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<title>Priority Queue </title>
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<h1>Priority Queue</h1>
<p class="editor-contents__short-description">In this tutorial, you will learn what priority queue is. Also, you will learn about it's implementations in Python, Java, C, and C++.</p>
<div id="node-1510" class="node node-algorithm clearfix" about="/dsa/priority-queue" typeof="sioc:Item foaf:Document">
<span property="dc:title" content="Priority Queue" class="rdf-meta element-hidden"></span>
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<p id="definition">A priority queue is a <strong>special type of queue</strong> in which each element is associated with a <strong>priority value</strong>. And, elements are served on the basis of their priority. That is, higher priority elements are served first.</p>
<p>However, if elements with the same priority occur, they are served according to their order in the queue.</p>
<p><strong>Assigning Priority Value</strong></p>
<p>Generally, the value of the element itself is considered for assigning the priority. For example,</p>
<p>The element with the highest value is considered the highest priority element. However, in other cases, we can assume the element with the lowest value as the highest priority element.</p>
<p>We can also set priorities according to our needs.</p>
<figure><img alt="the element with highest priority is removed from the priority queue" src="//cdn.programiz.com/sites/tutorial2program/files/Introduction.png" title="Priority Queue" width="450" height="399"><figcaption>Removing Highest Priority Element</figcaption></figure><hr><h3>Difference between Priority Queue and Normal Queue</h3>
<p>In a queue, the <strong>first-in-first-out rule</strong> is implemented whereas, in a priority queue, the values are removed <strong>on the basis of priority</strong>. The element with the highest priority is removed first.</p>
<hr><h2 id="implementation">Implementation of Priority Queue</h2>
<p>Priority queue can be implemented using an array, a linked list, a heap data structure, or a binary search tree. Among these data structures, heap data structure provides an efficient implementation of priority queues.</p>
<p>Hence, we will be using the heap data structure to implement the priority queue in this tutorial. A max-heap is implemented in the following operations. If you want to learn more about it, please visit <a href="/dsa/heap-sort.html#heap">max-heap and min-heap</a>.</p>
<p>A comparative analysis of different implementations of priority queue is given below.</p>
<div class="table-responsive">
<table border="0"><tbody><tr><th>Operations</th>
<th>peek</th>
<th>insert</th>
<th>delete</th>
</tr><tr><td>Linked List</td>
<td><code>O(1)</code></td>
<td><code>O(n)</code></td>
<td><code>O(1)</code></td>
</tr><tr><td>Binary Heap</td>
<td><code>O(1)</code></td>
<td><code>O(log n)</code></td>
<td><code>O(log n)</code></td>
</tr><tr><td>Binary Search Tree</td>
<td><code>O(1)</code></td>
<td><code>O(log n)</code></td>
<td><code>O(log n)</code></td>
</tr></tbody></table></div>
<hr><h2>Priority Queue Operations</h2>
<p>Basic operations of a priority queue are inserting, removing, and peeking elements.</p>
<p class="note-tip">Before studying the priority queue, please refer to the <a href="/dsa/heap-data-structure.html">heap data structure</a> for a better understanding of binary heap as it is used to implement the priority queue in this article.</p>
<hr><h3 id="insert">1. Inserting an Element into the Priority Queue</h3>
<p></p><div class="clearfix"></div><p>Inserting an element into a priority queue (max-heap) is done by the following steps.</p>
<ul><li>Insert the new element at the end of the tree.
<figure><img alt="insert an element at the end of the priority queue" src="//cdn.programiz.com/sites/tutorial2program/files/insert-1_0.png" title="Priority queue insertion" width="280" height="229"><figcaption>Insert an element at the end of the queue</figcaption></figure></li>
<li><a href="/dsa/heap-data-structure.html#heapify">Heapify</a> the tree.
