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<li class="toctree-l1"><a class="reference internal" href="../manual/introduction.html">Introduction</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../manual/functions.html#the-return-keyword">The <tt class="docutils literal"><span class="pre">return</span></tt> Keyword</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../manual/constructors.html#incomplete-initialization">Incomplete Initialization</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../manual/constructors.html#case-study-rational">Case Study: Rational</a></li>
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<li class="toctree-l1"><a class="reference internal" href="../manual/conversion-and-promotion.html">Conversion and Promotion</a><ul>
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<li class="toctree-l1"><a class="reference internal" href="../manual/metaprogramming.html">Metaprogramming</a><ul>
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<li class="toctree-l2"><a class="reference internal" href="../manual/metaprogramming.html#reflection">Reflection</a></li>
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<li class="toctree-l1"><a class="reference internal" href="../manual/arrays.html">Multi-dimensional Arrays</a><ul>
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<li class="toctree-l2"><a class="reference internal" href="../manual/networking-and-streams.html#working-with-files">Working with Files</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manual/networking-and-streams.html#a-simple-tcp-example">A simple TCP example</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manual/networking-and-streams.html#resolving-ip-addresses">Resolving IP Addresses</a></li>
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<li class="toctree-l1"><a class="reference internal" href="../manual/parallel-computing.html">Parallel Computing</a><ul>
<li class="toctree-l2"><a class="reference internal" href="../manual/parallel-computing.html#data-movement">Data Movement</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../manual/parallel-computing.html#shared-arrays-experimental">Shared Arrays (Experimental)</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manual/parallel-computing.html#clustermanagers">ClusterManagers</a></li>
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<li class="toctree-l1"><a class="reference internal" href="../manual/running-external-programs.html">Running External Programs</a><ul>
<li class="toctree-l2"><a class="reference internal" href="../manual/running-external-programs.html#interpolation">Interpolation</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manual/running-external-programs.html#quoting">Quoting</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manual/running-external-programs.html#pipelines">Pipelines</a></li>
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<li class="toctree-l1"><a class="reference internal" href="../manual/calling-c-and-fortran-code.html">Calling C and Fortran Code</a><ul>
<li class="toctree-l2"><a class="reference internal" href="../manual/calling-c-and-fortran-code.html#mapping-c-types-to-julia">Mapping C Types to Julia</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manual/calling-c-and-fortran-code.html#accessing-data-through-a-pointer">Accessing Data through a Pointer</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manual/calling-c-and-fortran-code.html#passing-pointers-for-modifying-inputs">Passing Pointers for Modifying Inputs</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manual/calling-c-and-fortran-code.html#garbage-collection-safety">Garbage Collection Safety</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manual/calling-c-and-fortran-code.html#non-constant-function-specifications">Non-constant Function Specifications</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manual/calling-c-and-fortran-code.html#indirect-calls">Indirect Calls</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manual/calling-c-and-fortran-code.html#calling-convention">Calling Convention</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manual/calling-c-and-fortran-code.html#accessing-global-variables">Accessing Global Variables</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manual/calling-c-and-fortran-code.html#passing-julia-callback-functions-to-c">Passing Julia Callback Functions to C</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manual/calling-c-and-fortran-code.html#c">C++</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manual/calling-c-and-fortran-code.html#handling-platform-variations">Handling Platform Variations</a></li>
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<li class="toctree-l1"><a class="reference internal" href="../manual/interacting-with-julia.html">Interacting With Julia</a><ul>
