{"id":49333,"date":"2025-05-17T14:05:28","date_gmt":"2025-05-17T08:35:28","guid":{"rendered":"https:\/\/www.iquanta.in\/blog\/?p=49333"},"modified":"2025-05-17T14:05:30","modified_gmt":"2025-05-17T08:35:30","slug":"heap-sort-algorithm-complete-guide","status":"publish","type":"post","link":"https:\/\/www.iquanta.in\/blog\/heap-sort-algorithm-complete-guide\/","title":{"rendered":"Heap Sort Algorithm (Complete Guide)"},"content":{"rendered":"\n<p>Heap Sort Algorithm is a sorting algorithm when we study trees. We have completed tutorial for most of the sorting algorithms like bubble sort, <a href=\"https:\/\/www.iquanta.in\/blog\/quicksort-algorithm-working-time-complexity-advantages\/\">quick sort<\/a>, merge sort, insertion sort, selection sort, radix sort, counting sort etc. <\/p>\n\n\n\n<p>In this blog we will be covering almost every method for the heap tree construction whether it is adding elements one by one or heapify method. Understanding the concept of complete binary tree before walkthrough the heap sorting.<\/p>\n\n\n\n<p>There are various steps involves in the creation of heap tree  along with discussing the time and space complexity of heap tree data structure. It&#8217;s applications, advantages, disadvantages and the implementation of heap tree data structure in python programming language.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><a href=\"https:\/\/chat.whatsapp.com\/B6weknl7133BQXjPva0pgB\"><img fetchpriority=\"high\" decoding=\"async\" width=\"875\" height=\"142\" src=\"https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-81.png\" alt=\"heap sort algorithm\" class=\"wp-image-49288\" srcset=\"https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-81.png 875w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-81-300x49.png 300w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-81-768x125.png 768w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-81-150x24.png 150w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-81-696x113.png 696w\" sizes=\"(max-width: 875px) 100vw, 875px\" \/><\/a><\/figure><\/div>\n\n\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_77 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/www.iquanta.in\/blog\/heap-sort-algorithm-complete-guide\/#What_is_a_heap_tree_data_structure\" >What is a heap tree data structure?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.iquanta.in\/blog\/heap-sort-algorithm-complete-guide\/#What_is_heap_sort_algorithm\" >What is heap sort algorithm?<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.iquanta.in\/blog\/heap-sort-algorithm-complete-guide\/#Key_Concepts\" >Key Concepts<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.iquanta.in\/blog\/heap-sort-algorithm-complete-guide\/#Heap_Sort_Steps\" >Heap Sort Steps<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.iquanta.in\/blog\/heap-sort-algorithm-complete-guide\/#Heap_Tree_Construction\" >Heap Tree Construction<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/www.iquanta.in\/blog\/heap-sort-algorithm-complete-guide\/#Insertion_of_elements_one_by_one\" >Insertion of elements one by one<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/www.iquanta.in\/blog\/heap-sort-algorithm-complete-guide\/#Heapify_Method\" >Heapify Method<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/www.iquanta.in\/blog\/heap-sort-algorithm-complete-guide\/#Step_1_Heapify_at_index_2\" >Step 1: Heapify at index 2<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/www.iquanta.in\/blog\/heap-sort-algorithm-complete-guide\/#Step_2_Heapify_at_index_1\" >Step 2: Heapify at index 1<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/www.iquanta.in\/blog\/heap-sort-algorithm-complete-guide\/#Step_3_Heapify_at_index_0\" >Step 3: Heapify at index 0<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/www.iquanta.in\/blog\/heap-sort-algorithm-complete-guide\/#Implementation_of_heap_sort_algorithm\" >Implementation of heap sort algorithm<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/www.iquanta.in\/blog\/heap-sort-algorithm-complete-guide\/#Advantages_of_Heap_Sort_Algorithm\" >Advantages of Heap Sort Algorithm<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/www.iquanta.in\/blog\/heap-sort-algorithm-complete-guide\/#Disadvantages_of_heap_sort_algorithm\" >Disadvantages of heap sort algorithm<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/www.iquanta.in\/blog\/heap-sort-algorithm-complete-guide\/#Appplications_of_heap_sort_algorithm\" >Appplications of heap sort algorithm<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/www.iquanta.in\/blog\/heap-sort-algorithm-complete-guide\/#Know_More_About_Heap_Sort_Algorithm\" >Know More About Heap Sort Algorithm<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-16\" href=\"https:\/\/www.iquanta.in\/blog\/heap-sort-algorithm-complete-guide\/#What_is_the_time_complexity_for_heap_sort_algorithm\" >What is the time complexity for heap sort algorithm?