{"id":9167,"date":"2025-08-10T12:06:37","date_gmt":"2025-08-10T06:36:37","guid":{"rendered":"https:\/\/namastedev.com\/blog\/?p=9167"},"modified":"2025-10-15T17:17:30","modified_gmt":"2025-10-15T11:47:30","slug":"extracting-values-in-heap-and-heapifydown","status":"publish","type":"post","link":"https:\/\/namastedev.com\/blog\/extracting-values-in-heap-and-heapifydown\/","title":{"rendered":"Extracting Values in Heap and HeapifyDown"},"content":{"rendered":"\n<!-- extract 4 -->\n<!-- Prism.js for Code Highlighting -->\n<link\n    href=\"https:\/\/cdn.jsdelivr.net\/npm\/prismjs@1.29.0\/themes\/prism-tomorrow.min.css\"\n    rel=\"stylesheet\"\n\/>\n<script src=\"https:\/\/cdn.jsdelivr.net\/npm\/prismjs@1.29.0\/prism.min.js\"><\/script>\n<script src=\"https:\/\/cdn.jsdelivr.net\/npm\/prismjs@1.29.0\/plugins\/autoloader\/prism-autoloader.min.js\"><\/script>\n\n<style>\n.wp_blog_theme {\n  --primary: #E58C32;\n  --secondary: #030302;\n  --light-bg: #fef9f4;\n  --text-dark: #2d2d2d;\n  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background: var(--primary);\n  color: white;\n  font-weight: bold;\n  cursor: pointer;\n  border: none;\n  box-shadow: var(--shadow);\n  transition: background 0.3s, transform 0.2s;\n}\n\n.wp_blog_toggle-btn:hover {\n  background: #cc772e;\n}\n\n.wp_blog_theme.dark-mode .wp_blog_code-tabs-container {\n  background: #1e1e1e;\n}\n<\/style>\n\n\n<div class=\"wp_blog_container wp_blog_theme\">\n      <button id=\"blogNotesThemeToggle\" class=\"wp_blog_toggle-btn\">\ud83c\udf19<\/button>\n    <h1 class=\"wp_blog_main-heading\"><\/h1>\n\n    <div class=\"wp_blog_explanation\">\n        <h2>Deleting (Extracting) Elements from a Heap<\/h2>\n        <h3>Min Heap:<\/h3>\n        <img decoding=\"async\" src=\"https:\/\/namastedev.com\/blog\/wp-content\/uploads\/2025\/08\/Screenshot-2025-08-10-at-10.19.29\u202fAM.png\" alt=\"\">\n        <ul>\n            <li>Extraction only happen <code>from the top<\/code> = <strong>heap[0]<\/strong>.<\/li>\n        <\/ul>\n        <img decoding=\"async\" src=\"https:\/\/namastedev.com\/blog\/wp-content\/uploads\/2025\/08\/Screenshot-2025-08-10-at-10.21.27\u202fAM.png\" alt=\"\">\n        <ul>\n            <li>Heapify down is the process of <code>restoring the heap property<\/code> after removing the root element (or moving an element downwards).<\/li>\n            <li><strong><code>MinHeap is formed<\/code><\/strong>.<\/li>\n        <\/ul>\n\n        <h3>Practice: <\/h3>\n        <img decoding=\"async\" src=\"https:\/\/namastedev.com\/blog\/wp-content\/uploads\/2025\/08\/Screenshot-2025-08-10-at-11.24.46\u202fAM.png\" alt=\"\">\n        <h3>Solution:<\/h3>\n        <img decoding=\"async\" src=\"https:\/\/namastedev.com\/blog\/wp-content\/uploads\/2025\/08\/Screenshot-2025-08-10-at-11.32.46\u202fAM.png\" alt=\"\">\n        <ul>\n            <li><code>Min Heap<\/code> is formed.