{"id":8716,"date":"2022-06-24T10:42:02","date_gmt":"2022-06-24T10:42:02","guid":{"rendered":"https:\/\/www.prepbytes.com\/blog\/?p=8716"},"modified":"2022-12-14T09:49:04","modified_gmt":"2022-12-14T09:49:04","slug":"check-if-a-given-binary-tree-is-heap","status":"publish","type":"post","link":"https:\/\/prepbytes.com\/blog\/check-if-a-given-binary-tree-is-heap\/","title":{"rendered":"Check if a given Binary Tree is Heap"},"content":{"rendered":"<p><img decoding=\"async\" src=\"https:\/\/prepbytes-misc-images.s3.ap-south-1.amazonaws.com\/assets\/1656063538039-Article.jpg\" alt=\"\" \/><\/p>\n<h3>Problem Statement:<\/h3>\n<p>Given a binary tree, our task is to check whether the given tree follows the max heap property or not.<\/p>\n<h3>What is a Binary Tree?<\/h3>\n<p>Binary tree is a type of Tree data structure in which every node in the tree will have 2 or less than 2 child nodes and those child nodes will be termed as the left child and the right child of the node.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/prepbytes-misc-images.s3.ap-south-1.amazonaws.com\/assets\/1656505923167-Image-02%20%282%29.png\" alt=\"\" \/><\/p>\n<h3>What is a Max-Heap?<\/h3>\n<p>Max &#8211; Heap follows the property of a complete binary tree in which the value of the internal node is greater than or equal to the value of the children of that node.<br \/>\nExamples of Max Heap:<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/prepbytes-misc-images.s3.ap-south-1.amazonaws.com\/assets\/1656505967812-Image-03.png\" alt=\"\" \/><\/p>\n<p><strong>There are two conditions that should be fulfilled for satisfying the max-heap property:<\/strong><\/p>\n<ul>\n<li>It must be a complete binary tree, i.e. except for the last level of the tree, all other levels must be fully filled with nodes.<\/li>\n<li>The value of every node must be greater than or equal to their children. (condition for max &#8211; heap).<\/li>\n<\/ul>\n<p><img decoding=\"async\" src=\"https:\/\/prepbytes-misc-images.s3.ap-south-1.amazonaws.com\/assets\/1656063562510-Image-01.png\" alt=\"\" \/><\/p>\n<p>We have to check the above conditions separately, we build the is_complete_tree function for checking whether the tree is a complete binary tree or not, and is_heap_property for checking the max &#8211; heap properties.<\/p>\n<p><strong>Following will be the procedure for implementing the Is_complete_tree function:<\/strong><\/p>\n<ul>\n<li>Firstly, calculate the number of nodes in the binary tree.<\/li>\n<li>Make the recursion call from the root of the binary tree with index i having an initial value of 0, and the count of nodes present in the binary tree.<\/li>\n<li>If the current node is NULL, then the given tree is a complete binary tree.<\/li>\n<li>If the ith index of the current node is greater than or equal to the number of nodes present in the binary tree, then it is not a complete binary tree and returns false.<\/li>\n<li>Check recursively for the left and right sub &#8211; tree for the same conditions. For the left sub &#8211; tree change the value of the index to (2 <em> i + 1) and for the right subtree change the value of the index to (2 <\/em> i + 2).<\/li>\n<\/ul>\n<p><strong>Following will be the procedure for implementing the is_heap_property function:<\/strong><\/p>\n<ul>\n<li>Every node can have 2 child nodes, 0 child nodes (if it is a leaf node), or 1 child node (it is only possible for at most 1 such node).