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-17\" href=\"https:\/\/www.iquanta.in\/blog\/heap-sort-algorithm-complete-guide\/#Is_heap_sort_a_stable_sorting_algorithm\" >Is heap sort a stable sorting algorithm?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-18\" href=\"https:\/\/www.iquanta.in\/blog\/heap-sort-algorithm-complete-guide\/#What_is_the_space_complexity_of_Heap_Sort\" >What is the space complexity of Heap Sort?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-19\" href=\"https:\/\/www.iquanta.in\/blog\/heap-sort-algorithm-complete-guide\/#Is_Heap_Sort_faster_than_Quick_Sort\" >Is Heap Sort faster than Quick Sort?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2 class=\"wp-block-heading\" id=\"h-what-is-a-heap-tree-data-structure\"><span class=\"ez-toc-section\" id=\"What_is_a_heap_tree_data_structure\"><\/span><strong>What is a heap tree data structure?<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>A heap tree data structure is a special type of complete binary tree data structure where the second last level of the entire tree is completely filled with nodes from left to right. <\/p>\n\n\n\n<p>It satisfies the heapify along with follows the structural and ordering property. Heap tree is classified into two types which is min heap and max heap. In min heap, parent node value is less than the child node whereas in max heap the parent node value is greater than the child node. <\/p>\n\n\n\n<p>If i will talk about the heap tree operations like insertion and deletion then i will add the nodes in a tree in such a way that the parent node should represent through variable &#8216;i&#8217; and the addition of the left child in a tree is represented by &#8216;2i+1&#8217; whereas the right child node of a tree is represented by &#8216;2i+2&#8217;.<\/p>\n\n\n\n<p> <\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" width=\"750\" height=\"449\" src=\"https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-87.png\" alt=\"heap sort algorithm\" class=\"wp-image-49354\" srcset=\"https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-87.png 750w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-87-300x180.png 300w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-87-702x420.png 702w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-87-150x90.png 150w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-87-696x417.png 696w\" sizes=\"(max-width: 750px) 100vw, 750px\" \/><\/figure><\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"h-what-is-heap-sort-algorithm\"><span class=\"ez-toc-section\" id=\"What_is_heap_sort_algorithm\"><\/span><strong>What is heap sort algorithm?<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>Heap Sort Algorithm is a comparison-based sorting technique based on a Binary Heap data structure. It is similar to selection sort where we first find the maximum element and place it at the end. We repeat the same process for the remaining elements.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" width=\"875\" height=\"142\" src=\"https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-94.png\" alt=\"\" class=\"wp-image-49374\" srcset=\"https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-94.png 875w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-94-300x49.png 300w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-94-768x125.png 768w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-94-150x24.png 150w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-94-696x113.png 696w\" sizes=\"(max-width: 875px) 100vw, 875px\" \/><\/figure><\/div>\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Key_Concepts\"><\/span>Key Concepts<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<ul>\n<li>A binary heap is a complete binary tree which satisfies the heap property:\n<ul>\n<li>Max Heap: parent is greater than or equal to its children.<\/li>\n\n\n\n<li>Min Heap: parent is less than or equal to its children.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>Heap sort uses a Max Heap to sort in ascending order.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Heap_Sort_Steps\"><\/span>Heap Sort Steps<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<ol>\n<li>Build a Max Heap from the input array.<\/li>\n\n\n\n<li>Swap the root (maximum value) with the last element.<\/li>\n\n\n\n<li>Reduce the heap size by one and heapify the root element.<\/li>\n\n\n\n<li>Repeat the process until the heap size is 1.