a href="lwg-status.html#LEWG">LEWG</a> status.</p>
<p><b>Discussion:</b></p>
<p>
At the moment, <code>inplace_merge</code> requires exactly <code><i>N</i> - 1</code> comparisons, if enough additional memory is 
available (and in practice enough additional memory is always available). However, this prohibits implementing the 
merge operation using forms of binary search, as in Timsort's 
<a href="https://hg.python.org/cpython/file/tip/Objects/listsort.txt#l451">'Galloping Mode'</a>, a useful optimization 
for non-uniform input data. It's not really useful to prohibit standard libraries from trying a few extra speculative 
compares like this, given that users must be prepared for the fallback "not enough memory" 
&#x1d4aa;(<code><i>N</i> lg <i>N</i></code>) algorithm.
</p>

<p><i>[2017-07 Toronto Monday issue prioritization]</i></p>

<p>Status to LEWG</p>


<p id="res-2973"><b>Proposed resolution:</b></p>
<p>This wording is relative to <a href="https://wg21.link/n4659">N4659</a>.</p>

<ol>
<li>
<p>Edit 26.8.6 <a href="https://wg21.link/alg.merge">[alg.merge]</a> as indicated:</p>

<blockquote>
<pre>template&lt;class BidirectionalIterator&gt;
void inplace_merge(BidirectionalIterator first,
    BidirectionalIterator middle,
    BidirectionalIterator last);
template&lt;class ExecutionPolicy, class BidirectionalIterator&gt;
void inplace_merge(ExecutionPolicy&amp;&amp; exec,
    BidirectionalIterator first,
    BidirectionalIterator middle,
    BidirectionalIterator last);
template&lt;class BidirectionalIterator, class Compare&gt;
void inplace_merge(BidirectionalIterator first,
    BidirectionalIterator middle,
    BidirectionalIterator last, Compare comp);
template&lt;class ExecutionPolicy, class BidirectionalIterator, class Compare&gt;
void inplace_merge(ExecutionPolicy&amp;&amp; exec,
    BidirectionalIterator first,
    BidirectionalIterator middle,
    BidirectionalIterator last, Compare comp);
</pre>
<blockquote>
<p>
[&hellip;]
<p/>
-8- <i>Complexity:</i> Let <code><i>N</i> = last - first</code>:
</p>
<ol style="list-style-type: none">
<li><p>(8.1) &mdash; For the overloads with no <code>ExecutionPolicy</code>, if enough additional memory is available, 
<del>exactly</del> <code><i>N</i> - 1</code> comparisons <ins>on average, &#x1d4aa;(<code><i>N</i></code>) comparisons in 
the worst case</ins>.</p></li>
<li><p>(8.2) &mdash; For the overloads with no <code>ExecutionPolicy</code> if no additional memory is available, 
&#x1d4aa;(<code><i>N</i> log <i>N</i></code>) comparisons.</p></li>
<li><p>(8.3) &mdash; For the overloads with an <code>ExecutionPolicy</code>, &#x1d4aa;(<code><i>N</i> log <i>N</i></code>)
comparisons.</p></li>
</ol>
<p>
-9- <i>Remarks:</i> Stable (16.4.6.8 <a href="https://wg21.link/algorithm.stable">[algorithm.stable]</a>).
</p>
</blockquote>
</blockquote>
</li>
</ol>






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