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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/types.html#bits-types">Bits Types</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../manual/types.html#man-parametric-types">Parametric Types</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../manual/types.html#operations-on-types">Operations on Types</a></li>
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<li class="toctree-l1"><a class="reference internal" href="../manual/methods.html">Methods</a><ul>
<li class="toctree-l2"><a class="reference internal" href="../manual/methods.html#defining-methods">Defining Methods</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manual/methods.html#method-ambiguities">Method Ambiguities</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manual/methods.html#parametric-methods">Parametric Methods</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manual/methods.html#note-on-optional-and-keyword-arguments">Note on Optional and keyword Arguments</a></li>
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<li class="toctree-l1"><a class="reference internal" href="../manual/constructors.html">Constructors</a><ul>
<li class="toctree-l2"><a class="reference internal" href="../manual/constructors.html#outer-constructor-methods">Outer Constructor Methods</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manual/constructors.html#inner-constructor-methods">Inner Constructor Methods</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manual/constructors.html#incomplete-initialization">Incomplete Initialization</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manual/constructors.html#parametric-constructors">Parametric Constructors</a></li>
<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>
<li class="toctree-l2"><a class="reference internal" href="../manual/conversion-and-promotion.html#conversion">Conversion</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manual/conversion-and-promotion.html#promotion">Promotion</a></li>
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<li class="toctree-l1"><a class="reference internal" href="../manual/modules.html">Modules</a><ul>
<li class="toctree-l2"><a class="reference internal" href="../manual/modules.html#summary-of-module-usage">Summary of module usage</a></li>
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<li class="toctree-l1"><a class="reference internal" href="../manual/metaprogramming.html">Metaprogramming</a><ul>
<li class="toctree-l2"><a class="reference internal" href="../manual/metaprogramming.html#expressions-and-eval">Expressions and Eval</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manual/metaprogramming.html#macros">Macros</a></li>
<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>
<li class="toctree-l2"><a class="reference internal" href="../manual/arrays.html#arrays">Arrays</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manual/arrays.html#sparse-matrices">Sparse Matrices</a></li>
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<li class="toctree-l1"><a class="reference internal" href="../manual/linear-algebra.html">Linear algebra</a><ul>
<li class="toctree-l2"><a class="reference internal" href="../manual/linear-algebra.html#matrix-factorizations">Matrix factorizations</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manual/linear-algebra.html#special-matrices">Special matrices</a></li>
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<li class="toctree-l1"><a class="reference internal" href="../manual/networking-and-streams.html">Networking and Streams</a><ul>
<li class="toctree-l2"><a class="reference internal" href="../manual/networking-and-streams.html#basic-stream-i-o">Basic Stream I/O</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manual/networking-and-streams.html#text-i-o">Text I/O</a></li>
<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>
<li class="toctree-l2"><a class="reference internal" href="../manual/parallel-computing.html#parallel-map-and-loops">Parallel Map and Loops</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manual/parallel-computing.html#synchronization-with-remote-references">Synchronization With Remote References</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manual/parallel-computing.html#scheduling">Scheduling</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manual/parallel-computing.html#distributed-arrays">Distributed Arrays</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manual/parallel-computing.html#constructing-distributed-arrays">Constructing Distributed Arrays</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manual/parallel-computing.html#distributed-array-operations">Distributed Array Operations</a></li>
<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>
<li class="toctree-l2"><a class="reference internal" href="../manual/embedding.html#high-level-embedding">High-Level Embedding</a></li>
<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>
<li class="toctree-l2"><a class="reference internal" href="../manual/embedding.html#working-with-arrays">Working with Arrays</a></li>
<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>
<li class="toctree-l2"><a class="reference internal" href="../manual/packages.html#package-status">Package Status</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manual/packages.html#adding-and-removing-packages">Adding and Removing Packages</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manual/packages.html#installing-unregistered-packages">Installing Unregistered Packages</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manual/packages.html#updating-packages">Updating Packages</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manual/packages.html#checkout-pin-and-free">Checkout, Pin and Free</a></li>
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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>
</ul>
</li>
<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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<span class="target" id="module-Base.Collections"></span><div class="section" id="collections-and-data-structures">
<h1>Collections and Data Structures<a class="headerlink" href="#collections-and-data-structures" title="Permalink to this headline">¶</a></h1>