<\/li>\n<\/ol>\n\n\n\n<pre class=\"wp-block-code\"><code>def heapify(arr, n, i):\r\n    largest = i          # Initialize largest as root\r\n    left = 2 * i + 1      # left = 2*i + 1\r\n    right = 2 * i + 2     # right = 2*i + 2\r\n\r\n    # Check if left child is larger than root\r\n    if left &lt; n and arr&#091;left] &gt; arr&#091;largest]:\r\n        largest = left\r\n\r\n    # Check if right child is larger than largest so far\r\n    if right &lt; n and arr&#091;right] &gt; arr&#091;largest]:\r\n        largest = right\r\n\r\n    # Change root, if needed\r\n    if largest != i:\r\n        arr&#091;i], arr&#091;largest] = arr&#091;largest], arr&#091;i]  # swap\r\n\r\n        # Heapify the root\r\n        heapify(arr, n, largest)\r\n\r\ndef heap_sort(arr):\r\n    n = len(arr)\r\n\r\n    # Build max heap\r\n    for i in range(n \/\/ 2 - 1, -1, -1):\r\n        heapify(arr, n, i)\r\n\r\n    # Extract elements from heap\r\n    for i in range(n - 1, 0, -1):\r\n        arr&#091;i], arr&#091;0] = arr&#091;0], arr&#091;i]  # swap\r\n        heapify(arr, i, 0)\r\n\r\n# Example\r\narr = &#091;12, 11, 13, 5, 6, 7]\r\nheap_sort(arr)\r\nprint(\"Sorted array is:\", arr)\r<\/code><\/pre>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"875\" height=\"142\" src=\"https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-95.png\" alt=\"\" class=\"wp-image-49375\" srcset=\"https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-95.png 875w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-95-300x49.png 300w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-95-768x125.png 768w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-95-150x24.png 150w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-95-696x113.png 696w\" sizes=\"(max-width: 875px) 100vw, 875px\" \/><\/figure><\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"h-heap-tree-construction\"><span class=\"ez-toc-section\" id=\"Heap_Tree_Construction\"><\/span><strong>Heap Tree Construction <\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>Heap tree construction can be possible by using two ways which include the inserting of elements one by one and another way is the heapify method. The time complexity to do inserting elements one by one in a given order is O(n logn) whereas the complexity for the heapify method is O(n).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-insertion-of-elements-one-by-one\"><span class=\"ez-toc-section\" id=\"Insertion_of_elements_one_by_one\"><\/span><strong>Insertion of elements one by one<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>First step is to insert elements one by one as we have taken the array of elements [27, 3, 4, 12, 16, 29]. In the first diagram which is mentioned below we are first inserting 27 then 3 and at last 4. In this stage there is no need tp swap the element to satisfy the property as everything is aligned in the correct position.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"631\" height=\"181\" src=\"https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-88.png\" alt=\"heap sort algorithm\" class=\"wp-image-49357\" style=\"width:755px;height:auto\" srcset=\"https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-88.png 631w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-88-300x86.png 300w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-88-150x43.png 150w\" sizes=\"(max-width: 631px) 100vw, 631px\" \/><\/figure><\/div>\n\n\n<p>In the second, we have added 12 due to this property is not satisfied now then we have to swap the element 12 with 3 after making comparison, post adding 16 again we have to perform the swapping operation to satisfy the heap property.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"671\" height=\"266\" src=\"https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-89.png\" alt=\"heap sort algorithm\" class=\"wp-image-49358\" style=\"width:767px;height:auto\" srcset=\"https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-89.png 671w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-89-300x119.png 300w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-89-150x59.png 150w\" sizes=\"(max-width: 671px) 100vw, 671px\" \/><\/figure><\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"251\" src=\"https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-90.png\" alt=\"heap sort\" class=\"wp-image-49359\" style=\"width:776px;height:auto\" srcset=\"https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-90.png 620w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-90-300x121.png 300w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-90-150x61.png 150w\" sizes=\"(max-width: 620px) 100vw, 620px\" \/><\/figure><\/div>\n\n\n<p>Post completing all 8 steps above now we are having 29 which is the largest element present in the array by using the comparison and swapping operation we have to fix that also and the final result is looking like this.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"875\" height=\"142\" src=\"https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-96.png\" alt=\"\" class=\"wp-image-49376\" srcset=\"https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-96.png 875w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-96-300x49.png 300w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-96-768x125.png 768w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-96-150x24.png 150w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-96-696x113.png 696w\" sizes=\"(max-width: 875px) 100vw, 875px\" \/><\/figure><\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"596\" height=\"341\" src=\"https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-91.png\" alt=\"heap sort algorithm\" class=\"wp-image-49360\" style=\"width:768px;height:auto\" srcset=\"https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-91.png 596w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-91-300x172.png 300w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-91-150x86.png 150w\" sizes=\"(max-width: 596px) 100vw, 596px\" \/><\/figure><\/div>\n\n\n<h3 class=\"wp-block-heading\" id=\"h-heapify-method\"><span class=\"ez-toc-section\" id=\"Heapify_Method\"><\/span><strong>Heapify Method <\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>We begin from the last non-leaf node, which is at index n\/\/2 &#8211; 1 = 6\/\/2 &#8211; 1 = 2.