<figure><img alt="heapify the priority queue after inserting new element" src="//cdn.programiz.com/sites/tutorial2program/files/insert-2_0.png" title="Priority queue insertion" width="280" height="229"><figcaption>Heapify after insertion</figcaption></figure></li>
</ul><p>Algorithm for insertion of an element into priority queue (max-heap)</p>
<pre>If there is no node,
create a newNode.
else (a node is already present)
insert the newNode at the end (last node from left to right.)
heapify the array</pre>
<p>For Min Heap, the above algorithm is modified so that <code>parentNode</code> is always smaller than <code>newNode</code>.</p>
<hr><h3 id="delete">2. Deleting an Element from the Priority Queue</h3>
<p>Deleting an element from a priority queue (max-heap) is done as follows:</p>
<ul><li>Select the element to be deleted.
<figure><img alt="choose the element to be deleted from the priority queue" src="//cdn.programiz.com/sites/tutorial2program/files/delete-1_0.png" title="Priority queue deletion" width="280" height="229"><figcaption>Select the element to be deleted</figcaption></figure></li>
<li>Swap it with the last element.
<figure><img alt="swap the element to be deleted with the last leaf node element" src="//cdn.programiz.com/sites/tutorial2program/files/delete-2_0.png" title="Swap the element with the last leaf of heap" width="280" height="229"><figcaption>Swap with the last leaf node element</figcaption></figure></li>
<li>Remove the last element.
<figure><img alt="remove the last leaf node element" src="//cdn.programiz.com/sites/tutorial2program/files/delete-3.png" title="Remove last leaf element" width="297" height="251"><figcaption>Remove the last element leaf</figcaption></figure></li>
<li>Heapify the tree.
<figure><img alt="heapify the priority queue" src="//cdn.programiz.com/sites/tutorial2program/files/delete-4.png" title="Heapify Priority Queue after deletion" width="297" height="274"><figcaption>Heapify the priority queue</figcaption></figure></li>
</ul><p>Algorithm for deletion of an element in the priority queue (max-heap)</p>
<pre>If nodeToBeDeleted is the leafNode
remove the node
Else swap nodeToBeDeleted with the lastLeafNode
remove noteToBeDeleted
heapify the array</pre>
<p>For Min Heap, the above algorithm is modified so that the both <code>childNodes</code> are smaller than <code>currentNode</code>.</p>
<hr><h3>3. Peeking from the Priority Queue (Find max/min)</h3>
<p>Peek operation returns the maximum element from Max Heap or minimum element from Min Heap without deleting the node.</p>
<p>For both Max heap and Min Heap</p>
<pre>return rootNode</pre>
<hr><h3>4. Extract-Max/Min from the Priority Queue</h3>
<p>Extract-Max returns the node with maximum value after removing it from a Max Heap whereas Extract-Min returns the node with minimum value after removing it from Min Heap.</p>
<hr><h2 id="code">Priority Queue Implementations in Python, Java, C, and C++</h2>
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<div class="pre-code-wrapper"><div title="Click to copy" class="copy-code-button"></div><pre class="exec" style="max-height: 600px;"><code class="python hljs"><span class="hljs-comment"># Priority Queue implementation in Python</span>
<span class="hljs-comment"># Function to heapify the tree</span>
<span class="hljs-function"><span class="hljs-keyword">def</span> <span class="hljs-title">heapify</span><span class="hljs-params">(arr, n, i)</span>:</span>
<span class="hljs-comment"># Find the largest among root, left child and right child</span>
largest = i
l = <span class="hljs-number">2</span> * i + <span class="hljs-number">1</span>
r = <span class="hljs-number">2</span> * i + <span class="hljs-number">2</span>
<span class="hljs-keyword">if</span> l < n <span class="hljs-keyword">and</span> arr[i] < arr[l]:
largest = l
<span class="hljs-keyword">if</span> r < n <span class="hljs-keyword">and</span> arr[largest] < arr[r]:
largest = r
<span class="hljs-comment"># Swap and continue heapifying if root is not largest</span>
<span class="hljs-keyword">if</span> largest != i:
arr[i], arr[largest] = arr[largest], arr[i]
heapify(arr, n, largest)
<span class="hljs-comment"># Function to insert an element into the tree</span>
