{"id":8636,"date":"2022-06-29T12:43:39","date_gmt":"2022-06-29T12:43:39","guid":{"rendered":"https:\/\/www.prepbytes.com\/blog\/?p=8636"},"modified":"2022-06-29T12:44:51","modified_gmt":"2022-06-29T12:44:51","slug":"merge-two-binary-max-heaps","status":"publish","type":"post","link":"https:\/\/prepbytes.com\/blog\/merge-two-binary-max-heaps\/","title":{"rendered":"Merge two Binary Max-Heaps"},"content":{"rendered":"<p><img decoding=\"async\" src=\"https:\/\/prepbytes-misc-images.s3.ap-south-1.amazonaws.com\/assets\/1656506668167-Article%20%282%29.jpg\" alt=\"\" \/><\/p>\n<h3>Binary Max &#8211; Heap<\/h3>\n<p>A binary max &#8211; heap follows two conditions:<\/p>\n<ul>\n<li>The given tree must be a complete binary tree (All levels are completely filled except the last level which can have nodes as left as possible. It will help in storing the Binary Heap in an array. <\/li>\n<li>All the nodes must have values greater than or equal to their children nodes. The parent will always have the maximum value in the sub-heap. <\/li>\n<\/ul>\n<p><img decoding=\"async\" src=\"https:\/\/prepbytes-misc-images.s3.ap-south-1.amazonaws.com\/assets\/1656062983497-Image-01.png\" alt=\"\" \/><\/p>\n<h3>Algorithm:<\/h3>\n<ol>\n<li>Initialize an array of size (n + m), where n is the size of given array1 and m is the size of given array2.<\/li>\n<li>Then, firstly add all the elements from array1 and then add all the elements from array2.<\/li>\n<li>At last, Apply the MaxHeapify method on the resultant array, to convert the resultant array into max &#8211; heap.<\/li>\n<\/ol>\n<p><img decoding=\"async\" src=\"https:\/\/prepbytes-misc-images.s3.ap-south-1.amazonaws.com\/assets\/1656506560746-Image-02%20%283%29.png\" alt=\"\" \/><\/p>\n<h4>Code Implementation<\/h4>\n\t\t\t\t\t\t<style>\r\n\t\t\t\t\r\n\t\t\t\t\t#tab_container_8637 {\r\n\toverflow:hidden;\r\n\tdisplay:block;\r\n\twidth:100%;\r\n\tborder:0px solid #ddd;\r\n\tmargin-bottom:30px;\r\n\t}\r\n\r\n#tab_container_8637 .tab-content{\r\n\tpadding:20px;\r\n\tborder: 1px solid #e6e6e6 !important;\r\n\tmargin-top: 0px;\r\n\tbackground-color:#ffffff !important;\r\n\tcolor: #000000 !important;\r\n\tfont-size:16px !important;\r\n\tfont-family: Open Sans !important;\r\n\t\r\n\t\tborder: 1px solid #e6e6e6 !important;\r\n\t}\r\n#tab_container_8637 .wpsm_nav-tabs {\r\n    border-bottom: 0px solid #ddd;\r\n}\r\n#tab_container_8637 .wpsm_nav-tabs > li.active > a, #tab_container_8637 .wpsm_nav-tabs > li.active > a:hover, #tab_container_8637 .wpsm_nav-tabs > li.active > a:focus {\r\n\tcolor: #000000 !important;\r\n\tcursor: default;\r\n\tbackground-color: #ffffff !important;\r\n\tborder: 1px solid #e6e6e6 !important;\r\n}\r\n\r\n#tab_container_8637 .wpsm_nav-tabs > li > a {\r\n    margin-right: 0px !important; \r\n    line-height: 1.42857143 !important;\r\n    border: 1px solid #d5d5d5 !important;\r\n    border-radius: 0px 0px 0 0 !important; \r\n\tbackground-color: #e8e8e8 !important;\r\n\tcolor: #000000 !important;\r\n\tpadding: 15px 18px 15px 18px !important;\r\n\ttext-decoration: none !important;\r\n\tfont-size: 14px !important;\r\n\ttext-align:center !important;\r\n\tfont-family: Open Sans !important;\r\n}\r\n#tab_container_8637 .wpsm_nav-tabs > li > a:focus {\r\noutline: 0px !important;\r\n}\r\n\r\n#tab_container_8637 .wpsm_nav-tabs > li > a:before {\r\n\tdisplay:none !important;\r\n}\r\n#tab_container_8637 .wpsm_nav-tabs > li > a:after {\r\n\tdisplay:none !important ;\r\n}\r\n#tab_container_8637 .wpsm_nav-tabs > li{\r\npadding:0px !important ;\r\nmargin:0px;\r\n}\r\n\r\n#tab_container_8637 .wpsm_nav-tabs > li > a:hover , #tab_container_8637 .wpsm_nav-tabs > li > a:focus {\r\n    color: #000000 !important;\r\n    background-color: #e8e8e8 !important;\r\n\tborder: 1px solid #d5d5d5 !important;\r\n\t\r\n}\r\n#tab_container_8637 .wpsm_nav-tabs > li > a .fa{\r\n\r\nmargin-right:5px !important;\r\n\r\nmargin-left:5px !important;\r\n\r\n\r\n}\r\n\r\n\t\t#tab_container_8637 .wpsm_nav-tabs a{\r\n\t\t\tbackground-image: none;\r\n\t\t\tbackground-position: 0 0;\r\n\t\t\tbackground-repeat: repeat-x;\r\n\t\t}\r\n\t\t\t\r\n\r\n\r\n#tab_container_8637 .wpsm_nav-tabs > li {\r\n    float: left;\r\n    margin-bottom: -1px !important;\r\n\tmargin-right:0px !important; \r\n}\r\n\r\n\r\n#tab_container_8637 .tab-content{\r\noverflow:hidden !important;\r\n}\r\n\r\n\r\n@media (min-width: 769px) {\r\n\r\n\t#tab_container_8637 .wpsm_nav-tabs > li{\r\n\t\tfloat:left !important ;\r\n\t\t\t\tmargin-right:-1px !important;\r\n\t\t\t\t\t}\r\n\t#tab_container_8637 .wpsm_nav-tabs{\r\n\t\tfloat:none !important;\r\n\t\tmargin:0px !important;\r\n\t}\r\n\r\n\t#tab_container_8637 .wpsm_nav-tabs > li {\r\n\t\t\t\t\r\n\t}\r\n\t#tab_container_8637 .wpsm_nav{\r\n\t\t\t}\r\n\r\n}\r\n\r\n\r\n\r\n@media (max-width: 768px) {\r\n\t#tab_container_8637 .wpsm_nav-tabs > li {\r\n\t\t\t\t\r\n\t}\r\n\t#tab_container_8637 .wpsm_nav{\r\n\t\t\t}\r\n}\r\n\r\n\r\n\t.wpsm_nav-tabs li:before{\r\n\t\tdisplay:none !important;\r\n\t}\r\n\r\n\t@media (max-width: 768px) {\r\n\t\t\t\t\r\n\t\t\t\t.wpsm_nav-tabs{\r\n\t\t\tmargin-left:0px !important;\r\n\t\t\tmargin-right:0px !important; \r\n\t\t\t\r\n\t\t}\r\n\t\t\t\t#tab_container_8637 .wpsm_nav-tabs > li{\r\n\t\t\tfloat:none !important;\r\n\t\t}\r\n\t\t\t\r\n\t}\t\t\t\t<\/style>\r\n\t\t\t\t<div id=\"tab_container_8637\" >\r\n\t \r\n\t\t\t\t\t<ul class=\"wpsm_nav wpsm_nav-tabs\" role=\"tablist\" id=\"myTab_8637\">\r\n\t\t\t\t\t\t\t\r\n\t\t\t\t\t\t\t<li role=\"presentation\"  class=\"active\"  onclick=\"do_resize()\">\r\n\t\t\t\t\t\t\t\t<a href=\"#tabs_desc_8637_1\" aria-controls=\"tabs_desc_8637_1\" role=\"tab\" data-toggle=\"tab\">\r\n\t\t\t\t\t\t\t\t\t\r\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<i class=\"fa fa-code\"><\/i> \t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\r\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\r\n\t\t\t\t\t\t\t\t\t<span>C++<\/span>\r\n\t\t\t\t\t\t\t\t\t\r\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\r\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\r\n\t\t\t\t\t\t\t\t\t\r\n\t\t\t\t\t\t\t\t<\/a>\r\n\t\t\t\t\t\t\t<\/li>\r\n\t\t\t\t\t\t\t\r\n\t\t\t\t\t\t\t<li role=\"presentation\"  onclick=\"do_resize()\">\r\n\t\t\t\t\t\t\t\t<a href=\"#tabs_desc_8637_2\" aria-controls=\"tabs_desc_8637_2\" role=\"tab\" data-toggle=\"tab\">\r\n\t\t\t\t\t\t\t\t\t\r\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<i class=\"fa fa-code\"><\/i> \t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\r\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\r\n\t\t\t\t\t\t\t\t\t<span>Java<\/span>\r\n\t\t\t\t\t\t\t\t\t\r\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\r\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\r\n\t\t\t\t\t\t\t\t\t\r\n\t\t\t\t\t\t\t\t<\/a>\r\n\t\t\t\t\t\t\t<\/li>\r\n\t\t\t\t\t\t\t\r\n\t\t\t\t\t\t\t<li