<\/li>\n        <\/ul>\n    \n        <h2>Code<\/h2>\n<div class=\"wp_blog_code-tab-content active\" data-lang=\"js\">\n<pre>\nclass MinHeap {\n    constructor() {\n        this.heap = [5, 10, 20, 30];\n    }\n    getLeftChildIndex(i) { return (2 * i) + 1; }\n    getRightChildIndex(i) { return (2 * i) + 2; }\n    getParentIndex(i) { return Math.floor((i - 1) \/ 2); }\n\n    insert(val) {\n        this.heap.push(val);\n        let lastIndex = this.heap.length - 1;\n        this.heapifyUp(lastIndex);\n    }\n\n    heapifyUp(i) {\n        while (i > 0) {\n            let parentIndex = this.getParentIndex(i);\n            if (this.heap[i] < this.heap[parentIndex]) {\n                [this.heap[i], this.heap[parentIndex]] = \n                [this.heap[parentIndex], this.heap[i]];\n                i = parentIndex;\n            } else break;\n        }\n    }\n    extract () {\n        if(this.heap.length < 1) return null;\n        let min = this.heap[0];\n        let lastIndex = this.heap.length - 1;\n        [this.heap[0], this.heap[lastIndex]] = [this.heap \n        [lastIndex], this.heap[0]];\n        \n        this.heap.pop();\n        \n        this.heapifyDown(0); \n        return min;\n    }\n    heapifyDown(i){\n        let left = this.getLeftChildIndex(i);\n        let right = this.getRightChildIndex(i);\n        let n = this.heap.length;\n\n        let smallest = i;\n        if(left < n &#038;&#038; this.heap[left] < this.heap[smallest]) {\n            smallest = left;\n        }\n        if(right < n &#038;&#038; this.heap[right] < this.heap[smallest]) {\n            smallest = right;\n        }\n        if(smallest != i){\n            [this.heap[smallest], this.heap[i]] = [this.heap[i],this.heap[smallest]];\n            this.heapifyDown(smallest);\n        }\n    }\n\n    \/\/ peek operation\n    peek() {\n        if(!this.heap.length) return null;\n        return this.heap[0];\n    }\n}\n\nlet heap = new MinHeap();\nheap.insert(5);\nheap.insert(20);\nheap.insert(4);\nheap.insert(10);\nheap.insert(1);\nheap.insert(0);\nconsole.log(heap.peek());\nconsole.log(heap.extract());\nconsole.log(heap.extract());\nconsole.log(heap.heap);\n\n<\/pre>\n<\/div>\n\n<h2>Dry Run<\/h2> <div style=\"border-left: 4px solid var(--primary); padding: 1rem; border-radius: var(--tab-radius); margin: 1rem 0;\"> <!-- First insertion --> <p><strong>Input:<\/strong><\/p> <pre> Initial heap = [5, 10, 20, 30] Insert value = 5 <\/pre> <p><strong>State Transitions:<\/strong><\/p> <pre> Step 1: Call insert(5) \u2192 push(5) \u2192 heap = [5, 10, 20, 30, 5] \u2192 lastIndex = 4\nStep 2: heapifyUp(4)\ni = 4 \u2192 parentIndex = 1 \u2192 Compare 5 < 10 \u2192 swap \u2192 [5, 5, 20, 30, 10]\ni = 1 \u2192 parentIndex = 0 \u2192 Compare 5 < 5 \u2192 false \u2192 break\n<\/pre>\n<p><strong>Final Output:<\/strong> <code>[5, 5, 20, 30, 10]<\/code><\/p> <p><strong>Final State:<\/strong> <code>heap = [5, 5, 20, 30, 10]<\/code><\/p> <!