<span class="hljs-function"><span class="hljs-keyword">def</span> <span class="hljs-title">insert</span><span class="hljs-params">(array, newNum)</span>:</span>
size = len(array)
<span class="hljs-keyword">if</span> size == <span class="hljs-number">0</span>:
array.append(newNum)
<span class="hljs-keyword">else</span>:
array.append(newNum)
<span class="hljs-keyword">for</span> i <span class="hljs-keyword">in</span> range((size // <span class="hljs-number">2</span>) - <span class="hljs-number">1</span>, <span class="hljs-number">-1</span>, <span class="hljs-number">-1</span>):
heapify(array, size, i)
<span class="hljs-comment"># Function to delete an element from the tree</span>
<span class="hljs-function"><span class="hljs-keyword">def</span> <span class="hljs-title">deleteNode</span><span class="hljs-params">(array, num)</span>:</span>
size = len(array)
i = <span class="hljs-number">0</span>
<span class="hljs-keyword">for</span> i <span class="hljs-keyword">in</span> range(<span class="hljs-number">0</span>, size):
<span class="hljs-keyword">if</span> num == array[i]:
<span class="hljs-keyword">break</span>
array[i], array[size - <span class="hljs-number">1</span>] = array[size - <span class="hljs-number">1</span>], array[i]
array.remove(size - <span class="hljs-number">1</span>)
<span class="hljs-keyword">for</span> i <span class="hljs-keyword">in</span> range((len(array) // <span class="hljs-number">2</span>) - <span class="hljs-number">1</span>, <span class="hljs-number">-1</span>, <span class="hljs-number">-1</span>):
heapify(array, len(array), i)
arr = []
insert(arr, <span class="hljs-number">3</span>)
insert(arr, <span class="hljs-number">4</span>)
insert(arr, <span class="hljs-number">9</span>)
insert(arr, <span class="hljs-number">5</span>)
insert(arr, <span class="hljs-number">2</span>)
<span class="hljs-keyword">print</span> (<span class="hljs-string">"Max-Heap array: "</span> + str(arr))
deleteNode(arr, <span class="hljs-number">4</span>)
<span class="hljs-keyword">print</span>(<span class="hljs-string">"After deleting an element: "</span> + str(arr))</code></pre></div>
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<div class="pre-code-wrapper"><div title="Click to copy" class="copy-code-button"></div><pre class="exec" style="max-height: 600px;"><code class="java hljs"><span class="hljs-comment">// Priority Queue implementation in Java</span>
<span class="hljs-keyword">import</span> java.util.ArrayList;
<span class="hljs-class"><span class="hljs-keyword">class</span> <span class="hljs-title">Heap</span> </span>{
<span class="hljs-comment">// Function to heapify the tree</span>
<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">heapify</span><span class="hljs-params">(ArrayList<Integer> hT, <span class="hljs-keyword">int</span> i)</span> </span>{
<span class="hljs-keyword">int</span> size = hT.size();
<span class="hljs-comment">// Find the largest among root, left child and right child</span>
<span class="hljs-keyword">int</span> largest = i;
<span class="hljs-keyword">int</span> l = <span class="hljs-number">2</span> * i + <span class="hljs-number">1</span>;
<span class="hljs-keyword">int</span> r = <span class="hljs-number">2</span> * i + <span class="hljs-number">2</span>;
<span class="hljs-keyword">if</span> (l < size && hT.get(l) > hT.get(largest))
largest = l;
<span class="hljs-keyword">if</span> (r < size && hT.get(r) > hT.get(largest))
largest = r;
<span class="hljs-comment">// Swap and continue heapifying if root is not largest</span>
<span class="hljs-keyword">if</span> (largest != i) {
<span class="hljs-keyword">int</span> temp = hT.get(largest);
hT.set(largest, hT.get(i));
hT.set(i, temp);
heapify(hT, largest);
}
}
<span class="hljs-comment">// Function to insert an element into the tree</span>
<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">insert</span><span class="hljs-params">(ArrayList<Integer> hT, <span class="hljs-keyword">int</span> newNum)</span> </span>{
<span class="hljs-keyword">int</span> size = hT.size();
<span class="hljs-keyword">if</span> (size == <span class="hljs-number">0</span>) {
hT.add(newNum);