role=\"presentation\"  onclick=\"do_resize()\">\r\n\t\t\t\t\t\t\t\t<a href=\"#tabs_desc_8637_3\" aria-controls=\"tabs_desc_8637_3\" role=\"tab\" data-toggle=\"tab\">\r\n\t\t\t\t\t\t\t\t\t\r\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<i class=\"fa fa-code\"><\/i> \t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\r\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\r\n\t\t\t\t\t\t\t\t\t<span>Python<\/span>\r\n\t\t\t\t\t\t\t\t\t\r\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\r\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\r\n\t\t\t\t\t\t\t\t\t\r\n\t\t\t\t\t\t\t\t<\/a>\r\n\t\t\t\t\t\t\t<\/li>\r\n\t\t\t\t\t\t\t\t\t\t\t <\/ul>\r\n\r\n\t\t\t\t\t  <!-- Tab panes -->\r\n\t\t\t\t\t  <div class=\"tab-content\" id=\"tab-content_8637\">\r\n\t\t\t\t\t\t\t\t\t\t\t\t <div role=\"tabpanel\" class=\"tab-pane  in active \" id=\"tabs_desc_8637_1\">\r\n\t\t\t\t\t\t\t\t<!-- wp:enlighter\/codeblock {\"language\":\"cpp\"} -->\r\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"cpp\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">\r\n#include &lt;bits\/stdc++.h&gt;\r\nusing namespace std;\r\n\r\nvoid maxHeapify(int arr[], int n, int idx)\r\n{\r\n\tif (idx &gt;= n)\r\n\t\treturn;\r\n\tint l = 2 * idx + 1;\r\n\tint r = 2 * idx + 2;\r\n\tint max;\r\n\tif (l &lt; n &amp;&amp; arr[l] &gt; arr[idx])\r\n\t\tmax = l;\r\n\telse\r\n\t\tmax = idx;\r\n\tif (r &lt; n &amp;&amp; arr[r] &gt; arr[max])\r\n\t\tmax = r;\r\n\r\n\tif (max != idx) {\r\n\t\tswap(arr[max], arr[idx]);\r\n\t\tmaxHeapify(arr, n, max);\r\n\t}\r\n}\r\n\r\nvoid buildMaxHeap(int arr[], int n)\r\n{\r\n\tfor (int i = n \/ 2 - 1; i &gt;= 0; i--)\r\n\t\tmaxHeapify(arr, n, i);\r\n}\r\n\r\nvoid mergeHeaps(int merged[], int a[], int b[],\r\n\t\t\t\tint n, int m)\r\n{\r\n\r\n\tfor (int i = 0; i &lt; n; i++)\r\n\t\tmerged[i] = a[i];\r\n\tfor (int i = 0; i &lt; m; i++)\r\n\t\tmerged[n + i] = b[i];\r\n\r\n\tbuildMaxHeap(merged, n + m);\r\n}\r\n\r\nint main()\r\n{\r\n\tint a[] = { 20, 15, 16, 12 };\r\n\tint b[] = { 22, 17, 19 };\r\n\r\n\tint n = sizeof(a) \/ sizeof(a[0]);\r\n\tint m = sizeof(b) \/ sizeof(b[0]);\r\n\r\n\tint merged[m + n];\r\n\tmergeHeaps(merged, a, b, n, m);\r\n\r\n\tfor (int i = 0; i &lt; n + m; i++)\r\n\t\tcout &lt;&lt; merged[i] &lt;&lt; &quot; &quot;;\r\n\r\n\treturn 0;\r\n}\r\n\r\n<\/pre>\r\n<!-- \/wp:enlighter\/codeblock -->\r\n\r\n\t\t\t\t\t\t <\/div>\r\n\t\t\t\t\t\t\t\t\t\t\t\t <div role=\"tabpanel\" class=\"tab-pane \" id=\"tabs_desc_8637_2\">\r\n\t\t\t\t\t\t\t\t<!-- wp:enlighter\/codeblock {\"language\":\"java\"} -->\r\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"java\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">\r\nclass Prepbytes {\r\n\r\n  public static void maxHeapify(int[] arr, int n,\r\n                      int i)\r\n  {\r\n    if (i &gt;= n) {\r\n      return;\r\n    }\r\n    int l = i * 2 + 1;\r\n    int r = i * 2 + 2;\r\n    int max;\r\n    if (l &lt; n &amp;&amp; arr[l] &gt; arr[i]) {\r\n      max = l;\r\n    }\r\n    else\r\n      max = i;\r\n    if (r &lt; n &amp;&amp; arr[r] &gt; arr[max]) {\r\n      max = r;\r\n    }\r\n    \r\n    if (max != i) {\r\n      int temp = arr[max];\r\n      arr[max] = arr[i];\r\n      arr[i] = temp;\r\n      maxHeapify(arr, n, max);\r\n    }\r\n  }\r\n  \r\n  public static void mergeHeaps(int[] arr, int[] a,\r\n                