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<article id="content">
<header>
<h1 class="title">Module <code>dalpy.heaps</code></h1>
</header>
<section id="section-intro">
<p>This module holds classes and functions related to heaps and priority queues.</p>
<p>This module contains <code><a title="dalpy.heaps.PriorityQueue" href="#dalpy.heaps.PriorityQueue">PriorityQueue</a></code>, an implementation of a priority queue, and <code><a title="dalpy.heaps.PriorityQueueUnderflowError" href="#dalpy.heaps.PriorityQueueUnderflowError">PriorityQueueUnderflowError</a></code>, an error
raised by <code><a title="dalpy.heaps.PriorityQueue" href="#dalpy.heaps.PriorityQueue">PriorityQueue</a></code>. This module also contains the function <code><a title="dalpy.heaps.build_min_heap" href="#dalpy.heaps.build_min_heap">build_min_heap()</a></code> which modifies the elements of an
<code><a title="dalpy.arrays.Array" href="arrays.html#dalpy.arrays.Array">Array</a></code> so that they construct a min heap.</p>
<h2 id="examples">Examples</h2>
<p>Initializing, adding, and removing elements from a <code><a title="dalpy.heaps.PriorityQueue" href="#dalpy.heaps.PriorityQueue">PriorityQueue</a></code>:</p>
<pre><code>q = PriorityQueue()
q.insert('a', 2)
q.insert('b', 1)
q.extract_min()
</code></pre>
<p>The following code will raise a <code><a title="dalpy.heaps.PriorityQueueUnderflowError" href="#dalpy.heaps.PriorityQueueUnderflowError">PriorityQueueUnderflowError</a></code> because the second extract min is done on an empty
<code><a title="dalpy.heaps.PriorityQueue" href="#dalpy.heaps.PriorityQueue">PriorityQueue</a></code>:</p>
<pre><code>q.extract_min()
q.extract_min()
</code></pre>
</section>
<section>
</section>
<section>
</section>
<section>
<h2 class="section-title" id="header-functions">Functions</h2>
<dl>
<dt id="dalpy.heaps.build_min_heap"><code class="name flex">
<span>def <span class="ident">build_min_heap</span></span>(<span>arr)</span>
</code></dt>
<dd>
<div class="desc"><p>Modifies an <code><a title="dalpy.arrays.Array" href="arrays.html#dalpy.arrays.Array">Array</a></code> so that its elements make up a min heap.</p>
<p>This method does not return a copy of the provided <code><a title="dalpy.arrays.Array" href="arrays.html#dalpy.arrays.Array">Array</a></code> whose elements make up a heap, it modifies it in place.
Furthermore, all the elements (starting from index 0) are in a min heap. A user may assume that this method runs in
<code>O(n)</code> time where <code>n</code> is the length of the input <code><a title="dalpy.arrays.Array" href="arrays.html#dalpy.arrays.Array">Array</a></code>.</p>
<h2 id="args">Args</h2>
<dl>
<dt><strong><code>arr</code></strong></dt>
<dd>The input <code><a title="dalpy.arrays.Array" href="arrays.html#dalpy.arrays.Array">Array</a></code>. Its elements should be comparable with <code><</code>, <code>>=</code>, etc.</dd>
</dl>
<h2 id="raises">Raises</h2>
<dl>
<dt><code>TypeError</code></dt>
<dd>If <code>arr</code> is not an <code><a title="dalpy.arrays.Array" href="arrays.html#dalpy.arrays.Array">Array</a></code>'.</dd>
</dl></div>
</dd>
</dl>
</section>
<section>
<h2 class="section-title" id="header-classes">Classes</h2>
<dl>
