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<title>Heap Data Structure</title>
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<li><a href="/dsa.html#data-structure-1" title="Data Structures (I)">Data Structures
(I)</a></li>
<li><a href="/dsa.html#data-structure-2" title="Data Structures (II)">Data Structures
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<h1>Heap Data Structure</h1>
<p class="editor-contents__short-description">In this tutorial, you will learn what heap data structure is. Also, you will find working examples of heap operations in C, C++, Java and Python.</p>
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<p id="definition">Heap data structure is <a href="/dsa/complete-binary-tree.html">a complete binary tree</a> that satisfies <strong>the heap property</strong>, where any given node is</p>
<ul><li>always greater than its child node/s and the key of the root node is the largest among all other nodes. This property is also called <strong>max heap property</strong>.</li>
<li>always smaller than the child node/s and the key of the root node is the smallest among all other nodes. This property is also called <strong>min heap property</strong>.</li>
</ul><figure><img alt="Max-heap" src="https://cdn.programiz.com/sites/tutorial2program/files/maxheap_1.png" title="Max-heap" width="496" height="432"><figcaption>Max-heap</figcaption></figure><figure><img alt="Min-heap" src="https://www.programiz.com/sites/tutorial2program/files/minheap_0.png" title="Min-heap" width="496" height="432"><figcaption>Min-heap</figcaption></figure><p>This type of data structure is also called a <strong>binary heap</strong>.</p>
<hr><h2 id="operations">Heap Operations</h2>
<p>Some of the important operations performed on a heap are described below along with their algorithms.</p>
<h3 id="heapify">Heapify</h3>
<p>Heapify is the process of creating a heap data structure from a binary tree. It is used to create a Min-Heap or a Max-Heap.</p>
<ol><li>Let the input array be
<figure><img alt="heap initial array" src="https://www.programiz.com/sites/tutorial2program/files/array_1.png" title="Initial Array" width="888" height="244"><figcaption>Initial Array</figcaption></figure></li>
<li>Create a complete binary tree from the array
<figure><img alt="Complete binary tree" src="https://www.programiz.com/sites/tutorial2program/files/completebt-1_0.png" title="Complete binary tree" width="496" height="458"><figcaption>Complete binary tree</figcaption></figure></li>
<li>Start from the first index of non-leaf node whose index is given by <code>n/2 - 1</code>.
<figure><img alt="heapify" src="https://www.programiz.com/sites/tutorial2program/files/start_1.png" title="start from the first on leaf node" width="496" height="458"><figcaption>Start from the first on leaf node</figcaption></figure></li>
<li>Set current element <code>i</code> as <code>largest</code>.</li>
<li>The index of left child is given by <code>2i + 1</code> and the right child is given by <code>2i + 2</code>.<br>
If <code>leftChild</code> is greater than <code>currentElement</code> (i.e. element at <code>ith</code> index), set <code>leftChildIndex</code> as largest.<br>
If <code>rightChild</code> is greater than element in <code>largest</code>, set <code>rightChildIndex</code> as <code>largest</code>.</li>
<li>Swap <code>largest</code> with <code>currentElement</code>
<figure><img alt="heapify" src="https://www.programiz.com/sites/tutorial2program/files/swap_1.png" title="swap if necessary" width="496" height="458"><figcaption>Swap if necessary</figcaption></figure></li>
<li>Repeat steps 3-7 until the subtrees are also heapified.</li>
</ol><p><strong>Algorithm</strong></p>
<pre style="max-height: 600px;"><code class="dsa hljs sql">Heapify(array, size, i)
<span class="hljs-keyword">set</span> i <span class="hljs-keyword">as</span> largest
leftChild = <span class="hljs-number">2</span>i + <span class="hljs-number">1</span>
rightChild = <span class="hljs-number">2</span>i + <span class="hljs-number">2</span>
<span class="hljs-keyword">if</span> leftChild > <span class="hljs-built_in">array</span>[largest]
<span class="hljs-keyword">set</span> leftChildIndex <span class="hljs-keyword">as</span> largest
<span class="hljs-keyword">if</span> rightChild > <span class="hljs-built_in">array</span>[largest]
<span class="hljs-keyword">set</span> rightChildIndex <span class="hljs-keyword">as</span> largest
swap <span class="hljs-built_in">array</span>[i] <span class="hljs-keyword">and</span> <span class="hljs-built_in">array</span>[largest]</code></pre>
<p>To create a Max-Heap:</p>
<pre style="max-height: 600px;"><code class="dsa hljs coffeescript">MaxHeap(array, size)
<span class="hljs-keyword">loop</span> <span class="hljs-keyword">from</span> the first index <span class="hljs-keyword">of</span> non-leaf node down to zero
call heapify</code></pre>
<p>For Min-Heap, both <code>leftChild</code> and <code>rightChild</code> must be larger than the parent for all nodes.</p>
<hr><h3 id="insert">Insert Element into Heap</h3>
<p>Algorithm for insertion in Max Heap</p>
<pre style="max-height: 600px;"><code class="dsa hljs sql">If there is no node,
<span class="hljs-keyword">create</span> a newNode.