int[] b, int n, int m)\r\n  {\r\n    for (int i = 0; i &lt; n; i++) {\r\n      arr[i] = a[i];\r\n    }\r\n    for (int i = 0; i &lt; m; i++) {\r\n      arr[n + i] = b[i];\r\n    }\r\n    n = n + m;\r\n\r\n  \r\n    for (int i = n \/ 2 - 1; i &gt;= 0; i--) {\r\n      maxHeapify(arr, n, i);\r\n    }\r\n  }\r\n  \r\n  public static void main(String[] args)\r\n  {\r\n    int[] a = {20, 15, 16, 12};\r\n    int[] b = {22, 17, 19};\r\n    int n = a.length;\r\n    int m = b.length;\r\n\r\n    int[] merged = new int[m + n];\r\n\r\n    mergeHeaps(merged, a, b, n, m);\r\n\r\n    for (int i = 0; i &lt; m + n; i++)\r\n      System.out.print(merged[i] + &quot; &quot;);\r\n    System.out.println();\r\n  }\r\n}\r\n<\/pre>\r\n<!-- \/wp:enlighter\/codeblock -->\r\n\r\n\t\t\t\t\t\t <\/div>\r\n\t\t\t\t\t\t\t\t\t\t\t\t <div role=\"tabpanel\" class=\"tab-pane \" id=\"tabs_desc_8637_3\">\r\n\t\t\t\t\t\t\t\t<!-- wp:enlighter\/codeblock {\"language\":\"Python\"} -->\r\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"Python\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">\r\ndef MaxHeapify(arr, n, idx):\r\n\t\r\n\tif idx >= n:\r\n\t\treturn\r\n\tl = 2 * idx + 1\r\n\tr = 2 * idx + 2\r\n\tMax = 0\r\n\tif l < n and arr[l] > arr[idx]:\r\n\t\tMax = l\r\n\telse:\r\n\t\tMax = idx\r\n\tif r < n and arr[r] > arr[Max]:\r\n\t\tMax = r\r\n\r\n\tif Max != idx:\r\n\t\tarr[Max], arr[idx] = arr[idx], arr[Max]\r\n\t\tMaxHeapify(arr, n, Max)\r\n\r\ndef buildMaxHeap(arr, n):\r\n\t\r\n\tfor i in range(int(n \/ 2) - 1, -1, -1):\r\n\t\tMaxHeapify(arr, n, i)\r\n\r\ndef mergeHeaps(merged, a, b, n, m):\r\n\t\r\n\tfor i in range(n):\r\n\t\tmerged[i] = a[i]\r\n\tfor i in range(m):\r\n\t\tmerged[n + i] = b[i]\r\n\r\n\tbuildMaxHeap(merged, n + m)\r\n\r\nif __name__ == '__main__':\r\n\ta = [20, 15, 16, 12]\r\n\tb = [22, 17, 19]\r\n\r\n\tn = len(a)\r\n\tm = len(b)\r\n\r\n\tmerged = [0] * (m + n)\r\n\tmergeHeaps(merged, a, b, n, m)\r\n\r\n\tfor i in range(n + m):\r\n\t\tprint(merged[i], end = \" \")\r\n\r\n\r\n<\/pre>\r\n<!-- \/wp:enlighter\/codeblock -->\r\n\r\n\t\t\t\t\t\t <\/div>\r\n\t\t\t\t\t\t\t\r\n\t\t\t\t\t <\/div>\r\n\t\t\t\t\t \r\n\t\t\t\t <\/div>\r\n <script>\r\n\t\tjQuery(function () {\r\n\t\t\tjQuery('#myTab_8637 a:first').tab('show')\r\n\t\t});\r\n\t\t\r\n\t\t\t\tjQuery(function(){\r\n\t\t\tvar b=\"fadeIn\";\r\n\t\t\tvar c;\r\n\t\t\tvar a;\r\n\t\t\td(jQuery(\"#myTab_8637 a\"),jQuery(\"#tab-content_8637\"));function d(e,f,g){\r\n\t\t\t\te.click(function(i){\r\n\t\t\t\t\ti.preventDefault();\r\n\t\t\t\t\tjQuery(this).tab(\"show\");\r\n\t\t\t\t\tvar h=jQuery(this).data(\"easein\");\r\n\t\t\t\t\tif(c){c.removeClass(a);}\r\n\t\t\t\t\tif(h){f.find(\"div.active\").addClass(\"animated \"+h);a=h;}\r\n\t\t\t\t\telse{if(g){f.find(\"div.active\").addClass(\"animated \"+g);a=g;}else{f.find(\"div.active\").addClass(\"animated \"+b);a=b;}}c=f.find(\"div.active\");\r\n\t\t\t\t});\r\n\t\t\t}\r\n\t\t});\r\n\t\t\r\n\r\n\t\tfunction do_resize(){\r\n\r\n\t\t\tvar width=jQuery( '.tab-content .tab-pane iframe' ).width();\r\n\t\t\tvar height=jQuery( '.tab-content .tab-pane iframe' ).height();\r\n\r\n\t\t\tvar toggleSize = true;\r\n\t\t\tjQuery('iframe').animate({\r\n\t\t\t    width: toggleSize ? width : 640,\r\n\t\t\t    height: toggleSize ? height : 360\r\n\t\t\t  }, 250);\r\n\r\n\t\t\t  toggleSize = !toggleSize;\r\n\t\t}\r\n\r\n\r\n\t<\/script>\r\n\t\t\t\t\r\n\t\t\t\n<\/p>\n<p><strong>Output:<\/strong> 22 20 19 12 15 17 16<\/p>\n<h3>Complexity<\/h3>\n<p>The time complexity for building a heap from an array of n elements is O(N). So, for the merging of two max-heaps, the time complexity will be O(N + M), where N will be the size of array1 and M will be the size of array2.