<li class="toctree-l2"><a class="reference internal" href="../manual/interacting-with-julia.html#the-different-prompt-modes">The different prompt modes</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manual/interacting-with-julia.html#key-bindings">Key bindings</a></li>
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<li class="toctree-l1"><a class="reference internal" href="../manual/embedding.html">Embedding Julia</a><ul>
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<li class="toctree-l2"><a class="reference internal" href="../manual/embedding.html#converting-types">Converting Types</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manual/embedding.html#calling-julia-functions">Calling Julia Functions</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manual/embedding.html#memory-management">Memory Management</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../manual/embedding.html#exceptions">Exceptions</a></li>
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<li class="toctree-l1"><a class="reference internal" href="../manual/packages.html">Packages</a><ul>
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<li class="toctree-l1"><a class="reference internal" href="../manual/packages.html#package-development">Package Development</a><ul>
<li class="toctree-l2"><a class="reference internal" href="../manual/packages.html#initial-setup">Initial Setup</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manual/packages.html#generating-a-new-package">Generating a New Package</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manual/packages.html#making-your-package-available">Making Your Package Available</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manual/packages.html#publishing-your-package">Publishing Your Package</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manual/packages.html#tagging-package-versions">Tagging Package Versions</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manual/packages.html#fixing-package-requirements">Fixing Package Requirements</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manual/packages.html#man-package-requirements">Requirements Specification</a></li>
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<li class="toctree-l1"><a class="reference internal" href="../manual/performance-tips.html">Performance Tips</a><ul>
<li class="toctree-l2"><a class="reference internal" href="../manual/performance-tips.html#avoid-global-variables">Avoid global variables</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manual/performance-tips.html#measure-performance-with-time-and-pay-attention-to-memory-allocation">Measure performance with <tt class="docutils literal"><span class="pre">@time</span></tt> and pay attention to memory allocation</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manual/performance-tips.html#tools">Tools</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manual/performance-tips.html#avoid-containers-with-abstract-type-parameters">Avoid containers with abstract type parameters</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manual/performance-tips.html#type-declarations">Type declarations</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manual/performance-tips.html#break-functions-into-multiple-definitions">Break functions into multiple definitions</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manual/performance-tips.html#write-type-stable-functions">Write “type-stable” functions</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manual/performance-tips.html#avoid-changing-the-type-of-a-variable">Avoid changing the type of a variable</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manual/performance-tips.html#separate-kernel-functions">Separate kernel functions</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manual/performance-tips.html#access-arrays-in-memory-order-along-columns">Access arrays in memory order, along columns</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manual/performance-tips.html#pre-allocating-outputs">Pre-allocating outputs</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manual/performance-tips.html#avoid-string-interpolation-for-i-o">Avoid string interpolation for I/O</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manual/performance-tips.html#fix-deprecation-warnings">Fix deprecation warnings</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manual/performance-tips.html#tweaks">Tweaks</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manual/performance-tips.html#performance-annotations">Performance Annotations</a></li>
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<div class="section" id="sorting-and-related-functions">
<h1>Sorting and Related Functions<a class="headerlink" href="#sorting-and-related-functions" title="Permalink to this headline">¶</a></h1>
<p>Julia has an extensive, flexible API for sorting and interacting with
already-sorted arrays of values. For many users, sorting in standard
ascending order, letting Julia pick reasonable default algorithms