<dt id="dalpy.heaps.PriorityQueue"><code class="flex name class">
<span>class <span class="ident">PriorityQueue</span></span>
</code></dt>
<dd>
<div class="desc"><p>This class represents a minimum priority queue.</p>
<p>One may assume that this <code><a title="dalpy.heaps.PriorityQueue" href="#dalpy.heaps.PriorityQueue">PriorityQueue</a></code> has no maximum capacity.</p>
<h2 id="examples">Examples</h2>
<p>To initialize a <code><a title="dalpy.heaps.PriorityQueue" href="#dalpy.heaps.PriorityQueue">PriorityQueue</a></code>:</p>
<pre><code>q = PriorityQueue()
</code></pre>
<p>To add elements to <code>q</code>:</p>
<pre><code>q.insert('a', 2)
q.insert('b', 1)
</code></pre>
<p>To remove and return the minimum priority element of <code>q</code> (in this case <code>x = 'b'</code>):</p>
<pre><code>x = q.extract_min()
</code></pre>
<p>To see the minimum priority element of <code>q</code> (in this case <code>y = 'a'</code>):</p>
<pre><code>y = q.front()
</code></pre>
<p>To decrease the priority of an element in <code>q</code>:</p>
<pre><code>q.decrease_key('a', 0)
</code></pre>
<p>Initializes an empty <code><a title="dalpy.heaps.PriorityQueue" href="#dalpy.heaps.PriorityQueue">PriorityQueue</a></code> in <code>O(1)</code> time.</p></div>
<h3>Methods</h3>
<dl>
<dt id="dalpy.heaps.PriorityQueue.decrease_key"><code class="name flex">
<span>def <span class="ident">decrease_key</span></span>(<span>self, element, new_priority)</span>
</code></dt>
<dd>
<div class="desc"><p>Decreases the priority of an element in this <code><a title="dalpy.heaps.PriorityQueue" href="#dalpy.heaps.PriorityQueue">PriorityQueue</a></code>.</p>
<p>One may assume that this operation runs in <code>O(log(n))</code> time where <code>n</code> is the size of this <code><a title="dalpy.heaps.PriorityQueue" href="#dalpy.heaps.PriorityQueue">PriorityQueue</a></code>.</p>
<h2 id="args">Args</h2>
<dl>
<dt><strong><code>element</code></strong></dt>
<dd>The element whose priority is being updated.</dd>
<dt><strong><code>new_priority</code></strong></dt>
<dd>The new priority of <code>element</code>. It should be <code><=</code> its existing priority.</dd>
</dl>
<h2 id="raises">Raises</h2>
<dl>
<dt><code>ValueError</code></dt>
<dd>If <code>element</code> is not in this <code><a title="dalpy.heaps.PriorityQueue" href="#dalpy.heaps.PriorityQueue">PriorityQueue</a></code> or <code>new_priority</code> is greater than the existing
priority of <code>element</code>.</dd>
</dl></div>
</dd>
<dt id="dalpy.heaps.PriorityQueue.extract_min"><code class="name flex">
<span>def <span class="ident">extract_min</span></span>(<span>self)</span>
</code></dt>
<dd>
<div class="desc"><p>Removes the minimum priority element of this <code><a title="dalpy.heaps.PriorityQueue" href="#dalpy.heaps.PriorityQueue">PriorityQueue</a></code>.</p>
<p>One may assume that this operation runs in <code>O(log(n))</code> time where <code>n</code> is the size of this <code><a title="dalpy.heaps.PriorityQueue" href="#dalpy.heaps.PriorityQueue">PriorityQueue</a></code>.</p>
<h2 id="returns">Returns</h2>
<p>The element with the minimum priority in this <code><a title="dalpy.heaps.PriorityQueue" href="#dalpy.heaps.PriorityQueue">PriorityQueue</a></code>.</p>