<p>The <tt class="docutils literal"><span class="pre">Collections</span></tt> module contains implementations of some common data
structures.</p>
<div class="section" id="priorityqueue">
<h2>PriorityQueue<a class="headerlink" href="#priorityqueue" title="Permalink to this headline">¶</a></h2>
<p>The <tt class="docutils literal"><span class="pre">PriorityQueue</span></tt> type is a basic priority queue implementation allowing for
arbitrary key and priority types. Multiple identical keys are not permitted, but
the priority of existing keys can be changed efficiently.</p>
<dl class="function">
<dt id="Base.Collections.PriorityQueue{K,V}">
<tt class="descname">PriorityQueue{K,V}</tt><big>(</big><span class="optional">[</span><em>ord</em><span class="optional">]</span><big>)</big><a class="headerlink" href="#Base.Collections.PriorityQueue{K,V}" title="Permalink to this definition">¶</a></dt>
<dd><p>Construct a new PriorityQueue, with keys of type K and values/priorites of
type V. If an order is not given, the priority queue is min-ordered using
the default comparison for V.</p>
</dd></dl>
<dl class="function">
<dt id="Base.Collections.enqueue!">
<tt class="descname">enqueue!</tt><big>(</big><em>pq</em>, <em>k</em>, <em>v</em><big>)</big><a class="headerlink" href="#Base.Collections.enqueue!" title="Permalink to this definition">¶</a></dt>
<dd><p>Insert the a key <tt class="docutils literal"><span class="pre">k</span></tt> into a priority queue <tt class="docutils literal"><span class="pre">pq</span></tt> with priority <tt class="docutils literal"><span class="pre">v</span></tt>.</p>
</dd></dl>
<dl class="function">
<dt id="Base.Collections.dequeue!">
<tt class="descname">dequeue!</tt><big>(</big><em>pq</em><big>)</big><a class="headerlink" href="#Base.Collections.dequeue!" title="Permalink to this definition">¶</a></dt>
<dd><p>Remove and return the lowest priority key from a priority queue.</p>
</dd></dl>
<dl class="function">
<dt id="Base.Collections.peek">
<tt class="descname">peek</tt><big>(</big><em>pq</em><big>)</big><a class="headerlink" href="#Base.Collections.peek" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the lowest priority key from a priority queue without removing that key from the queue.</p>
</dd></dl>
<p><tt class="docutils literal"><span class="pre">PriorityQueue</span></tt> also behaves similarly to a <tt class="docutils literal"><span class="pre">Dict</span></tt> so that keys can be
inserted and priorities accessed or changed using indexing notation:</p>
<div class="highlight-julia"><div class="highlight"><pre><span class="c"># Julia code</span>
<span class="n">pq</span> <span class="o">=</span> <span class="n">PriorityQueue</span><span class="p">()</span>
<span class="c"># Insert keys with associated priorities</span>
<span class="n">pq</span><span class="p">[</span><span class="s">"a"</span><span class="p">]</span> <span class="o">=</span> <span class="mi">10</span>
<span class="n">pq</span><span class="p">[</span><span class="s">"b"</span><span class="p">]</span> <span class="o">=</span> <span class="mi">5</span>
<span class="n">pq</span><span class="p">[</span><span class="s">"c"</span><span class="p">]</span> <span class="o">=</span> <span class="mi">15</span>
<span class="c"># Change the priority of an existing key</span>
<span class="n">pq</span><span class="p">[</span><span class="s">"a"</span><span class="p">]</span> <span class="o">=</span> <span class="mi">0</span>
</pre></div>
</div>
</div>
<div class="section" id="heap-functions">
<h2>Heap Functions<a class="headerlink" href="#heap-functions" title="Permalink to this headline">¶</a></h2>
<p>Along with the <tt class="docutils literal"><span class="pre">PriorityQueue</span></tt> type are lower level functions for performing
binary heap operations on arrays. Each function takes an optional ordering
argument. If not given, default ordering is used, so that elements popped from
the heap are given in ascending order.</p>
<dl class="function">
<dt id="Base.Collections.heapify">
<tt class="descname">heapify</tt><big>(</big><em>v</em><span class="optional">[</span>, <em>ord</em><span class="optional">]</span><big>)</big><a class="headerlink" href="#Base.Collections.heapify" title="Permalink to this definition">¶</a></dt>
<dd><p>Return a new vector in binary heap order, optionally using the given
ordering.</p>
</dd></dl>
<dl class="function">
<dt id="Base.Collections.heapify!">
<tt class="descname">heapify!</tt><big>(</big><em>v</em><span class="optional">[</span>, <em>ord</em><span class="optional">]</span><big>)</big><a class="headerlink" href="#Base.Collections.heapify!" title="Permalink to this definition">¶</a></dt>
<dd><p>In-place heapify.</p>
</dd></dl>
<dl class="function">
<dt id="Base.Collections.isheap">
<tt class="descname">isheap</tt><big>(</big><em>v</em><span class="optional">[</span>, <em>ord</em><span class="optional">]</span><big>)</big><a class="headerlink" href="#Base.Collections.isheap" title="Permalink to this definition">¶</a></dt>
<dd><p>Return true iff an array is heap-ordered according to the given order.</p>
</dd></dl>
<dl class="function">
<dt id="Base.Collections.heappush!">
<tt class="descname">heappush!</tt><big>(</big><em>v</em>, <em>x</em><span class="optional">[</span>, <em>ord</em><span class="optional">]</span><big>)</big><a class="headerlink" href="#Base.Collections.heappush!" title="Permalink to this definition">¶</a></dt>
<dd><p>Given a binary heap-ordered array, push a new element <tt class="docutils literal"><span class="pre">x</span></tt>, preserving the heap
property. For efficiency, this function does not check that the array is
indeed heap-ordered.</p>
</dd></dl>
<dl class="function">
<dt id="Base.Collections.heappop!">
<tt class="descname">heappop!</tt><big>(</big><em>v</em><span class="optional">[</span>, <em>ord</em><span class="optional">]</span><big>)</big><a class="headerlink" href="#Base.Collections.heappop!" title="Permalink to this definition">¶</a></dt>
<dd><p>Given a binary heap-ordered array, remove and return the lowest ordered
element. For efficiency, this function does not check that the array is
indeed heap-ordered.</p>
</dd></dl>
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