will be sufficient:</p>
<div class="highlight-julia"><div class="highlight"><pre><span class="n">julia</span><span class="o">></span> <span class="n">sort</span><span class="p">([</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">1</span><span class="p">])</span>
<span class="mi">3</span><span class="o">-</span><span class="n">element</span> <span class="kt">Int64</span> <span class="n">Array</span><span class="p">:</span>
<span class="mi">1</span>
<span class="mi">2</span>
<span class="mi">3</span>
</pre></div>
</div>
<p>You can easily sort in reverse order as well:</p>
<div class="highlight-julia"><div class="highlight"><pre><span class="n">julia</span><span class="o">></span> <span class="n">sort</span><span class="p">([</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">1</span><span class="p">],</span> <span class="n">rev</span><span class="o">=</span><span class="n">true</span><span class="p">)</span>
<span class="mi">3</span><span class="o">-</span><span class="n">element</span> <span class="kt">Int64</span> <span class="n">Array</span><span class="p">:</span>
<span class="mi">3</span>
<span class="mi">2</span>
<span class="mi">1</span>
</pre></div>
</div>
<p>To sort an array in-place, use the “bang” version of the sort function:</p>
<div class="highlight-julia"><div class="highlight"><pre><span class="n">julia</span><span class="o">></span> <span class="n">a</span> <span class="o">=</span> <span class="p">[</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">1</span><span class="p">];</span>
<span class="n">julia</span><span class="o">></span> <span class="n">sort</span><span class="o">!</span><span class="p">(</span><span class="n">a</span><span class="p">);</span>
<span class="n">julia</span><span class="o">></span> <span class="n">a</span>
<span class="mi">3</span><span class="o">-</span><span class="n">element</span> <span class="kt">Int64</span> <span class="n">Array</span><span class="p">:</span>
<span class="mi">1</span>
<span class="mi">2</span>
<span class="mi">3</span>
</pre></div>
</div>
<p>Instead of directly sorting an array, you can compute a permutation of the array’s indices that puts the array into sorted order:</p>
<div class="highlight-julia"><div class="highlight"><pre><span class="n">julia</span><span class="o">></span> <span class="n">v</span> <span class="o">=</span> <span class="n">randn</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
<span class="mi">5</span><span class="o">-</span><span class="n">element</span> <span class="kt">Float64</span> <span class="n">Array</span><span class="p">:</span>
<span class="mf">0.587746</span>
<span class="o">-</span><span class="mf">0.870797</span>
<span class="o">-</span><span class="mf">0.111843</span>
<span class="mf">1.08793</span>
<span class="o">-</span><span class="mf">1.25061</span>
<span class="n">julia</span><span class="o">></span> <span class="n">p</span> <span class="o">=</span> <span class="n">sortperm</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
<span class="mi">5</span><span class="o">-</span><span class="n">element</span> <span class="kt">Int64</span> <span class="n">Array</span><span class="p">:</span>
<span class="mi">5</span>
<span class="mi">2</span>
<span class="mi">3</span>
<span class="mi">1</span>
<span class="mi">4</span>
<span class="n">julia</span><span class="o">></span> <span class="n">v</span><span class="p">[</span><span class="n">p</span><span class="p">]</span>
<span class="mi">5</span><span class="o">-</span><span class="n">element</span> <span class="kt">Float64</span> <span class="n">Array</span><span class="p">:</span>
<span class="o">-</span><span class="mf">1.25061</span>
<span class="o">-</span><span class="mf">0.870797</span>
<span class="o">-</span><span class="mf">0.111843</span>
<span class="mf">0.587746</span>
<span class="mf">1.08793</span>
</pre></div>
</div>
<p>Arrays can easily be sorted acording to an arbitrary transformation of their values:</p>
<div class="highlight-julia"><div class="highlight"><pre><span class="n">julia</span><span class="o">></span> <span class="n">sort</span><span class="p">(</span><span class="n">v</span><span class="p">,</span> <span class="n">by</span><span class="o">=</span><span class="n">abs</span><span class="p">)</span>
<span class="mi">5</span><span class="o">-</span><span class="n">element</span> <span class="kt">Float64</span> <span class="n">Array</span><span class="p">:</span>
<span class="o">-</span><span class="mf">0.111843</span>
<span class="mf">0.587746</span>
<span class="o">-</span><span class="mf">0.870797</span>
<span class="mf">1.08793</span>
<span class="o">-</span><span class="mf">1.25061</span>
</pre></div>
</div>
<p>Or in reverse order by a transformation:</p>