<br>So we start heapifying from index 2 and move up to index 0.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Step_1_Heapify_at_index_2\"><\/span>Step 1: Heapify at index 2<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<ul>\n<li>Subtree: Parent = 4 (index 2), Left = 29 (index 5), Right = None<\/li>\n\n\n\n<li>29 &gt; 4 \u2192 Swap them<\/li>\n<\/ul>\n\n\n\n<p>Array becomes: [27, 3, 29, 12, 16, 4]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Step_2_Heapify_at_index_1\"><\/span>Step 2: Heapify at index 1<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<ul>\n<li>Subtree: Parent = 3 (index 1), Left = 12 (index 3), Right = 16 (index 4)<\/li>\n\n\n\n<li>16 &gt; 3 \u2192 Swap them<\/li>\n<\/ul>\n\n\n\n<p>Array becomes: [27, 16, 29, 12, 3, 4]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Step_3_Heapify_at_index_0\"><\/span>Step 3: Heapify at index 0<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"875\" height=\"142\" src=\"https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-97.png\" alt=\"\" class=\"wp-image-49377\" srcset=\"https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-97.png 875w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-97-300x49.png 300w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-97-768x125.png 768w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-97-150x24.png 150w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-97-696x113.png 696w\" sizes=\"(max-width: 875px) 100vw, 875px\" \/><\/figure><\/div>\n\n\n<ul>\n<li>Subtree: Parent = 27 (index 0), Left = 16 (index 1), Right = 29 (index 2)<\/li>\n\n\n\n<li>29 &gt; 27 \u2192 Swap them<\/li>\n<\/ul>\n\n\n\n<p>Array becomes: [29, 16, 27, 12, 3, 4]<\/p>\n\n\n\n<p>Now, the heap property is satisfied throughout the tree.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"683\" height=\"1024\" src=\"https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-93-683x1024.png\" alt=\"heap sort algo\" class=\"wp-image-49363\" style=\"width:354px;height:auto\" srcset=\"https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-93-683x1024.png 683w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-93-200x300.png 200w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-93-768x1152.png 768w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-93-280x420.png 280w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-93-150x225.png 150w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-93-300x450.png 300w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-93-696x1044.png 696w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-93.png 1024w\" sizes=\"(max-width: 683px) 100vw, 683px\" \/><\/figure><\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"h-implementation-of-heap-sort-algorithm\"><span class=\"ez-toc-section\" id=\"Implementation_of_heap_sort_algorithm\"><\/span><strong>Implementation of heap sort algorithm<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<pre class=\"wp-block-code\"><code>def heapify(arr, n, i):\r\n    largest = i\r\n    left = 2 * i + 1\r\n    right = 2 * i + 2\r\n\r\n    if left &lt; n and arr&#091;left] &gt; arr&#091;largest]:\r\n        largest = left\r\n    if right &lt; n and arr&#091;right] &gt; arr&#091;largest]:\r\n        largest = right\r\n    if largest != i:\r\n        arr&#091;i], arr&#091;largest] = arr&#091;largest], arr&#091;i]\r\n        heapify(arr, n, largest)\r\n\r\ndef heap_sort(arr):\r\n    n = len(arr)\r\n    for i in range(n \/\/ 2 - 1, -1, -1):\r\n        heapify(arr, n, i)\r\n    for i in range(n - 1, 0, -1):\r\n        arr&#091;i], arr&#091;0] = arr&#091;0], arr&#091;i]\r\n        heapify(arr, i, 0)\r\n\r\narr = &#091;12, 11, 13, 5, 6, 7]\r\nheap_sort(arr)\r\nprint(\"Sorted array is:\", arr)\r<\/code><\/pre>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-advantages-of-heap-sort-algorithm\"><span class=\"ez-toc-section\" id=\"Advantages_of_Heap_Sort_Algorithm\"><\/span><strong>Advantages of Heap Sort Algorithm<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"875\" height=\"142\" src=\"https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-98.png\" alt=\"\" class=\"wp-image-49378\" srcset=\"https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-98.png 875w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-98-300x49.png 300w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-98-768x125.png 768w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-98-150x24.png 150w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-98-696x113.png 696w\" sizes=\"(max-width: 875px) 100vw, 875px\" \/><\/figure><\/div>\n\n\n<ol>\n<li>Heap sort always runs in O(n log n) time, no matter what the input data looks like. This makes it reliable even for worst-case scenarios.