<h2 id="raises">Raises</h2>
<dl>
<dt><code><a title="dalpy.heaps.PriorityQueueUnderflowError" href="#dalpy.heaps.PriorityQueueUnderflowError">PriorityQueueUnderflowError</a></code></dt>
<dd>If this <code><a title="dalpy.heaps.PriorityQueue" href="#dalpy.heaps.PriorityQueue">PriorityQueue</a></code> is empty.</dd>
</dl></div>
</dd>
<dt id="dalpy.heaps.PriorityQueue.insert"><code class="name flex">
<span>def <span class="ident">insert</span></span>(<span>self, element, priority)</span>
</code></dt>
<dd>
<div class="desc"><p>Inserts an element into the <code><a title="dalpy.heaps.PriorityQueue" href="#dalpy.heaps.PriorityQueue">PriorityQueue</a></code> with an associated priority.</p>
<p>One may assume that this operation runs in <code>O(log(n))</code> time where <code>n</code> is the size of this <code>Queue</code>.</p>
<h2 id="args">Args</h2>
<dl>
<dt><strong><code>element</code></strong></dt>
<dd>An element to add to this <code><a title="dalpy.heaps.PriorityQueue" href="#dalpy.heaps.PriorityQueue">PriorityQueue</a></code>. This can be of any type.</dd>
<dt><strong><code>priority</code></strong></dt>
<dd>The integer priority <code>element</code> should have in this <code><a title="dalpy.heaps.PriorityQueue" href="#dalpy.heaps.PriorityQueue">PriorityQueue</a></code>.</dd>
</dl></div>
</dd>
<dt id="dalpy.heaps.PriorityQueue.is_empty"><code class="name flex">
<span>def <span class="ident">is_empty</span></span>(<span>self)</span>
</code></dt>
<dd>
<div class="desc"><p>Returns whether this <code><a title="dalpy.heaps.PriorityQueue" href="#dalpy.heaps.PriorityQueue">PriorityQueue</a></code> is empty in <code>O(1)</code> time w/r/t the size of this <code><a title="dalpy.heaps.PriorityQueue" href="#dalpy.heaps.PriorityQueue">PriorityQueue</a></code>.</p>
<h2 id="returns">Returns</h2>
<p><code>True</code> if this <code><a title="dalpy.heaps.PriorityQueue" href="#dalpy.heaps.PriorityQueue">PriorityQueue</a></code> is empty, <code>False</code> otherwise.</p></div>
</dd>
<dt id="dalpy.heaps.PriorityQueue.minimum"><code class="name flex">
<span>def <span class="ident">minimum</span></span>(<span>self)</span>
</code></dt>
<dd>
<div class="desc"><p>Gets the minimum priority element of this <code><a title="dalpy.heaps.PriorityQueue" href="#dalpy.heaps.PriorityQueue">PriorityQueue</a></code>.</p>
<p>One may assume that this operation runs in <code>O(1)</code> time with respect to the size of this <code><a title="dalpy.heaps.PriorityQueue" href="#dalpy.heaps.PriorityQueue">PriorityQueue</a></code>.</p>
<h2 id="returns">Returns</h2>
<p>The element with the minimum priority in this <code><a title="dalpy.heaps.PriorityQueue" href="#dalpy.heaps.PriorityQueue">PriorityQueue</a></code>.</p>
<h2 id="raises">Raises</h2>
<dl>
<dt><code><a title="dalpy.heaps.PriorityQueueUnderflowError" href="#dalpy.heaps.PriorityQueueUnderflowError">PriorityQueueUnderflowError</a></code></dt>
<dd>If this <code><a title="dalpy.heaps.PriorityQueue" href="#dalpy.heaps.PriorityQueue">PriorityQueue</a></code> is empty.</dd>
</dl></div>
</dd>
<dt id="dalpy.heaps.PriorityQueue.size"><code class="name flex">
<span>def <span class="ident">size</span></span>(<span>self)</span>
</code></dt>
<dd>