<div class="highlight-julia"><div class="highlight"><pre><span class="n">julia</span><span class="o">></span> <span class="n">sort</span><span class="p">(</span><span class="n">v</span><span class="p">,</span> <span class="n">by</span><span class="o">=</span><span class="n">abs</span><span class="p">,</span> <span class="n">rev</span><span class="o">=</span><span class="n">true</span><span class="p">)</span>
<span class="mi">5</span><span class="o">-</span><span class="n">element</span> <span class="kt">Float64</span> <span class="n">Array</span><span class="p">:</span>
<span class="o">-</span><span class="mf">1.25061</span>
<span class="mf">1.08793</span>
<span class="o">-</span><span class="mf">0.870797</span>
<span class="mf">0.587746</span>
<span class="o">-</span><span class="mf">0.111843</span>
</pre></div>
</div>
<p>Reasonable sorting algorithms are used by default, but you can choose
other algorithms as well:</p>
<div class="highlight-julia"><div class="highlight"><pre><span class="n">julia</span><span class="o">></span> <span class="n">sort</span><span class="p">(</span><span class="n">v</span><span class="p">,</span> <span class="n">alg</span><span class="o">=</span><span class="n">InsertionSort</span><span class="p">)</span>
<span class="mi">5</span><span class="o">-</span><span class="n">element</span> <span class="kt">Float64</span> <span class="n">Array</span><span class="p">:</span>
<span class="o">-</span><span class="mf">1.25061</span>
<span class="o">-</span><span class="mf">0.870797</span>
<span class="o">-</span><span class="mf">0.111843</span>
<span class="mf">0.587746</span>
<span class="mf">1.08793</span>
</pre></div>
</div>
<div class="section" id="sorting-functions">
<h2>Sorting Functions<a class="headerlink" href="#sorting-functions" title="Permalink to this headline">¶</a></h2>
<dl class="function">
<dt id="Base.sort!">
<tt class="descname">sort!</tt><big>(</big><em>v, [alg=<algorithm>,] [by=<transform>,] [lt=<comparison>,] [rev=false]</em><big>)</big><a class="headerlink" href="#Base.sort!" title="Permalink to this definition">¶</a></dt>
<dd><p>Sort the vector <tt class="docutils literal"><span class="pre">v</span></tt> in place. <tt class="docutils literal"><span class="pre">QuickSort</span></tt> is used by default for numeric arrays
while <tt class="docutils literal"><span class="pre">MergeSort</span></tt> is used for other arrays. You can specify an algorithm to use via
the <tt class="docutils literal"><span class="pre">alg</span></tt> keyword (see <a class="reference internal" href="#sorting-algorithms">Sorting Algorithms</a> for available algorithms). The <tt class="docutils literal"><span class="pre">by</span></tt>
keyword lets you provide a function that will be applied to each element before
comparison; the <tt class="docutils literal"><span class="pre">lt</span></tt> keyword allows providing a custom “less than” function; use
<tt class="docutils literal"><span class="pre">rev=true</span></tt> to reverse the sorting order. These options are independent and can be
used together in all possible combinations: if both <tt class="docutils literal"><span class="pre">by</span></tt> and <tt class="docutils literal"><span class="pre">lt</span></tt> are specified,
the <tt class="docutils literal"><span class="pre">lt</span></tt> function is applied to the result of the <tt class="docutils literal"><span class="pre">by</span></tt> function; <tt class="docutils literal"><span class="pre">rev=true</span></tt>
reverses whatever ordering specified via the <tt class="docutils literal"><span class="pre">by</span></tt> and <tt class="docutils literal"><span class="pre">lt</span></tt> keywords.</p>
</dd></dl>
<dl class="function">
<dt id="Base.sort">
<tt class="descname">sort</tt><big>(</big><em>v, [alg=<algorithm>,] [by=<transform>,] [lt=<comparison>,] [rev=false]</em><big>)</big><a class="headerlink" href="#Base.sort" title="Permalink to this definition">¶</a></dt>
<dd><p>Variant of <tt class="docutils literal"><span class="pre">sort!</span></tt> that returns a sorted copy of <tt class="docutils literal"><span class="pre">v</span></tt> leaving <tt class="docutils literal"><span class="pre">v</span></tt> itself unmodified.</p>
</dd></dl>
<dl class="function">
<dt>
<tt class="descname">sort</tt><big>(</big><em>A, dim, [alg=<algorithm>,] [by=<transform>,] [lt=<comparison>,] [rev=false]</em><big>)</big></dt>
<dd><p>Sort a multidimensional array <tt class="docutils literal"><span class="pre">A</span></tt> along the given dimension.</p>
</dd></dl>
<dl class="function">
<dt id="Base.sortperm">
<tt class="descname">sortperm</tt><big>(</big><em>v, [alg=<algorithm>,] [by=<transform>,] [lt=<comparison>,] [rev=false]</em><big>)</big><a class="headerlink" href="#Base.sortperm" title="Permalink to this definition">¶</a></dt>
<dd><p>Return a permutation vector of indices of <tt class="docutils literal"><span class="pre">v</span></tt> that puts it in sorted order.
Specify <tt class="docutils literal"><span class="pre">alg</span></tt> to choose a particular sorting algorithm (see <a class="reference internal" href="#sorting-algorithms">Sorting Algorithms</a>).