<\/p>\n<p>This article tried to discuss the concept to <strong> Merge two Binary Max-Heaps <\/strong>. Hope this blog helps you understand the concept. To practice problems on Heap you can check out <a href=\"#\/heaps\"> &#8211; Heaps<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Binary Max &#8211; Heap A binary max &#8211; heap follows two conditions: The given tree must be a complete binary tree (All levels are completely filled except the last level which can have nodes as left as possible. It will help in storing the Binary Heap in an array. All the nodes must have values [&hellip;]<\/p>\n","protected":false},"author":52,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[131],"tags":[175],"class_list":["post-8636","post","type-post","status-publish","format-standard","hentry","category-heap","tag-heap"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v25.8 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Merge two Binary Max-Heaps | Heap | Prepbytes<\/title>\n<meta name=\"description\" content=\"Given two binary max-heaps. In this tutorial, we&#039;ll see how to merge them into a single binary max-heap\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/prepbytes.com\/blog\/merge-two-binary-max-heaps\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Merge two Binary Max-Heaps | Heap | Prepbytes\" \/>\n<meta property=\"og:description\" content=\"Given two binary max-heaps. In this tutorial, we&#039;ll see how to merge them into a single binary max-heap\" \/>\n<meta property=\"og:url\" content=\"https:\/\/prepbytes.com\/blog\/merge-two-binary-max-heaps\/\" \/>\n<meta property=\"og:site_name\" content=\"PrepBytes Blog\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/prepbytes0211\/\" \/>\n<meta property=\"article:published_time\" content=\"2022-06-29T12:43:39+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2022-06-29T12:44:51+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/prepbytes-misc-images.s3.ap-south-1.amazonaws.com\/assets\/1656506668167-Article%20%282%29.jpg\" \/>\n<meta name=\"author\" content=\"Prepbytes\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Prepbytes\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/prepbytes.com\/blog\/merge-two-binary-max-heaps\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/prepbytes.com\/blog\/merge-two-binary-max-heaps\/\"},\"author\":{\"name\":\"Prepbytes\",\"@id\":\"http:\/\/43.205.93.38\/#\/schema\/person\/3f7dc4ae851791d5947a7f99df363d5e\"},\"headline\":\"Merge two Binary Max-Heaps\",\"datePublished\":\"2022-06-29T12:43:39+00:00\",\"dateModified\":\"2022-06-29T12:44:51+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/prepbytes.com\/blog\/merge-two-binary-max-heaps\/\"},\"wordCount\":222,\"commentCount\":0,\"publisher\":{\"@id\":\"http:\/\/43.205.93.38\/#organization\"},\"image\":{\"@id\":\"https:\/\/prepbytes.com\/blog\/merge-two-binary-max-heaps\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/prepbytes-misc-images.s3.ap-south-1.amazonaws.com\/assets\/1656506668167-Article%20%282%29.jpg\",\"keywords\":[\"heap\"],\"articleSection\":[\"Heap\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/prepbytes.com\/blog\/merge-two-binary-max-heaps\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/prepbytes.com\/blog\/merge-two-binary-max-heaps\/\",\"url\":\"https:\/\/prepbytes.com\/blog\/merge-two-binary-max-heaps\/\",\"name\":\"Merge