<\/li>\n<li>If there is no child node present for the given node, then return true.<\/li>\n<li>If the node has 1 child node, it must be the left child node for following the complete binary tree condition. We have to compare the given node to its single child node only. <\/li>\n<li>If there are 2 child nodes present for the given node, then check the heap property at the node at recursion for both sub-trees.<\/li>\n<\/ul>\n<h3>Code Implementation<\/h3>\n\t\t\t\t\t\t<style>\r\n\t\t\t\t\r\n\t\t\t\t\t#tab_container_8715 {\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_8715 .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_8715 .wpsm_nav-tabs {\r\n    border-bottom: 0px solid #ddd;\r\n}\r\n#tab_container_8715 .wpsm_nav-tabs > li.active > a, #tab_container_8715 .wpsm_nav-tabs > li.active > a:hover, #tab_container_8715 .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_8715 .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_8715 .wpsm_nav-tabs > li > a:focus {\r\noutline: 0px !important;\r\n}\r\n\r\n#tab_container_8715 .wpsm_nav-tabs > li > a:before {\r\n\tdisplay:none !important;\r\n}\r\n#tab_container_8715 .wpsm_nav-tabs > li > a:after {\r\n\tdisplay:none !important ;\r\n}\r\n#tab_container_8715 .wpsm_nav-tabs > li{\r\npadding:0px !important ;\r\nmargin:0px;\r\n}\r\n\r\n#tab_container_8715 .wpsm_nav-tabs > li > a:hover , #tab_container_8715 .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_8715 .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_8715 .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_8715 .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_8715 .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_8715 .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_8715 .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_8715 .wpsm_nav-tabs > li {\r\n\t\t\t\t\r\n\t}\r\n\t#tab_container_8715 .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_8715 .wpsm_nav-tabs > li {\r\n\t\t\t\t\r\n\t}\r\n\t#tab_container_8715 .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_8715 .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_8715\" >\r\n\t \r\n\t\t\t\t\t<ul class=\"wpsm_nav wpsm_nav-tabs\" role=\"tablist\" id=\"myTab_8715\">\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_8715_1\" aria-controls=\"tabs_desc_8715_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_8715_2\" aria-controls=\"tabs_desc_8715_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>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_8715_3\" aria-controls=\"tabs_desc_8715_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>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_8715_4\" aria-controls=\"tabs_desc_8715_4\" 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_8715\">\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_8715_1\">\r\n\t\t\t\t\t\t\t\t<!-- wp:enlighter\/codeblock {\"language\":\"C\"} -->\r\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"C\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">\r\n#include &lt;stdbool.h&gt;\r\n#include &lt;stdio.h&gt;\r\n#include &lt;stdlib.h&gt;\r\n\r\nstruct Node {\r\n\tint key;\r\n\tstruct Node* left;\r\n\tstruct Node* right;\r\n};\r\n\r\n\r\nstruct Node* newNode(int k)\r\n{\r\n\tstruct Node* node\r\n\t\t= (struct Node*)malloc(sizeof(struct Node));\r\n\tnode-&gt;key = k;\r\n\tnode-&gt;right = node-&gt;left = NULL;\r\n\treturn node;\r\n}\r\n\r\n\r\nunsigned int countNodes(struct Node* root)\r\n{\r\n\tif (root == NULL)\r\n\t\treturn (0);\r\n\treturn (1 + countNodes(root-&gt;left)\r\n\t\t\t+ countNodes(root-&gt;right));\r\n}\r\n\r\n\r\nbool isCompleteUtil(struct Node* root,\r\n\t\t\t\t\tunsigned int index,\r\n\t\t\t\t\tunsigned int number_nodes)\r\n{\r\n\r\n\tif (root == NULL)\r\n\t\treturn (true);\r\n\r\n\r\n\tif (index &gt;= number_nodes)\r\n\t\treturn (false);\r\n\r\n\r\n\treturn (isCompleteUtil(root-&gt;left,\r\n\t\t\t\t\t\t2 * index + 1,\r\n\t\t\t\t\t\tnumber_nodes)\r\n\t\t\t&amp;&amp; isCompleteUtil(root-&gt;right,\r\n\t\t\t\t\t\t\t2 * index + 2,\r\n\t\t\t\t\t\t\tnumber_nodes));\r\n}\r\n\r\n\r\nbool isHeapUtil(struct Node* root)\r\n{\r\n\r\n\tif (root-&gt;left == NULL &amp;&amp; root-&gt;right == NULL)\r\n\t\treturn (true);\r\n\r\n\r\n\tif (root-&gt;right == NULL) {\r\n\r\n\t\treturn (root-&gt;key &gt;= root-&gt;left-&gt;key);\r\n\t}\r\n\telse {\r\n\r\n\t\tif (root-&gt;key &gt;= root-&gt;left-&gt;key\r\n\t\t\t&amp;&amp; root-&gt;key &gt;= root-&gt;right-&gt;key)\r\n\t\t\treturn ((isHeapUtil(root-&gt;left))\r\n\t\t\t\t\t&amp;&amp; (isHeapUtil(root-&gt;right)));\r\n\t\telse\r\n\t\t\treturn (false);\r\n\t}\r\n}\r\n\r\n\r\nbool isHeap(struct Node* root)\r\n{\r\n\r\n\tunsigned int node_count = countNodes(root);\r\n\tunsigned int index = 0;\r\n\r\n\tif (isCompleteUtil(root, index, node_count)\r\n\t\t&amp;&amp; isHeapUtil(root))\r\n\t\treturn true;\r\n\treturn false;\r\n}\r\n\r\n\r\nint main()\r\n{\r\n\tstruct Node* root = NULL;\r\n\troot = newNode(10);\r\n\troot-&gt;left = newNode(9);\r\n\troot-&gt;right = newNode(8);\r\n\troot-&gt;left-&gt;left = newNode(7);\r\n\troot-&gt;left-&gt;right = newNode(6);\r\n\troot-&gt;right-&gt;left = newNode(5);\r\n\troot-&gt;right-&gt;right = newNode(4);\r\n\troot-&gt;left-&gt;left-&gt;left = newNode(3);\r\n\troot-&gt;left-&gt;left-&gt;right = newNode(2);\r\n\troot-&gt;left-&gt;right-&gt;left = newNode(1);\r\n\r\n\tif (isHeap(root))\r\n\t\tprintf(&quot;Given Binary Tree is a Max-Heap&#92;n&quot;);\r\n\telse\r\n\t\tprintf(&quot;Given Binary Tree is not a Max-Heap&#92;n&quot;);\r\n\r\n\treturn 0;\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_8715_2\">\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\n\r\nusing namespace std;\r\n\r\n\r\nstruct Node\r\n{\r\n\tint key;\r\n\tstruct Node *left;\r\n\tstruct Node *right;\r\n};\r\n\r\n\r\nstruct Node *newNode(int k)\r\n{\r\n\tstruct Node *node = new Node;\r\n\tnode-&gt;key = k;\r\n\tnode-&gt;right = node-&gt;left = NULL;\r\n\treturn node;\r\n}\r\n\r\nunsigned int countNodes(struct Node* root)\r\n{\r\n\tif (root == NULL)\r\n\t\treturn (0);\r\n\treturn (1 + countNodes(root-&gt;left)\r\n\t\t\t+ countNodes(root-&gt;right));\r\n}\r\n\r\n\r\nbool is_complete_tree (struct Node* root,\r\n\t\t\t\t\tunsigned int index,\r\n\t\t\t\t\tunsigned int number_nodes)\r\n{\r\n\r\n\tif (root == NULL)\r\n\t\treturn (true);\r\n\r\n\r\n\tif (index &gt;= number_nodes)\r\n\t\treturn (false);\r\n\r\n\treturn (is_complete_tree(root-&gt;left, 2*index + 1,\r\n\t\t\t\t\t\tnumber_nodes) &amp;&amp;\r\n\t\t\tis_complete_tree(root-&gt;right, 2*index + 2,\r\n\t\t\t\t\t\tnumber_nodes));\r\n}\r\n\r\nbool is_heap_property(struct Node* root)\r\n{\r\n\t\r\n\tif (root-&gt;left == NULL &amp;&amp; root-&gt;right == NULL)\r\n\t\treturn (true);\r\n\r\n\r\n\tif (root-&gt;right == NULL)\r\n\t{\r\n\t\treturn (root-&gt;key &gt;= root-&gt;left-&gt;key);\r\n\t}\r\n\telse\r\n\t{\r\n\r\n\t\tif (root-&gt;key &gt;= root-&gt;left-&gt;key &amp;&amp;\r\n\t\t\troot-&gt;key &gt;= root-&gt;right-&gt;key)\r\n\t\t\treturn ((is_heap_property(root-&gt;left)) &amp;&amp;\r\n\t\t\t\t\t(is_heap_property(root-&gt;right)));\r\n\t\telse\r\n\t\t\treturn (false);\r\n\t}\r\n}\r\n\r\n\r\nbool isHeap(struct Node* root)\r\n{\r\n\r\n\tunsigned int node_count = countNodes(root);\r\n\tunsigned int index = 0;\r\n\r\n\tif (is_complete_tree(root, index,\r\n\t\t\t\t\tnode_count)\r\n\t\t&amp;&amp; is_heap_property(root))\r\n\t\treturn true;\r\n\treturn false;\r\n}\r\n\r\nint main()\r\n{\r\n\tstruct Node* root = NULL;\r\n\troot = newNode(25);\r\n\troot-&gt;left = newNode(11);\r\n\troot-&gt;right = newNode(16);\r\n\troot-&gt;left-&gt;left = newNode(3);\r\n\troot-&gt;left-&gt;right = newNode(8);\r\n\r\n\tif (isHeap(root))\r\n\t\tcout &lt;&lt; &quot;Given Binary Tree is a Max - Heap&#92;n&quot;;\r\n\telse\r\n\t\tcout &lt;&lt; &quot;Given Binary Tree is not a Max - Heap&#92;n&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_8715_3\">\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 Node {\r\n\tint key;\r\n\tNode left, right;\r\n\r\n\tNode(int k)\r\n\t{\r\n\t\tkey = k;\r\n\t\tleft = right = null;\r\n\t}\r\n}\r\n\r\nclass Is_BinaryTree_MaxHeap\r\n{\r\n\r\n\tint countNodes(Node root)\r\n\t{\r\n\t\tif (root == null)\r\n\t\t\treturn 0;\r\n\t\treturn (1 + countNodes(root.left)\r\n\t\t\t\t+ countNodes(root.right));\r\n\t}\r\n\r\n\tboolean isCompleteUtil(Node root, int index,\r\n\t\t\t\t\t\tint number_nodes)\r\n\t{\r\n\r\n\t\tif (root == null)\r\n\t\t\treturn true;\r\n\r\n\r\n\t\tif (index &gt;= number_nodes)\r\n\t\t\treturn false;\r\n\r\n\r\n\t\treturn isCompleteUtil(root.left,\r\n\t\t\t\t\t\t\t2 * index + 1,\r\n\t\t\t\t\t\t\tnumber_nodes)\r\n\t\t\t&amp;&amp; isCompleteUtil(root.right,\r\n\t\t\t\t\t\t\t2 * index + 2,\r\n\t\t\t\t\t\t\tnumber_nodes);\r\n\t}\r\n\r\n\r\n\tboolean isHeapUtil(Node root)\r\n\t{\r\n\r\n\t\tif (root.left == null &amp;&amp; root.right == null)\r\n\t\t\treturn true;\r\n\r\n\r\n\t\tif (root.right == null) {\r\n\r\n\t\t\treturn root.key &gt;= root.left.key;\r\n\t\t}\r\n\t\telse {\r\n\r\n\t\t\tif (root.key &gt;= root.left.key\r\n\t\t\t\t&amp;&amp; root.key &gt;= root.right.key)\r\n\t\t\t\treturn isHeapUtil(root.left)\r\n\t\t\t\t\t&amp;&amp; isHeapUtil(root.right);\r\n\t\t\telse\r\n\t\t\t\treturn false;\r\n\t\t}\r\n\t}\r\n\r\n\r\n\tboolean isHeap(Node root)\r\n\t{\r\n\t\tif (root == null)\r\n\t\t\treturn true;\r\n\r\n\t\tint node_count = countNodes(root);\r\n\r\n\t\tif (isCompleteUtil(root, 0, node_count) == true\r\n\t\t\t&amp;&amp; isHeapUtil(root) == true)\r\n\t\t\treturn true;\r\n\t\treturn false;\r\n\t}\r\n\r\n\r\n\tpublic static void main(String args[])\r\n\t{\r\n\t\tIs_BinaryTree_MaxHeap bt\r\n\t\t\t= new Is_BinaryTree_MaxHeap();\r\n\r\n\t\tNode root = new Node(10);\r\n\t\troot.left = new Node(9);\r\n\t\troot.right = new Node(8);\r\n\t\troot.left.left = new Node(7);\r\n\t\troot.left.right = new Node(6);\r\n\t\troot.right.left = new Node(5);\r\n\t\troot.right.right = new Node(4);\r\n\t\troot.left.left.left = new Node(3);\r\n\t\troot.left.left.right = new Node(2);\r\n\t\troot.left.right.left = new Node(1);\r\n\r\n\t\tif (bt.isHeap(root) == true)\r\n\t\t\tSystem.out.println(\r\n\t\t\t\t&quot;Given Binary Tree is a Max-Heap&quot;);\r\n\t\telse\r\n\t\t\tSystem.out.println(\r\n\t\t\t\t&quot;Given Binary Tree is not a Max-Heap&quot;);\r\n\t}\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_8715_4\">\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\nclass binary_tree:\r\n\tdef __init__(self, value):\r\n\t\tself.key = value\r\n\t\tself.left = None\r\n\t\tself.right = None\r\n\r\n\tdef count_nodes(self, root):\r\n\t\tif root is None:\r\n\t\t\treturn 0\r\n\t\telse:\r\n\t\t\treturn (1 + self.count_nodes(root.left) + self.count_nodes(root.right))\r\n\r\n\tdef is_heap_property(self, root):\r\n\r\n\t\tif (root.left is None and\r\n\t\t\t\troot.right is None):\r\n\t\t\treturn True\r\n\r\n\t\tif root.right is None:\r\n\t\t\treturn root.key >= root.left.key\r\n\t\telse:\r\n\t\t\tif (root.key >= root.left.key and\r\n\t\t\t\t\troot.key >= root.right.key):\r\n\t\t\t\treturn (self.is_heap_property(root.left) and self.is_heap_property(root.right))\r\n\t\t\telse:\r\n\t\t\t\treturn False\r\n\r\n\tdef is_complete_tree(self, root,\r\n\t\t\t\t\t\tindex, node_count):\r\n\t\tif root is None:\r\n\t\t\treturn True\r\n\t\tif index >= node_count:\r\n\t\t\treturn False\r\n\t\treturn (self.is_complete_tree(root.left, 2 * index + 1, node_count) and self.is_complete_tree(root.right, 2 * index + 2, node_count))\r\n\r\n\tdef isHeap(self):\r\n\t\tnode_count = self.count_nodes(self)\r\n\t\tif (self.is_complete_tree(self, 0, node_count) and self.is_heap_property(self)):\r\n\t\t\treturn True\r\n\t\telse:\r\n\t\t\treturn False\r\n\r\n\r\nroot = binary_tree(25)\r\nroot.left = binary_tree(11)\r\nroot.right = binary_tree(16)\r\nroot.left.left = binary_tree(3)\r\nroot.left.right = binary_tree(8)\r\n\r\nif root.isHeap():\r\n\tprint(\"Given Binary Tree is a Max - Heap\")\r\nelse:\r\n\tprint(\"Given Binary Tree is not a Max - Heap\")\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_8715 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_8715 a\"),jQuery(\"#tab-content_8715\"));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><strong>Output:<\/strong><br \/>\nGiven Binary Tree is a Max-Heap<\/p>\n<p>This article tried to discuss <strong>How to Check if a given Binary Tree is Heap<\/strong>. Hope this blog helps you understand the concept. To practice more problems feel free to check <a href=\"#\"><\/a> at  <a href=\"https:\/\/www.prepbytes.com\/\"> Prepbytes.<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Problem Statement: Given a binary tree, our task is to check whether the given tree follows the max heap property or not. What is a Binary Tree? Binary tree is a type of Tree data structure in which every node in the tree will have 2 or less than 2 child nodes and those child [&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":[],"class_list":["post-8716","post","type-post","status-publish","format-standard","hentry","category-heap"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v25.8 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Check if a given Binary Tree is Heap | Heap | Prepbytes<\/title>\n<meta name=\"description\" content=\"Given a binary tree, we need to check if it follows the property of Max-Heap or not. There are two conditions that should be fulfilled. It must be a complete binary tree, i.e. except for the last level of the tree, all other levels must be fully filled with nodes.\" \/>\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\/check-if-a-given-binary-tree-is-heap\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Check if a given Binary Tree is Heap | Heap | Prepbytes\" \/>\n<meta property=\"og:description\" content=\"Given a binary tree, we need to check if it follows the property of Max-Heap or not. There are two conditions that should be fulfilled. 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