<div class="desc"><p>Returns the size of this <code><a title="dalpy.heaps.PriorityQueue" href="#dalpy.heaps.PriorityQueue">PriorityQueue</a></code> in <code>O(1)</code> time w/r/t the size of this <code><a title="dalpy.heaps.PriorityQueue" href="#dalpy.heaps.PriorityQueue">PriorityQueue</a></code>.</p>
<h2 id="returns">Returns</h2>
<p>The integer number of elements in this <code><a title="dalpy.heaps.PriorityQueue" href="#dalpy.heaps.PriorityQueue">PriorityQueue</a></code>.</p></div>
</dd>
</dl>
</dd>
<dt id="dalpy.heaps.PriorityQueueUnderflowError"><code class="flex name class">
<span>class <span class="ident">PriorityQueueUnderflowError</span></span>
<span>(</span><span>operation)</span>
</code></dt>
<dd>
<div class="desc"><p>This class is used by <code><a title="dalpy.heaps.PriorityQueue" href="#dalpy.heaps.PriorityQueue">PriorityQueue</a></code> to raise errors for operations done on an empty <code><a title="dalpy.heaps.PriorityQueue" href="#dalpy.heaps.PriorityQueue">PriorityQueue</a></code>.</p>
<p>Initializes a <code><a title="dalpy.heaps.PriorityQueueUnderflowError" href="#dalpy.heaps.PriorityQueueUnderflowError">PriorityQueueUnderflowError</a></code> that will be raised associated with a <code><a title="dalpy.heaps.PriorityQueue" href="#dalpy.heaps.PriorityQueue">PriorityQueue</a></code> operation.</p>
<h2 id="args">Args</h2>
<dl>
<dt><strong><code>operation</code></strong></dt>
<dd>a string specifying the operation to raise an error on</dd>
</dl></div>
<h3>Ancestors</h3>
<ul class="hlist">
<li>builtins.Exception</li>
<li>builtins.BaseException</li>
</ul>
</dd>
</dl>
</section>
</article>
<nav id="sidebar">
<h1>Index</h1>
<div class="toc">
<ul></ul>
</div>
<ul id="index">
<li><h3>Super-module</h3>
<ul>
<li><code><a title="dalpy" href="index.html">dalpy</a></code></li>
</ul>
</li>
<li><h3><a href="#header-functions">Functions</a></h3>
<ul class="">
<li><code><a title="dalpy.heaps.build_min_heap" href="#dalpy.heaps.build_min_heap">build_min_heap</a></code></li>
</ul>
</li>
<li><h3><a href="#header-classes">Classes</a></h3>
<ul>
<li>
<h4><code><a title="dalpy.heaps.PriorityQueue" href="#dalpy.heaps.PriorityQueue">PriorityQueue</a></code></h4>
<ul class="two-column">
<li><code><a title="dalpy.heaps.PriorityQueue.decrease_key" href="#dalpy.heaps.PriorityQueue.decrease_key">decrease_key</a></code></li>
<li><code><a title="dalpy.heaps.PriorityQueue.extract_min" href="#dalpy.heaps.PriorityQueue.extract_min">extract_min</a></code></li>
<li><code><a title="dalpy.heaps.PriorityQueue.insert" href="#dalpy.heaps.PriorityQueue.insert">insert</a></code></li>
<li><code><a title="dalpy.heaps.PriorityQueue.is_empty" href="#dalpy.heaps.PriorityQueue.is_empty">is_empty</a></code></li>
<li><code><a title="dalpy.heaps.PriorityQueue.minimum" href="#dalpy.heaps.PriorityQueue.minimum">minimum</a></code></li>
<li><code><a title="dalpy.heaps.PriorityQueue.size" href="#dalpy.heaps.PriorityQueue.size">size</a></code></li>
</ul>
</li>
<li>
<h4><code><a title="dalpy.heaps.PriorityQueueUnderflowError" href="#dalpy.heaps.PriorityQueueUnderflowError">PriorityQueueUnderflowError</a></code></h4>
</li>
</ul>
</li>
</ul>
</nav>
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