two Binary Max-Heaps | Heap | Prepbytes\",\"isPartOf\":{\"@id\":\"http:\/\/43.205.93.38\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/prepbytes.com\/blog\/merge-two-binary-max-heaps\/#primaryimage\"},\"image\":{\"@id\":\"https:\/\/prepbytes.com\/blog\/merge-two-binary-max-heaps\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/prepbytes-misc-images.s3.ap-south-1.amazonaws.com\/assets\/1656506668167-Article%20%282%29.jpg\",\"datePublished\":\"2022-06-29T12:43:39+00:00\",\"dateModified\":\"2022-06-29T12:44:51+00:00\",\"description\":\"Given two binary max-heaps. In this tutorial, we'll see how to merge them into a single binary max-heap\",\"breadcrumb\":{\"@id\":\"https:\/\/prepbytes.com\/blog\/merge-two-binary-max-heaps\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/prepbytes.com\/blog\/merge-two-binary-max-heaps\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/prepbytes.com\/blog\/merge-two-binary-max-heaps\/#primaryimage\",\"url\":\"https:\/\/prepbytes-misc-images.s3.ap-south-1.amazonaws.com\/assets\/1656506668167-Article%20%282%29.jpg\",\"contentUrl\":\"https:\/\/prepbytes-misc-images.s3.ap-south-1.amazonaws.com\/assets\/1656506668167-Article%20%282%29.jpg\"},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/prepbytes.com\/blog\/merge-two-binary-max-heaps\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"http:\/\/43.205.93.38\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Heap\",\"item\":\"https:\/\/prepbytes.com\/blog\/category\/heap\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Merge two Binary Max-Heaps\"}]},{\"@type\":\"WebSite\",\"@id\":\"http:\/\/43.205.93.38\/#website\",\"url\":\"http:\/\/43.205.93.38\/\",\"name\":\"PrepBytes Blog\",\"description\":\"ONE-STOP RESOURCE FOR EVERYTHING RELATED TO CODING\",\"publisher\":{\"@id\":\"http:\/\/43.205.93.38\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"http:\/\/43.205.93.38\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"},{\"@type\":\"Organization\",\"@id\":\"http:\/\/43.205.93.38\/#organization\",\"name\":\"Prepbytes\",\"url\":\"http:\/\/43.205.93.38\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"http:\/\/43.205.93.38\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/blog.prepbytes.com\/wp-content\/uploads\/2025\/07\/uzxxllgloialmn9mhwfe.webp\",\"contentUrl\":\"https:\/\/blog.prepbytes.com\/wp-content\/uploads\/2025\/07\/uzxxllgloialmn9mhwfe.webp\",\"width\":160,\"height\":160,\"caption\":\"Prepbytes\"},\"image\":{\"@id\":\"http:\/\/43.205.93.38\/#\/schema\/logo\/image\/\"},\"sameAs\":[\"https:\/\/www.facebook.com\/prepbytes0211\/\",\"https:\/\/www.instagram.com\/prepbytes\/\",\"https:\/\/www.linkedin.com\/company\/prepbytes\/\",\"https:\/\/www.youtube.com\/channel\/UC0xGnHDrjUM1pDEK2Ka5imA\"]},{\"@type\":\"Person\",\"@id\":\"http:\/\/43.205.93.38\/#\/schema\/person\/3f7dc4ae851791d5947a7f99df363d5e\",\"name\":\"Prepbytes\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"http:\/\/43.205.93.38\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/232042cd1a1ea0e982c96d2a2ec93fb70a8e864e00784491231e7bfe5a9e06b5?