} <span class="hljs-keyword">else</span> {
hT.add(newNum);
<span class="hljs-keyword">for</span> (<span class="hljs-keyword">int</span> i = size / <span class="hljs-number">2</span> - <span class="hljs-number">1</span>; i >= <span class="hljs-number">0</span>; i--) {
heapify(hT, i);
}
}
}
<span class="hljs-comment">// Function to delete an element from the tree</span>
<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">deleteNode</span><span class="hljs-params">(ArrayList<Integer> hT, <span class="hljs-keyword">int</span> num)</span> </span>{
<span class="hljs-keyword">int</span> size = hT.size();
<span class="hljs-keyword">int</span> i;
<span class="hljs-keyword">for</span> (i = <span class="hljs-number">0</span>; i < size; i++) {
<span class="hljs-keyword">if</span> (num == hT.get(i))
<span class="hljs-keyword">break</span>;
}
<span class="hljs-keyword">int</span> temp = hT.get(i);
hT.set(i, hT.get(size - <span class="hljs-number">1</span>));
hT.set(size - <span class="hljs-number">1</span>, temp);
hT.remove(size - <span class="hljs-number">1</span>);
<span class="hljs-keyword">for</span> (<span class="hljs-keyword">int</span> j = size / <span class="hljs-number">2</span> - <span class="hljs-number">1</span>; j >= <span class="hljs-number">0</span>; j--) {
heapify(hT, j);
}
}
<span class="hljs-comment">// Print the tree</span>
<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">printArray</span><span class="hljs-params">(ArrayList<Integer> array, <span class="hljs-keyword">int</span> size)</span> </span>{
<span class="hljs-keyword">for</span> (Integer i : array) {
System.out.print(i + <span class="hljs-string">" "</span>);
}
System.out.println();
}
<span class="hljs-comment">// Driver code</span>
<span class="hljs-function"><span class="hljs-keyword">public</span> <span class="hljs-keyword">static</span> <span class="hljs-keyword">void</span> <span class="hljs-title">main</span><span class="hljs-params">(String args[])</span> </span>{
ArrayList<Integer> array = <span class="hljs-keyword">new</span> ArrayList<Integer>();
<span class="hljs-keyword">int</span> size = array.size();
Heap h = <span class="hljs-keyword">new</span> Heap();
h.insert(array, <span class="hljs-number">3</span>);
h.insert(array, <span class="hljs-number">4</span>);
h.insert(array, <span class="hljs-number">9</span>);
h.insert(array, <span class="hljs-number">5</span>);
h.insert(array, <span class="hljs-number">2</span>);
System.out.println(<span class="hljs-string">"Max-Heap array: "</span>);
h.printArray(array, size);
h.deleteNode(array, <span class="hljs-number">4</span>);
System.out.println(<span class="hljs-string">"After deleting an element: "</span>);
h.printArray(array, size);
}
}</code></pre></div>
</div>
<div class="code-editor__area" id="c-code">
<div class="pre-code-wrapper"><div title="Click to copy" class="copy-code-button"></div><pre class="exec" style="max-height: 600px;"><code class="c hljs cpp"><span class="hljs-comment">// Priority Queue implementation in C</span>
<span class="hljs-meta">#<span class="hljs-meta-keyword">include</span> <span class="hljs-meta-string"><stdio.h></span></span>
<span class="hljs-keyword">int</span> size = <span class="hljs-number">0</span>;
<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">swap</span><span class="hljs-params">(<span class="hljs-keyword">int</span> *a, <span class="hljs-keyword">int</span> *b)</span> </span>{
<span class="hljs-keyword">int</span> temp = *b;
*b = *a;
*a = temp;
}
<span class="hljs-comment">// Function to heapify the tree</span>
<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">heapify</span><span class="hljs-params">(<span class="hljs-keyword">int</span> <span class="hljs-built_in">array</span>[], <span class="hljs-keyword">int</span> size, <span class="hljs-keyword">int</span> i)</span> </span>{
<span class="hljs-keyword">if</span> (size == <span class="hljs-number">1</span>) {
<span class="hljs-built_in">printf</span>(<span class="hljs-string">"Single element in the heap"</span>);
} <span class="hljs-keyword">else</span> {
<span class="hljs-comment">// Find the largest among root, left child and right child</span>
<span class="hljs-keyword">int</span> largest = i;