<\/li>\n\n\n\n<li>It sorts the data in place meaning it does not need extra memory or temporary arrays like merge sort does.<\/li>\n\n\n\n<li>Because of its efficiency and low memory usage heap sort is a good choice for sorting large datasets.<\/li>\n\n\n\n<li>Heap sort performs the same regardless of whether the input is already sorted, reverse sorted, or completely random.<\/li>\n\n\n\n<li>Its consistent performance and non-recursive implementation make it suitable for systems where predictable execution time is important.<\/li>\n<\/ol>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-disadvantages-of-heap-sort-algorithm\"><span class=\"ez-toc-section\" id=\"Disadvantages_of_heap_sort_algorithm\"><\/span><strong>Disadvantages of heap sort algorithm<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<ol>\n<li>Heap sort is not a stable sorting algorithm which means it may change the relative order of equal elements during sorting.<\/li>\n\n\n\n<li>Heap sort algorithm involves jumping around the array (due to the binary heap structure) which leads to inefficient use of the CPU cache and slower performance compared to quicksort in practice.<\/li>\n\n\n\n<li>It tends to do more comparisons than other efficient sorting algorithms like quicksort or merge sort, which can make it slower for small or nearly sorted datasets.<\/li>\n\n\n\n<li>The logic for maintaining the heap structure can be more difficult to implement and understand compared to simpler sorting methods like insertion sort or bubble sort.<\/li>\n\n\n\n<li>Heap sort does not take advantage of existing order in the data. Even if the array is already partially sorted that means heap sort still performs the full sorting process without any performance gain.<\/li>\n<\/ol>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-appplications-of-heap-sort-algorithm\"><span class=\"ez-toc-section\" id=\"Appplications_of_heap_sort_algorithm\"><\/span><strong>Appplications of heap sort algorithm<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<ol>\n<li>Priority Queue Implementation<br>Heap sort is commonly used in implementing priority queues. The max-heap or min-heap structure allows quick access to the highest or lowest priority element.<\/li>\n\n\n\n<li>Job Scheduling Systems<br>In CPU scheduling, heap sort helps in prioritizing tasks based on their deadlines or execution time. It ensures tasks are executed in the desired order efficiently.<\/li>\n<\/ol>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"875\" height=\"142\" src=\"https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-99.png\" alt=\"\" class=\"wp-image-49379\" srcset=\"https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-99.png 875w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-99-300x49.png 300w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-99-768x125.png 768w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-99-150x24.png 150w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-99-696x113.png 696w\" sizes=\"(max-width: 875px) 100vw, 875px\" \/><\/figure><\/div>\n\n\n<ol>\n<li>Graph Algorithms<br>Algorithms like Dijkstra\u2019s shortest path and Prim\u2019s minimum spanning tree use heaps to repeatedly select the next minimum-weight edge or vertex. This improves performance in large graphs.<\/li>\n\n\n\n<li>Real-Time Event Simulation<br>Heap sort can organize and manage future events based on their timestamps. Events are triggered in the correct sequence without delay.<\/li>\n\n\n\n<li>Data Stream Handling<br>When dealing with continuous data streams, heaps help in finding the top K largest or smallest elements on the fly. This is especially useful in analytics and monitoring systems.<\/li>\n\n\n\n<li>Memory-Constrained Environments<br>Since heap sort doesn\u2019t require additional memory, it is  suitable for embedded systems or environments with strict memory limits.<\/li>\n<\/ol>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-know-more-about-heap-sort-algorithm\"><span class=\"ez-toc-section\" id=\"Know_More_About_Heap_Sort_Algorithm\"><\/span><strong>Know More About Heap Sort Algorithm<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-what-is-the-time-complexity-for-heap-sort-algorithm\"><span class=\"ez-toc-section\" id=\"What_is_the_time_complexity_for_heap_sort_algorithm\"><\/span><strong>What is the time complexity for heap sort algorithm?