{"id":8587,"date":"2022-06-21T12:35:14","date_gmt":"2022-06-21T12:35:14","guid":{"rendered":"https:\/\/www.prepbytes.com\/blog\/?p=8587"},"modified":"2022-06-27T12:15:07","modified_gmt":"2022-06-27T12:15:07","slug":"minimum-element-in-a-max-heap","status":"publish","type":"post","link":"https:\/\/prepbytes.com\/blog\/minimum-element-in-a-max-heap\/","title":{"rendered":"Minimum element in a max heap"},"content":{"rendered":"<p><img decoding=\"async\" src=\"https:\/\/prepbytes-misc-images.s3.ap-south-1.amazonaws.com\/assets\/1655814214213-Minimum%20element%20in%20a%20max%20heap.jpg\" alt=\"\" \/><\/p>\n<h3>Problem statement:<\/h3>\n<p>The Statement is quite straightforward given a max heap, find the minimum element present in the heap.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/prepbytes-misc-images.s3.ap-south-1.amazonaws.com\/assets\/1655814860250-Image-02%20%281%29.png\" alt=\"\" \/><\/p>\n<p>A Max heap is a complete binary tree and in the max heap, the value at the root node is greater than its children.<\/p>\n<h3>Dry Run<\/h3>\n<p><img decoding=\"async\" src=\"https:\/\/prepbytes-misc-images.s3.ap-south-1.amazonaws.com\/assets\/1655814269159-Image-01.png\" alt=\"\" \/><\/p>\n<h3>Brute force Approach:<\/h3>\n<p>You can check all the nodes present in the tree and pick out the minimum element from the tree, but in this solution, we do not use the property of max heap, and the time and space complexity are O(N).<br \/>\nWe\u2019ll use an array to store them. After that, we can traverse the array and find the minimum element present in the array.<\/p>\n\t\t\t\t\t\t<style>\r\n\t\t\t\t\r\n\t\t\t\t\t#tab_container_8588 {\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_8588 .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_8588 .wpsm_nav-tabs {\r\n    border-bottom: 0px solid #ddd;\r\n}\r\n#tab_container_8588 .wpsm_nav-tabs > li.active > a, #tab_container_8588 .wpsm_nav-tabs > li.active > a:hover, #tab_container_8588 .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_8588 .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_8588 .wpsm_nav-tabs > li > a:focus {\r\noutline: 0px !important;\r\n}\r\n\r\n#tab_container_8588 .wpsm_nav-tabs > li > a:before {\r\n\tdisplay:none !important;\r\n}\r\n#tab_container_8588 .wpsm_nav-tabs > li > a:after {\r\n\tdisplay:none !important ;\r\n}\r\n#tab_container_8588 .wpsm_nav-tabs > li{\r\npadding:0px !important ;\r\nmargin:0px;\r\n}\r\n\r\n#tab_container_8588 .wpsm_nav-tabs > li > a:hover , #tab_container_8588 .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_8588 .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_8588 .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_8588 .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_8588 .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_8588 .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_8588 .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_8588 .wpsm_nav-tabs > li {\r\n\t\t\t\t\r\n\t}\r\n\t#tab_container_8588 .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_8588 .wpsm_nav-tabs > li {\r\n\t\t\t\t\r\n\t}\r\n\t#tab_container_8588 .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_8588 .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_8588\" >\r\n\t \r\n\t\t\t\t\t<ul class=\"wpsm_nav wpsm_nav-tabs\" role=\"tablist\" id=\"myTab_8588\">\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_8588_1\" aria-controls=\"tabs_desc_8588_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_8588_2\" aria-controls=\"tabs_desc_8588_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_8588_3\" aria-controls=\"tabs_desc_8588_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_8588\">\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_8588_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\nint findMinimumElement(int heap[], int n)\r\n{\r\n    int minimumElement = heap[0];\r\n \r\n    for (int i = 1; i &lt; n; ++i)\r\n        minimumElement = min(minimumElement, heap[i]);\r\n \r\n    return minimumElement;\r\n}\r\n \r\nint main()\r\n{\r\n    int n = 10;\r\n   \r\n    int heap[] = { 200, 180, 100, 12, 9, 9, 3, 5, 6, 8 };\r\n \r\n    cout &lt;&lt; findMinimumElement(heap, n);\r\n \r\n    return 0;\r\n}\r\n<\/pre>\r\n<!