<span class="hljs-keyword">int</span> l = <span class="hljs-number">2</span> * i + <span class="hljs-number">1</span>;
<span class="hljs-keyword">int</span> r = <span class="hljs-number">2</span> * i + <span class="hljs-number">2</span>;
<span class="hljs-keyword">if</span> (l < size && <span class="hljs-built_in">array</span>[l] > <span class="hljs-built_in">array</span>[largest])
largest = l;
<span class="hljs-keyword">if</span> (r < size && <span class="hljs-built_in">array</span>[r] > <span class="hljs-built_in">array</span>[largest])
largest = r;
<span class="hljs-comment">// Swap and continue heapifying if root is not largest</span>
<span class="hljs-keyword">if</span> (largest != i) {
swap(&<span class="hljs-built_in">array</span>[i], &<span class="hljs-built_in">array</span>[largest]);
heapify(<span class="hljs-built_in">array</span>, size, largest);
}
}
}
<span class="hljs-comment">// Function to insert an element into the tree</span>
<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">insert</span><span class="hljs-params">(<span class="hljs-keyword">int</span> <span class="hljs-built_in">array</span>[], <span class="hljs-keyword">int</span> newNum)</span> </span>{
<span class="hljs-keyword">if</span> (size == <span class="hljs-number">0</span>) {
<span class="hljs-built_in">array</span>[<span class="hljs-number">0</span>] = newNum;
size += <span class="hljs-number">1</span>;
} <span class="hljs-keyword">else</span> {
<span class="hljs-built_in">array</span>[size] = newNum;
size += <span class="hljs-number">1</span>;
<span class="hljs-keyword">for</span> (<span class="hljs-keyword">int</span> i = size / <span class="hljs-number">2</span> - <span class="hljs-number">1</span>; i >= <span class="hljs-number">0</span>; i--) {
heapify(<span class="hljs-built_in">array</span>, size, i);
}
}
}
<span class="hljs-comment">// Function to delete an element from the tree</span>
<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">deleteRoot</span><span class="hljs-params">(<span class="hljs-keyword">int</span> <span class="hljs-built_in">array</span>[], <span class="hljs-keyword">int</span> num)</span> </span>{
<span class="hljs-keyword">int</span> i;
<span class="hljs-keyword">for</span> (i = <span class="hljs-number">0</span>; i < size; i++) {
<span class="hljs-keyword">if</span> (num == <span class="hljs-built_in">array</span>[i])
<span class="hljs-keyword">break</span>;
}
swap(&<span class="hljs-built_in">array</span>[i], &<span class="hljs-built_in">array</span>[size - <span class="hljs-number">1</span>]);
size -= <span class="hljs-number">1</span>;
<span class="hljs-keyword">for</span> (<span class="hljs-keyword">int</span> i = size / <span class="hljs-number">2</span> - <span class="hljs-number">1</span>; i >= <span class="hljs-number">0</span>; i--) {
heapify(<span class="hljs-built_in">array</span>, size, i);
}
}
<span class="hljs-comment">// Print the array</span>
<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">printArray</span><span class="hljs-params">(<span class="hljs-keyword">int</span> <span class="hljs-built_in">array</span>[], <span class="hljs-keyword">int</span> size)</span> </span>{
<span class="hljs-keyword">for</span> (<span class="hljs-keyword">int</span> i = <span class="hljs-number">0</span>; i < size; ++i)
<span class="hljs-built_in">printf</span>(<span class="hljs-string">"%d "</span>, <span class="hljs-built_in">array</span>[i]);
<span class="hljs-built_in">printf</span>(<span class="hljs-string">"\n"</span>);
}
<span class="hljs-comment">// Driver code</span>
<span class="hljs-function"><span class="hljs-keyword">int</span> <span class="hljs-title">main</span><span class="hljs-params">()</span> </span>{
<span class="hljs-keyword">int</span> <span class="hljs-built_in">array</span>[<span class="hljs-number">10</span>];
insert(<span class="hljs-built_in">array</span>, <span class="hljs-number">3</span>);
insert(<span class="hljs-built_in">array</span>, <span class="hljs-number">4</span>);
insert(<span class="hljs-built_in">array</span>, <span class="hljs-number">9</span>);
insert(<span class="hljs-built_in">array</span>, <span class="hljs-number">5</span>);