<tt class="docutils literal"><span class="pre">MergeSort</span></tt> is used by default, and since it is stable, the resulting permutation
will be the lexicographically first one that puts the input array into sorted order –
i.e. indices of equal elements appear in ascending order. If you choose a non-stable
sorting algorithm such as <tt class="docutils literal"><span class="pre">QuickSort</span></tt>, a different permutation that puts the array
into order may be returned. The order is specified using the same keywords as <tt class="docutils literal"><span class="pre">sort!</span></tt>.</p>
</dd></dl>
<dl class="function">
<dt id="Base.sortrows">
<tt class="descname">sortrows</tt><big>(</big><em>A, [alg=<algorithm>,] [by=<transform>,] [lt=<comparison>,] [rev=false]</em><big>)</big><a class="headerlink" href="#Base.sortrows" title="Permalink to this definition">¶</a></dt>
<dd><p>Sort the rows of matrix <tt class="docutils literal"><span class="pre">A</span></tt> lexicographically.</p>
</dd></dl>
<dl class="function">
<dt id="Base.sortcols">
<tt class="descname">sortcols</tt><big>(</big><em>A, [alg=<algorithm>,] [by=<transform>,] [lt=<comparison>,] [rev=false]</em><big>)</big><a class="headerlink" href="#Base.sortcols" title="Permalink to this definition">¶</a></dt>
<dd><p>Sort the columns of matrix <tt class="docutils literal"><span class="pre">A</span></tt> lexicographically.</p>
</dd></dl>
</div>
<div class="section" id="order-related-functions">
<h2>Order-Related Functions<a class="headerlink" href="#order-related-functions" title="Permalink to this headline">¶</a></h2>
<dl class="function">
<dt id="Base.issorted">
<tt class="descname">issorted</tt><big>(</big><em>v, [by=<transform>,] [lt=<comparison>,] [rev=false]</em><big>)</big><a class="headerlink" href="#Base.issorted" title="Permalink to this definition">¶</a></dt>
<dd><p>Test whether a vector is in sorted order. The <tt class="docutils literal"><span class="pre">by</span></tt>, <tt class="docutils literal"><span class="pre">lt</span></tt> and <tt class="docutils literal"><span class="pre">rev</span></tt>
keywords modify what order is considered to be sorted just as they do for <tt class="docutils literal"><span class="pre">sort</span></tt>.</p>
</dd></dl>
<dl class="function">
<dt id="Base.searchsorted">
<tt class="descname">searchsorted</tt><big>(</big><em>a, x, [by=<transform>,] [lt=<comparison>,] [rev=false]</em><big>)</big><a class="headerlink" href="#Base.searchsorted" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the range of indices of <tt class="docutils literal"><span class="pre">a</span></tt> which compare as equal to <tt class="docutils literal"><span class="pre">x</span></tt> according to the
order specified by the <tt class="docutils literal"><span class="pre">by</span></tt>, <tt class="docutils literal"><span class="pre">lt</span></tt> and <tt class="docutils literal"><span class="pre">rev</span></tt> keywords, assuming that <tt class="docutils literal"><span class="pre">a</span></tt> is
already sorted in that order. Returns an empty range located at the insertion point if
<tt class="docutils literal"><span class="pre">a</span></tt> does not contain values equal to <tt class="docutils literal"><span class="pre">x</span></tt>.</p>
</dd></dl>
<dl class="function">
<dt id="Base.searchsortedfirst">
<tt class="descname">searchsortedfirst</tt><big>(</big><em>a, x, [by=<transform>,] [lt=<comparison>,] [rev=false]</em><big>)</big><a class="headerlink" href="#Base.searchsortedfirst" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the index of the first value in <tt class="docutils literal"><span class="pre">a</span></tt> greater than or equal to <tt class="docutils literal"><span class="pre">x</span></tt>,
according to the specified order. Returns <tt class="docutils literal"><span class="pre">length(a)+1</span></tt> if <tt class="docutils literal"><span class="pre">x</span></tt> is greater
than all values in <tt class="docutils literal"><span class="pre">a</span></tt>.</p>
</dd></dl>
<dl class="function">
<dt id="Base.searchsortedlast">
<tt class="descname">searchsortedlast</tt><big>(</big><em>a, x, [by=<transform>,] [lt=<comparison>,] [rev=false]</em><big>)</big><a class="headerlink" href="#Base.searchsortedlast" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the index of the last value in <tt class="docutils literal"><span class="pre">a</span></tt> less than or equal to <tt class="docutils literal"><span class="pre">x</span></tt>,
