{"id":8545,"date":"2022-06-21T09:18:43","date_gmt":"2022-06-21T09:18:43","guid":{"rendered":"https:\/\/www.prepbytes.com\/blog\/?p=8545"},"modified":"2022-12-14T07:44:46","modified_gmt":"2022-12-14T07:44:46","slug":"array-representation-of-a-binary-heap","status":"publish","type":"post","link":"https:\/\/prepbytes.com\/blog\/array-representation-of-a-binary-heap\/","title":{"rendered":"Array Representation of a Binary Heap"},"content":{"rendered":"<p><img decoding=\"async\" src=\"https:\/\/prepbytes-misc-images.s3.ap-south-1.amazonaws.com\/assets\/1655801616756-Array%20Representation%20of%20a%20Binary%20Heap.jpg\" alt=\"\" \/><\/p>\n<h3>What is Binary Heap?<\/h3>\n<p>A Binary Heap is a complete binary tree that follows a heap ordering property. The representation is done as:<\/p>\n<\/p>\n<p><strong><em>Parent Node:<\/em><\/strong> (i-1)\/2<br \/>\n<strong><em>Left Child:<\/em><\/strong> (2<em>i) + 1<br \/>\n<strong>Right Child<\/strong>: (2<\/em>i) + 2<\/p>\n<p>The above table shows the indexes of the i<sup>th<\/sup> node.<br \/>\nBased on the Ordering property of binary heap, it can be of two types:<\/p>\n<p><strong>Min Heap:<\/strong> In Min heap, The value of the node is greater than or equal to the value of its parent\u2019s node. The root node is the smallest in the min-heap.<\/p>\n<p><strong><em>For Example 1 :<\/em><\/strong> Using the above rules of array representation we can represent a heap in the array:<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/prepbytes-misc-images.s3.ap-south-1.amazonaws.com\/assets\/1655801674896-Image-01-01.png\"><br \/>\n<img decoding=\"async\" src=\"https:\/\/prepbytes-misc-images.s3.ap-south-1.amazonaws.com\/assets\/1655801743958-Image-01-02.png\"><\/p>\n<p>For node with value 2, its index value is 1 have left child is at (2<em>1) + 1 = 3 i.e. node with value 3 and      right child is at (2<\/em>1) + 2 = 4 i.e. node with value 7. And we can see here that, both the children are bigger than their parent node.<\/p>\n<p><strong><em>For Example 2:<\/em><\/strong> Using the above rules of array representation we can represent a heap in the array:<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/prepbytes-misc-images.s3.ap-south-1.amazonaws.com\/assets\/1656502977347-Image%202-02.png\" alt=\"\" \/><\/p>\n<p>For node with value 4, its index value is 2 have left child is at (2<em>2) + 1 = 5 i.e. node with value 16 and right child is at (2<\/em>2) + 2 = 6 i.e. node with value 18. And we can see here that, both the children are bigger than their parent node. Also its parent node will be at (2-1)\/2 = 0 i.e. node with value 2.<\/p>\n<p><strong>Max Heap:<\/strong> In Max Heap, The value of the node is smaller than or equal to the value of its parent\u2019s node. The root node is the greatest in max Heap.<\/p>\n<p><strong><em>For Example 1:<\/em><\/strong><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/prepbytes-misc-images.s3.ap-south-1.amazonaws.com\/assets\/1655801793905-Image-01-03.png\"><br \/>\n<img decoding=\"async\" src=\"https:\/\/prepbytes-misc-images.s3.ap-south-1.amazonaws.com\/assets\/1655801854145-Image-01-04.png\"><\/p>\n<p>For node with value 6, its index value is 1 have left child is at (2<em>1) + 1 = 3 i.e. node with value 3 and right child is at (2<\/em>1) + 2 = 4 i.e. node with value 2. And we can see here that, both the children are bigger than their parent node.<\/p>\n<p><strong><em>For Example 2:<\/em><\/strong> Using the above rules of array representation we can represent a heap in the array:<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/prepbytes-misc-images.s3.ap-south-1.amazonaws.com\/assets\/1656498347292-Image%202-04.png\" alt=\"\" \/><\/p>\n<p>For node with value 14, its index value is 2 have left child is at (2<em>2) + 1 = 5 i.e. node with value 6 and right child is at (2<\/em>2) + 2 = 6 i.e. node with value 8. And we can see here that, both the children are smaller than their parent node. Also its parent node will be at (2-1)\/2 = 0 i.e. node with value 18.<\/p>\n<p>This article tried to discuss the <strong>Array Representation of a Binary Heap<\/strong>. Hope this blog helps you understand the concept. 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>What is Binary Heap? A Binary Heap is a complete binary tree that follows a heap ordering property. The representation is done as: Parent Node: (i-1)\/2 Left Child: (2i) + 1 Right Child: (2i) + 2 The above table shows the indexes of the ith node. Based on the Ordering property of binary heap, it [&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":[40,176,175],"class_list":["post-8545","post","type-post","status-publish","format-standard","hentry","category-heap","tag-array","tag-binary-tree","tag-heap"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v25.8 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Array Representation of a Binary Heap | Heap | Prepbytes<\/title>\n<meta name=\"description\" content=\"A binary heap is an efficient data structure used to store items in order of their priority. 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