insert(<span class="hljs-built_in">array</span>, <span class="hljs-number">2</span>);
<span class="hljs-built_in">printf</span>(<span class="hljs-string">"Max-Heap array: "</span>);
printArray(<span class="hljs-built_in">array</span>, size);
deleteRoot(<span class="hljs-built_in">array</span>, <span class="hljs-number">4</span>);
<span class="hljs-built_in">printf</span>(<span class="hljs-string">"After deleting an element: "</span>);
printArray(<span class="hljs-built_in">array</span>, size);
}</code></pre></div>
</div>
<div class="code-editor__area" id="cpp-code">
<div class="pre-code-wrapper"><div title="Click to copy" class="copy-code-button"></div><pre class="exec" style="max-height: 600px;"><code class="cpp hljs"><span class="hljs-comment">// Priority Queue implementation in C++</span>
<span class="hljs-meta">#<span class="hljs-meta-keyword">include</span> <span class="hljs-meta-string"><iostream></span></span>
<span class="hljs-meta">#<span class="hljs-meta-keyword">include</span> <span class="hljs-meta-string"><vector></span></span>
<span class="hljs-keyword">using</span> <span class="hljs-keyword">namespace</span> <span class="hljs-built_in">std</span>;
<span class="hljs-comment">// Function to swap position of two elements</span>
<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">swap</span><span class="hljs-params">(<span class="hljs-keyword">int</span> *a, <span class="hljs-keyword">int</span> *b)</span> </span>{
<span class="hljs-keyword">int</span> temp = *b;
*b = *a;
*a = temp;
}
<span class="hljs-comment">// Function to heapify the tree</span>
<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">heapify</span><span class="hljs-params">(<span class="hljs-built_in">vector</span><<span class="hljs-keyword">int</span>> &hT, <span class="hljs-keyword">int</span> i)</span> </span>{
<span class="hljs-keyword">int</span> size = hT.size();
<span class="hljs-comment">// Find the largest among root, left child and right child</span>
<span class="hljs-keyword">int</span> largest = i;
<span class="hljs-keyword">int</span> l = <span class="hljs-number">2</span> * i + <span class="hljs-number">1</span>;
<span class="hljs-keyword">int</span> r = <span class="hljs-number">2</span> * i + <span class="hljs-number">2</span>;
<span class="hljs-keyword">if</span> (l < size && hT[l] > hT[largest])
largest = l;
<span class="hljs-keyword">if</span> (r < size && hT[r] > hT[largest])
largest = r;
<span class="hljs-comment">// Swap and continue heapifying if root is not largest</span>
<span class="hljs-keyword">if</span> (largest != i) {
swap(&hT[i], &hT[largest]);
heapify(hT, largest);
}
}
<span class="hljs-comment">// Function to insert an element into the tree</span>
<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">insert</span><span class="hljs-params">(<span class="hljs-built_in">vector</span><<span class="hljs-keyword">int</span>> &hT, <span class="hljs-keyword">int</span> newNum)</span> </span>{
<span class="hljs-keyword">int</span> size = hT.size();
<span class="hljs-keyword">if</span> (size == <span class="hljs-number">0</span>) {
hT.push_back(newNum);
} <span class="hljs-keyword">else</span> {
hT.push_back(newNum);
<span class="hljs-keyword">for</span> (<span class="hljs-keyword">int</span> i = size / <span class="hljs-number">2</span> - <span class="hljs-number">1</span>; i >= <span class="hljs-number">0</span>; i--) {
heapify(hT, i);
}
}
}
<span class="hljs-comment">// Function to delete an element from the tree</span>
<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">deleteNode</span><span class="hljs-params">(<span class="hljs-built_in">vector</span><<span class="hljs-keyword">int</span>> &hT, <span class="hljs-keyword">int</span> num)</span> </span>{
<span class="hljs-keyword">int</span> size = hT.size();
<span class="hljs-keyword">int</span> i;
<span class="hljs-keyword">for</span> (i = <span class="hljs-number">0</span>; i < size; i++) {
<span class="hljs-keyword">if</span> (num == hT[i])
<span class="hljs-keyword">break</span>;
}
swap(&hT[i], &hT[size - <span class="hljs-number">1</span>]);
hT.pop_back();