<span class="hljs-keyword">else</span> (a node <span class="hljs-keyword">is</span> already <span class="hljs-keyword">present</span>)
<span class="hljs-keyword">insert</span> the newNode <span class="hljs-keyword">at</span> the <span class="hljs-keyword">end</span> (<span class="hljs-keyword">last</span> node <span class="hljs-keyword">from</span> <span class="hljs-keyword">left</span> <span class="hljs-keyword">to</span> right.)
heapify the <span class="hljs-built_in">array</span></code></pre>
<ol><li>Insert the new element at the end of the tree.
<figure><img alt="insertion in heap" src="https://www.programiz.com/sites/tutorial2program/files/insert-heap-1.png" title="insert at the end" width="560" height="458"><figcaption>Insert at the end</figcaption></figure></li>
<li>Heapify the tree.</li>
</ol><figure><img alt="insertion in heap" src="https://www.programiz.com/sites/tutorial2program/files/insert-heap-2.png" title="heapify the array" width="560" height="458"><figcaption>Heapify the array</figcaption></figure><p></p>
<div class="clearfix"></div><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">Delete Element from Heap</h3>
<p>Algorithm for deletion in Max Heap</p>
<pre style="max-height: 600px;"><code class="dsa hljs properties"><span class="hljs-attr">If</span> <span class="hljs-string">nodeToBeDeleted is the leafNode</span>
<span class="hljs-attr">remove</span> <span class="hljs-string">the node</span>
<span class="hljs-attr">Else</span> <span class="hljs-string">swap nodeToBeDeleted with the lastLeafNode</span>
<span class="hljs-attr">remove</span> <span class="hljs-string">noteToBeDeleted</span>
<span class="hljs-attr">heapify</span> <span class="hljs-string">the array</span></code></pre>
<ol><li>Select the element to be deleted.
<figure><img alt="deletion in heap" src="https://www.programiz.com/sites/tutorial2program/files/delete-1_1.png" title="select the element to be deleted" width="560" height="458"><figcaption>Select the element to be deleted</figcaption></figure></li>
<li>Swap it with the last element.
<figure><img alt="deletion in heap" src="https://www.programiz.com/sites/tutorial2program/files/delete-2_1.png" title="swap with the last element" width="560" height="458"><figcaption>Swap with the last element</figcaption></figure></li>
<li>Remove the last element.
<figure><img alt="deletion in heap" src="https://www.programiz.com/sites/tutorial2program/files/delete-3_0.png" title="remove the last element" width="594" height="502"><figcaption>Remove the last element</figcaption></figure></li>
<li>Heapify the tree.</li>
</ol><figure><img alt="deletion in heap" src="https://www.programiz.com/sites/tutorial2program/files/delete-4_0.png" title="heapify the array" width="496" height="458"><figcaption>Heapify the array</figcaption></figure><p>For Min Heap, above algorithm is modified so that both <code>childNodes</code> are greater smaller than <code>currentNode</code>.</p>
<hr><h3>Peek (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>Extract-Max/Min</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 after removing it from Min Heap.</p>
<hr><h2 id="code">Python, Java, C/C++ Examples</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"># Max-Heap data structure in Python</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>
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-keyword">if</span> largest != i:
arr[i],arr[largest] = arr[largest],arr[i]
heapify(arr, n, largest)
<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-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(num)
<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>
</div>
<div class="code-editor__area" id="java-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="java hljs"><span class="hljs-comment">// Max-Heap data structure 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-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-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-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-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-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-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-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">// Max-Heap data structure 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-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-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-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-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-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-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-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">// Max-Heap data structure 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-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-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-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-keyword">if</span> (largest != i)
{
swap(&hT[i], &hT[largest]);
heapify(hT, largest);
}
}
<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-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-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-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">Heap Data Structure Applications</h2>
<ul><li>Heap is used while implementing a priority queue.</li>
<li>Dijkstra's Algorithm</li>
<li>Heap Sort</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="#heapify">Heapify</a></li>
<li><a href="#insert">Insert Element into Heap</a></li>
<li><a href="#delete">Delete Element from Heap</a></li>
<li><a href="#code">Python, Java and C/C++ Examples</a></li>
<li><a href="#applications">Heap Data Structure 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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Circular Queue</a></button>
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Priority Queue</a></button>
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Deque</a></button>
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Linked List</a></button>
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Linked List Operations</a></button>
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Types of Linked List</a></button>
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Hash Table</a></button>
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Heap Data Structure</a></button>
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Fibonacci Heap</a></button>
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Decrease Key and Delete node from Fibonacci Heap</a></button>
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Tree Data Structure</a></button>
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Tree Traversal</a></button>
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Binary Tree</a></button>
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Full Binary Tree</a></button>
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Complete Binary Tree</a></button>
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Balanced Binary Tree</a></button>
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Binary Search Tree</a></button>
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AVL Tree</a></button>
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B Tree</a></button>
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Insertion into B-tree</a></button>
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Deletion from B-tree</a></button>
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B+ Tree</a></button>
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Insertion on a B+ Tree</a></button>
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Red Black Tree</a></button>
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Insertion in Red Black Tree</a></button>
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Deletion from Red Black Tree</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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Adjacency List</a></button>
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Huffman Code</a></button>
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Dynamic Programming</a></button>
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Longest Common Subsequence</a></button>
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