-- \/wp:enlighter\/codeblock -->\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_8588_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\npublic class Improve {\r\n \r\n    static int findMinimumElement(int heap[], int n)\r\n    {\r\n        int minimumElement = heap[0];\r\n \r\n        for (int i = 1; i &lt; n; ++i)\r\n            minimumElement\r\n                = Math.min(minimumElement, heap[i]);\r\n \r\n        return minimumElement;\r\n    }\r\n \r\n    public static void main(String args[])\r\n    {\r\n    \r\n        int n = 10;\r\n        \r\n        int heap[] = { 20, 18, 10, 12, 9, 9, 3, 5, 6, 8 };\r\n \r\n        System.out.println(findMinimumElement(heap, n));\r\n    }\r\n   \r\n}\r\n<\/pre>\r\n<!-- \/wp:enlighter\/codeblock -->\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_8588_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\n\r\n \r\n \r\ndef findMiniumumElement(heap, n):\r\n \r\n    minimumElement = heap[0]\r\n \r\n    for i in range(1, n):\r\n        minimumElement = min(minimumElement, heap[i])\r\n \r\n    return minimumElement\r\n \r\n \r\nn = 10  # Numbers Of Node\r\n \r\n \r\nheap = [20, 18, 10, 12, 8,\r\n        9, 3, 5, 6, 8]\r\n \r\nprint(findMiniumumElement(heap, n))\r\n<\/pre>\r\n<!-- \/wp:enlighter\/codeblock -->\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_8588 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_8588 a\"),jQuery(\"#tab-content_8588\"));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<h3>Efficient Approach:<\/h3>\n<p>As we know the property of max heap i.e. the value of the parent must be greater than its children due to which we can easily conclude that parent nodes are not the minimum element so we can search for the minimum element in the leaf nodes.<br \/>\nIf the heap contains n nodes then there will be ceil(n\/2) leaf nodes.<\/p>\n\t\t\t\t\t\t<style>\r\n\t\t\t\t\r\n\t\t\t\t\t#tab_container_8589 {\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_8589 .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_8589 .wpsm_nav-tabs {\r\n    border-bottom: 0px solid #ddd;\r\n}\r\n#tab_container_8589 .wpsm_nav-tabs > li.active > a, #tab_container_8589 .wpsm_nav-tabs > li.active > a:hover, #tab_container_8589 .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_8589 .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_8589 .wpsm_nav-tabs > li > a:focus {\r\noutline: 0px !important;\r\n}\r\n\r\n#tab_container_8589 .wpsm_nav-tabs > li > a:before {\r\n\tdisplay:none !important;\r\n}\r\n#tab_container_8589 .wpsm_nav-tabs > li > a:after {\r\n\tdisplay:none !important ;\r\n}\r\n#tab_container_8589 .wpsm_nav-tabs > li{\r\npadding:0px !important ;\r\nmargin:0px;\r\n}\r\n\r\n#tab_container_8589 .wpsm_nav-tabs > li > a:hover , #tab_container_8589 .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_8589 .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_8589 .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_8589 .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_8589 .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_8589 .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_8589 .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_8589 .wpsm_nav-tabs > li {\r\n\t\t\t\t\r\n\t}\r\n\t#tab_container_8589 .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_8589 .wpsm_nav-tabs > li {\r\n\t\t\t\t\r\n\t}\r\n\t#tab_container_8589 .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_8589 .