<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>Best case: O(n log n)<\/p>\n\n\n\n<p>Average case: O(n log n)<\/p>\n\n\n\n<p>Worst case: O(n log n)<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"875\" height=\"142\" src=\"https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-100.png\" alt=\"\" class=\"wp-image-49380\" srcset=\"https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-100.png 875w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-100-300x49.png 300w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-100-768x125.png 768w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-100-150x24.png 150w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-100-696x113.png 696w\" sizes=\"(max-width: 875px) 100vw, 875px\" \/><\/figure><\/div>\n\n\n<h3 class=\"wp-block-heading\" id=\"h-is-heap-sort-a-stable-sorting-algorithm\"><span class=\"ez-toc-section\" id=\"Is_heap_sort_a_stable_sorting_algorithm\"><\/span><strong>Is heap sort a stable sorting algorithm?<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>Heap sort is not stable. It may change the order of equal elements.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-what-is-the-space-complexity-of-heap-sort\"><span class=\"ez-toc-section\" id=\"What_is_the_space_complexity_of_Heap_Sort\"><\/span><strong>What is the space complexity of Heap Sort?<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>The space complexity of heap sort is O(1).<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"875\" height=\"142\" src=\"https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-101.png\" alt=\"\" class=\"wp-image-49381\" srcset=\"https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-101.png 875w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-101-300x49.png 300w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-101-768x125.png 768w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-101-150x24.png 150w, https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-101-696x113.png 696w\" sizes=\"(max-width: 875px) 100vw, 875px\" \/><\/figure><\/div>\n\n\n<h3 class=\"wp-block-heading\" id=\"h-is-heap-sort-faster-than-quick-sort\"><span class=\"ez-toc-section\" id=\"Is_Heap_Sort_faster_than_Quick_Sort\"><\/span><strong>Is Heap Sort faster than Quick Sort?<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>Heap Sort has better worst-case performance but in practice Quick Sort is faster due to better cache usage and average case performance.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Heap Sort Algorithm is a sorting algorithm when we study trees. We have completed tutorial for most of the sorting algorithms like bubble sort, quick sort, merge sort, insertion sort, selection sort, radix sort, counting sort etc. In this blog we will be covering almost every method for the heap tree construction whether it is [&hellip;]<\/p>\n","protected":false},"author":560,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1075,1073],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v21.4 (Yoast SEO v21.9.1) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Heap Sort Algorithm (Complete Guide) - iQuanta<\/title>\n<meta name=\"description\" content=\"Learn how the Heap Sort algorithm works with examples, code implementation, advantages, disadvantages, and real-world applications.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.iquanta.in\/blog\/heap-sort-algorithm-complete-guide\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Heap Sort Algorithm (Complete Guide)\" \/>\n<meta property=\"og:description\" content=\"Learn how the Heap Sort algorithm works with examples, code implementation, advantages, disadvantages, and real-world applications.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.iquanta.in\/blog\/heap-sort-algorithm-complete-guide\/\" \/>\n<meta property=\"og:site_name\" content=\"iQuanta\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/facebook.com\/iquanta.in\" \/>\n<meta property=\"article:published_time\" content=\"2025-05-17T08:35:28+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2025-05-17T08:35:30+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/www.iquanta.in\/blog\/wp-content\/uploads\/2025\/05\/image-81.png\" \/>\n<meta name=\"author\" content=\"Nidhi Goswami\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Nidhi Goswami\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"9 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/www.iquanta.in\/blog\/heap-sort-algorithm-complete-guide\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/www.iquanta.in\/blog\/heap-sort-algorithm-complete-guide\/\"},\"author\":{\"name\":\"Nidhi Goswami\",\"@id\":\"https:\/\/www.iquanta.in\/blog\/#\/schema\/person\/ec8c8c25d0526dd86557b6fed064f7f3\"},\"headline\":\"Heap Sort Algorithm (Complete Guide)\",\"datePublished\":\"2025-05-17T08:35:28+00:00\",\"dateModified\":\"2025-05-17T08:35:30+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/www.iquanta.in\/blog\/heap-sort-algorithm-complete-guide\/\"},\"wordCount\":1209,\"publisher\":{\"@id\":\"https:\/\/www.iquanta.in\/blog\/#organization\"},\"articleSection\":[\"DSA and Competitive Programming\",\"iSkills\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/www.iquanta.in\/blog\/heap-sort-algorithm-complete-guide\/\",\"url\":\"https:\/\/www.iquanta.in\/blog\/heap-sort-algorithm-complete-guide\/\",\"name\":\"Heap Sort Algorithm (Complete Guide) - 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