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/232042cd1a1ea0e982c96d2a2ec93fb70a8e864e00784491231e7bfe5a9e06b5?s=96&d=mm&r=g\",\"caption\":\"Prepbytes\"},\"url\":\"https:\/\/prepbytes.com\/blog\/author\/gourav-jaincollegedekho-com\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Merge two Binary Max-Heaps | Heap | Prepbytes","description":"Given two binary max-heaps. In this tutorial, we'll see how to merge them into a single binary max-heap","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/prepbytes.com\/blog\/merge-two-binary-max-heaps\/","og_locale":"en_US","og_type":"article","og_title":"Merge two Binary Max-Heaps | Heap | Prepbytes","og_description":"Given two binary max-heaps. In this tutorial, we'll see how to merge them into a single binary max-heap","og_url":"https:\/\/prepbytes.com\/blog\/merge-two-binary-max-heaps\/","og_site_name":"PrepBytes Blog","article_publisher":"https:\/\/www.facebook.com\/prepbytes0211\/","article_published_time":"2022-06-29T12:43:39+00:00","article_modified_time":"2022-06-29T12:44:51+00:00","og_image":[{"url":"https:\/\/prepbytes-misc-images.s3.ap-south-1.amazonaws.com\/assets\/1656506668167-Article%20%282%29.jpg","type":"","width":"","height":""}],"author":"Prepbytes","twitter_card":"summary_large_image","twitter_misc":{"Written by":"Prepbytes","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/prepbytes.com\/blog\/merge-two-binary-max-heaps\/#article","isPartOf":{"@id":"https:\/\/prepbytes.com\/blog\/merge-two-binary-max-heaps\/"},"author":{"name":"Prepbytes","@id":"http:\/\/43.205.93.38\/#\/schema\/person\/3f7dc4ae851791d5947a7f99df363d5e"},"headline":"Merge two Binary Max-Heaps","datePublished":"2022-06-29T12:43:39+00:00","dateModified":"2022-06-29T12:44:51+00:00","mainEntityOfPage":{"@id":"https:\/\/prepbytes.com\/blog\/merge-two-binary-max-heaps\/"},"wordCount":222,"commentCount":0,"publisher":{"@id":"http:\/\/43.205.93.38\/#organization"},"image":{"@id":"https:\/\/prepbytes.com\/blog\/merge-two-binary-max-heaps\/#primaryimage"},"thumbnailUrl":"https:\/\/prepbytes-misc-images.s3.ap-south-1.amazonaws.com\/assets\/1656506668167-Article%20%282%29.jpg","keywords":["heap"],"articleSection":["Heap"],"inLanguage":"en-US","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/prepbytes.com\/blog\/merge-two-binary-max-heaps\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/prepbytes.com\/blog\/merge-two-binary-max-heaps\/","url":"https:\/\/prepbytes.com\/blog\/merge-two-binary-max-heaps\/","name":"Merge two Binary Max-Heaps | Heap | Prepbytes","isPartOf":{"@id":"http:\/\/43.205.93.38\/#website"},"primaryImageOfPage":{"@id":"https:\/\/prepbytes.com\/blog\/merge-two-binary-max-heaps\/#primaryimage"},"image":{"@id":"https:\/\/prepbytes.com\/blog\/merge-two-binary-max-heaps\/#primaryimage"},"thumbnailUrl":"https:\/\/prepbytes-misc-images.s3.ap-south-1.amazonaws.com\/assets\/1656506668167-Article%20%282%29.jpg","datePublished":"2022-06-29T12:43:39+00:00","dateModified":"2022-06-29T12:44:51+00:00","description":"Given two binary max-heaps. In this tutorial, we'll see how to merge them into a single binary