according to the specified order. Returns <tt class="docutils literal"><span class="pre">0</span></tt> if <tt class="docutils literal"><span class="pre">x</span></tt> is less than all
values in <tt class="docutils literal"><span class="pre">a</span></tt>.</p>
</dd></dl>
<dl class="function">
<dt id="Base.select!">
<tt class="descname">select!</tt><big>(</big><em>v, k, [by=<transform>,] [lt=<comparison>,] [rev=false]</em><big>)</big><a class="headerlink" href="#Base.select!" title="Permalink to this definition">¶</a></dt>
<dd><p>Partially sort the vector <tt class="docutils literal"><span class="pre">v</span></tt> in place, according to the order specified by <tt class="docutils literal"><span class="pre">by</span></tt>,
<tt class="docutils literal"><span class="pre">lt</span></tt> and <tt class="docutils literal"><span class="pre">rev</span></tt> so that the value at index <tt class="docutils literal"><span class="pre">k</span></tt> (or range of adjacent values if
<tt class="docutils literal"><span class="pre">k</span></tt> is a range) occurs at the position where it would appear if the array were
fully sorted. If <tt class="docutils literal"><span class="pre">k</span></tt> is a single index, that values is returned; if <tt class="docutils literal"><span class="pre">k</span></tt> is a
range, an array of values at those indices is returned. Note that <tt class="docutils literal"><span class="pre">select!</span></tt> does
not fully sort the input array, but does leave the returned elements where they
would be if the array were fully sorted.</p>
</dd></dl>
<dl class="function">
<dt id="Base.select">
<tt class="descname">select</tt><big>(</big><em>v, k, [by=<transform>,] [lt=<comparison>,] [rev=false]</em><big>)</big><a class="headerlink" href="#Base.select" title="Permalink to this definition">¶</a></dt>
<dd><p>Variant of <tt class="docutils literal"><span class="pre">select!</span></tt> which copies <tt class="docutils literal"><span class="pre">v</span></tt> before partially sorting it, thereby
returning the same thing as <tt class="docutils literal"><span class="pre">select!</span></tt> but leaving <tt class="docutils literal"><span class="pre">v</span></tt> unmodified.</p>
</dd></dl>
</div>
<div class="section" id="sorting-algorithms">
<h2>Sorting Algorithms<a class="headerlink" href="#sorting-algorithms" title="Permalink to this headline">¶</a></h2>
<p>There are currently three sorting algorithms available in base Julia:</p>
<ul class="simple">
<li><tt class="docutils literal"><span class="pre">InsertionSort</span></tt></li>
<li><tt class="docutils literal"><span class="pre">QuickSort</span></tt></li>
<li><tt class="docutils literal"><span class="pre">MergeSort</span></tt></li>
</ul>
<p><tt class="docutils literal"><span class="pre">InsertionSort</span></tt> is an O(n^2) stable sorting algorithm. It is efficient
for very small <tt class="docutils literal"><span class="pre">n</span></tt>, and is used internally by <tt class="docutils literal"><span class="pre">QuickSort</span></tt>.</p>
<p><tt class="docutils literal"><span class="pre">QuickSort</span></tt> is an O(n log n) sorting algorithm which is in-place,
very fast, but not stable – i.e. elements which are considered
equal will not remain in the same order in which they originally
appeared in the array to be sorted. <tt class="docutils literal"><span class="pre">QuickSort</span></tt> is the default
algorithm for numeric values, including integers and floats.</p>
<p><tt class="docutils literal"><span class="pre">MergeSort</span></tt> is an O(n log n) stable sorting algorithm but is not
in-place – it requires a temporary array of equal size to the
input array – and is typically not quite as fast as <tt class="docutils literal"><span class="pre">QuickSort</span></tt>.
It is the default algorithm for non-numeric data.</p>
<p>The sort functions select a reasonable default algorithm, depending on
the type of the array to be sorted. To force a specific algorithm to be
used for <tt class="docutils literal"><span class="pre">sort</span></tt> or other soring functions, supply <tt class="docutils literal"><span class="pre">alg=<algorithm></span></tt>
as a keyword argument after the array to be sorted.</p>
</div>
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