<span class="hljs-keyword">for</span> (<span class="hljs-keyword">int</span> i = size / <span class="hljs-number">2</span> - <span class="hljs-number">1</span>; i >= <span class="hljs-number">0</span>; i--) {
heapify(hT, i);
}
}
<span class="hljs-comment">// Print the tree</span>
<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">printArray</span><span class="hljs-params">(<span class="hljs-built_in">vector</span><<span class="hljs-keyword">int</span>> &hT)</span> </span>{
<span class="hljs-keyword">for</span> (<span class="hljs-keyword">int</span> i = <span class="hljs-number">0</span>; i < hT.size(); ++i)
<span class="hljs-built_in">cout</span> << hT[i] << <span class="hljs-string">" "</span>;
<span class="hljs-built_in">cout</span> << <span class="hljs-string">"\n"</span>;
}
<span class="hljs-comment">// Driver code</span>
<span class="hljs-function"><span class="hljs-keyword">int</span> <span class="hljs-title">main</span><span class="hljs-params">()</span> </span>{
<span class="hljs-built_in">vector</span><<span class="hljs-keyword">int</span>> heapTree;
insert(heapTree, <span class="hljs-number">3</span>);
insert(heapTree, <span class="hljs-number">4</span>);
insert(heapTree, <span class="hljs-number">9</span>);
insert(heapTree, <span class="hljs-number">5</span>);
insert(heapTree, <span class="hljs-number">2</span>);
<span class="hljs-built_in">cout</span> << <span class="hljs-string">"Max-Heap array: "</span>;
printArray(heapTree);
deleteNode(heapTree, <span class="hljs-number">4</span>);
<span class="hljs-built_in">cout</span> << <span class="hljs-string">"After deleting an element: "</span>;
printArray(heapTree);
}</code></pre></div>
</div>
</div>
<hr><h2 id="applications">Priority Queue Applications</h2>
<p>Some of the applications of a priority queue are:</p>
<ul><li>Dijkstra's algorithm</li>
<li>for implementing stack</li>
<li>for load balancing and interrupt handling in an operating system</li>
<li>for data compression in Huffman code</li>
</ul></div>
</div>
<div class="tutorial-toc"><div class="tutorial-toc__inner"><h3 class="tutorial-toc__title">Table of Contents
<button class="btn btn--clear align-items-center">
<svg class="programiz-icon"><use xlink:href="/sites/all/themes/programiz/assets/feather-sprite.svg#x"></use></svg></button></h3><div class="tutorial-toc__links"><ul><li><a href="#definition">Definition</a></li>
<li><a href="#implementation">Implementation of Priority Queue</a></li>
<li><a href="#insert">Inserting an Element</a></li>
<li><a href="#delete">Deleting an Element</a></li>
<li><a href="#code">Python, Java and C/C++ Examples</a></li>
<li><a href="#applications">Priority Queue Applications</a></li>
</ul></div></div></div> </div>
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Stack</a></button>
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Queue</a></button>
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Types of Queue</a></button>
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Deque</a></button>
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Graph Data Structure</a></button>
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Spanning Tree</a></button>
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Strongly Connected Components</a></button>
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Adjacency Matrix</a></button>
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Selection Sort</a></button>
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Kruskal's Algorithm</a></button>
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Prim's Algorithm</a></button>
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Huffman Code</a></button>
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Dynamic Programming</a></button>
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Floyd Warshall Algorithm</a></button>
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Longest Common Subsequence</a></button>
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Backtracking Algorithm</a></button>
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Rabin-Karp Algorithm</a></button>
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<h2>Free Courses on YouTube</h2>
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