max-heap","breadcrumb":{"@id":"https:\/\/prepbytes.com\/blog\/merge-two-binary-max-heaps\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/prepbytes.com\/blog\/merge-two-binary-max-heaps\/"]}]},{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/prepbytes.com\/blog\/merge-two-binary-max-heaps\/#primaryimage","url":"https:\/\/prepbytes-misc-images.s3.ap-south-1.amazonaws.com\/assets\/1656506668167-Article%20%282%29.jpg","contentUrl":"https:\/\/prepbytes-misc-images.s3.ap-south-1.amazonaws.com\/assets\/1656506668167-Article%20%282%29.jpg"},{"@type":"BreadcrumbList","@id":"https:\/\/prepbytes.com\/blog\/merge-two-binary-max-heaps\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"http:\/\/43.205.93.38\/"},{"@type":"ListItem","position":2,"name":"Heap","item":"https:\/\/prepbytes.com\/blog\/category\/heap\/"},{"@type":"ListItem","position":3,"name":"Merge two Binary Max-Heaps"}]},{"@type":"WebSite","@id":"http:\/\/43.205.93.38\/#website","url":"http:\/\/43.205.93.38\/","name":"PrepBytes Blog","description":"ONE-STOP RESOURCE FOR EVERYTHING RELATED TO CODING","publisher":{"@id":"http:\/\/43.205.93.38\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"http:\/\/43.205.93.38\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"},{"@type":"Organization","@id":"http:\/\/43.205.93.38\/#organization","name":"Prepbytes","url":"http:\/\/43.205.93.38\/","logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"http:\/\/43.205.93.38\/#\/schema\/logo\/image\/","url":"https:\/\/blog.prepbytes.com\/wp-content\/uploads\/2025\/07\/uzxxllgloialmn9mhwfe.webp","contentUrl":"https:\/\/blog.prepbytes.com\/wp-content\/uploads\/2025\/07\/uzxxllgloialmn9mhwfe.webp","width":160,"height":160,"caption":"Prepbytes"},"image":{"@id":"http:\/\/43.205.93.38\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.facebook.com\/prepbytes0211\/","https:\/\/www.instagram.com\/prepbytes\/","https:\/\/www.linkedin.com\/company\/prepbytes\/","https:\/\/www.youtube.com\/channel\/UC0xGnHDrjUM1pDEK2Ka5imA"]},{"@type":"Person","@id":"http:\/\/43.205.93.38\/#\/schema\/person\/3f7dc4ae851791d5947a7f99df363d5e","name":"Prepbytes","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"http:\/\/43.205.93.38\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/232042cd1a1ea0e982c96d2a2ec93fb70a8e864e00784491231e7bfe5a9e06b5?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/232042cd1a1ea0e982c96d2a2ec93fb70a8e864e00784491231e7bfe5a9e06b5?s=96&d=mm&r=g","caption":"Prepbytes"},"url":"https:\/\/prepbytes.com\/blog\/author\/gourav-jaincollegedekho-com\/"}]}},"_links":{"self":[{"href":"https:\/\/prepbytes.com\/blog\/wp-json\/wp\/v2\/posts\/8636","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/prepbytes.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/prepbytes.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/prepbytes.com\/blog\/wp-json\/wp\/v2\/users\/52"}],"replies":[{"embeddable":true,"href":"https:\/\/prepbytes.com\/blog\/wp-json\/wp\/v2\/comments?post=8636"}],"version-history":[{"count":4,"href":"https:\/\/prepbytes.com\/blog\/wp-json\/wp\/v2\/posts\/8636\/revisions"}],"predecessor-version":[{"id":8882,"href":"https:\/\/prepbytes.com\/blog\/wp-json\/wp\/v2\/posts\/8636\/revisions\/8882"}],"wp:attachment":[{"href":"https:\/\/prepbytes.com\/blog\/wp-json\/wp\/v2\/media?parent=8636"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/prepbytes.com\/blog\/wp-json\/wp\/v2\/categories?post=8636"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/prepbytes.com\/blog\/wp-json\/wp\/v2\/tags?post=8636"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}