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_8589\" >\r\n\t \r\n\t\t\t\t\t<ul class=\"wpsm_nav wpsm_nav-tabs\" role=\"tablist\" id=\"myTab_8589\">\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_8589_1\" aria-controls=\"tabs_desc_8589_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_8589_2\" aria-controls=\"tabs_desc_8589_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_8589_3\" aria-controls=\"tabs_desc_8589_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_8589\">\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_8589_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\nint findMinimumElement(int heap[], int n)\r\n{\r\n    int minimumElement = heap[n \/ 2];\r\n \r\n    for (int i = 1 + n \/ 2; i &lt; n; ++i)\r\n        minimumElement = min(minimumElement, heap[i]);\r\n \r\n    return minimumElement;\r\n}\r\n \r\nint main()\r\n{\r\n    \/\/ Number of nodes\r\n    int n = 10;\r\n    \r\n    int heap[] = { 200, 180, 100, 12, 9, 9, 3, 5, 6, 8 };\r\n \r\n    cout &lt;&lt; findMinimumElement(heap, n);\r\n \r\n    return 0;\r\n}\r\n<\/pre>\r\n<!-- \/wp:enlighter\/codeblock -->\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_8589_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\n\r\nimport java.util.*;\r\nimport java.lang.*;\r\n \r\nclass prepbytes {\r\n \r\n    static int findMinimumElement(int heap[], int n)\r\n    {\r\n        int minimumElement = heap[n \/ 2];\r\n \r\n        for (int i = 1 + n \/ 2; i &lt; n; ++i)\r\n            minimumElement\r\n                = Math.min(minimumElement, heap[i]);\r\n \r\n        return minimumElement;\r\n    }\r\n \r\n    public static void main(String args[])\r\n    {\r\n        \/\/ Number of nodes\r\n        int n = 10;\r\n        \r\n        int heap[] = new int[] { 20, 18, 10, 12, 9,\r\n                                 9,  3,  5,  6,  8 };\r\n \r\n        System.out.println(findMinimumElement(heap, n));\r\n    }\r\n}\r\n<\/pre>\r\n<!-- \/wp:enlighter\/codeblock -->\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_8589_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\n\r\n \r\ndef findMiniumumElement(heap, n):\r\n \r\n   \r\n    minimumElement = heap[n \/\/ 2]\r\n \r\n    for i in range(1 + n \/\/ 2, n):\r\n        minimumElement = min(minimumElement,\r\n                             heap[i])\r\n \r\n    return minimumElement\r\n \r\n \r\nn = 10  # Numbers Of Node\r\n \r\n\r\n \r\nheap = [20, 18, 10, 12, 9,\r\n        9, 3, 5, 6, 8]\r\n \r\nprint(findMiniumumElement(heap, n))\r\n<\/pre>\r\n<!-- \/wp:enlighter\/codeblock -->\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_8589 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_8589 a\"),jQuery(\"#tab-content_8589\"));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<h3>Complexity<\/h3>\n<p>Time and space complexity remains O(N) as a constant factor of 1\/2 does not affect any asymptotic complexity.<\/p>\n<p>This article tried to discuss <strong>How to find Minimum element in a max heap<\/strong>. Hope this blog helps you understand the implementation. To practice more problems you can check out <a href=\"#\"><\/a> at <a href=\"https:\/\/www.prepbytes.com\/\"> Prepbytes<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Problem statement: The Statement is quite straightforward given a max heap, find the minimum element present in the heap. A Max heap is a complete binary tree and in the max heap, the value at the root node is greater than its children. Dry Run Brute force Approach: You can check all the nodes present [&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-8587","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>Minimum element in a max heap | Heap | Prepbytes<\/title>\n<meta name=\"description\" content=\"A Max heap is a complete binary tree. In this article, we are given a max heap, find the minimum element in the 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\/minimum-element-in-a-max-heap\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Minimum element in a max heap | Heap | Prepbytes\" \/>\n<meta property=\"og:description\" content=\"A Max heap is a complete binary tree. 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