-- Second insertion --> <p><strong>Input:<\/strong><\/p> <pre> heap = [5, 5, 20, 30, 10] Insert value = 20 <\/pre> <p><strong>State Transitions:<\/strong><\/p> <pre> Step 1: Call insert(20) \u2192 push(20) \u2192 heap = [5, 5, 20, 30, 10, 20] \u2192 lastIndex = 5\nStep 2: heapifyUp(5)\ni = 5 \u2192 parentIndex = 2 \u2192 Compare 20 < 20 \u2192 false \u2192 break\n<\/pre>\n<p><strong>Final Output:<\/strong> <code>[5, 5, 20, 30, 10, 20]<\/code><\/p> <p><strong>Final State:<\/strong> <code>heap = [5, 5, 20, 30, 10, 20]<\/code><\/p> <!-- Third insertion --> <p><strong>Input:<\/strong><\/p> <pre> heap = [5, 5, 20, 30, 10, 20] Insert value = 4 <\/pre> <p><strong>State Transitions:<\/strong><\/p> <pre> Step 1: Call insert(4) \u2192 push(4) \u2192 heap = [5, 5, 20, 30, 10, 20, 4] \u2192 lastIndex = 6\nStep 2: heapifyUp(6)\ni = 6 \u2192 parentIndex = 2 \u2192 Compare 4 < 20 \u2192 swap \u2192 [5, 5, 4, 30, 10, 20, 20]\ni = 2 \u2192 parentIndex = 0 \u2192 Compare 4 < 5 \u2192 swap \u2192 [4, 5, 5, 30, 10, 20, 20]\ni = 0 \u2192 loop ends\n<\/pre>\n<p><strong>Final Output:<\/strong> <code>[4, 5, 5, 30, 10, 20, 20]<\/code><\/p> <p><strong>Final State:<\/strong> <code>heap = [4, 5, 5, 30, 10, 20, 20]<\/code><\/p> <!-- Fourth insertion --> <p><strong>Input:<\/strong><\/p> <pre> heap = [4, 5, 5, 30, 10, 20, 20] Insert value = 10 <\/pre> <p><strong>State Transitions:<\/strong><\/p> <pre> Step 1: Call insert(10) \u2192 push(10) \u2192 heap = [4, 5, 5, 30, 10, 20, 20, 10] \u2192 lastIndex = 7\nStep 2: heapifyUp(7)\ni = 7 \u2192 parentIndex = 3 \u2192 Compare 10 < 30 \u2192 swap \u2192 [4, 5, 5, 10, 10, 20, 20, 30]\ni = 3 \u2192 parentIndex = 1 \u2192 Compare 10 < 5 \u2192 false \u2192 break\n<\/pre>\n<p><strong>Final Output:<\/strong> <code>[4, 5, 5, 10, 10, 20, 20, 30]<\/code><\/p> <p><strong>Final State:<\/strong> <code>heap = [4, 5, 5, 10, 10, 20, 20, 30]<\/code><\/p> <!-- Fifth insertion --> <p><strong>Input:<\/strong><\/p> <pre> heap = [4, 5, 5, 10, 10, 20, 20, 30] Insert value = 1 <\/pre> <p><strong>State Transitions:<\/strong><\/p> <pre> Step 1: Call insert(1) \u2192 push(1) \u2192 heap = [4, 5, 5, 10, 10, 20, 20, 30, 1] \u2192 lastIndex = 8\nStep 2: heapifyUp(8)\ni = 8 \u2192 parentIndex = 3 \u2192 Compare 1 < 10 \u2192 swap \u2192 [4, 5, 5, 1, 10, 20, 20, 30, 10]\ni = 3 \u2192 parentIndex = 1 \u2192 Compare 1 < 5 \u2192 swap \u2192 [4, 1, 5, 5, 10, 20, 20, 30, 10]\ni = 1 \u2192 parentIndex = 0 \u2192 Compare 1 < 4 \u2192 swap \u2192 [1, 4, 5, 5, 10, 20, 20, 30, 10]\ni = 0 \u2192 loop ends\n<\/pre>\n<p><strong>Final Output:<\/strong> <code>[1, 4, 5, 5, 10, 20, 20, 30, 10]<\/code><\/p> <p><strong>Final State:<\/strong> <code>heap = [1, 4, 5, 5, 10, 20, 20, 30, 10]<\/code><\/p> <!-- Sixth insertion --> <p><strong>Input:<\/strong><\/p> <pre> heap = [1, 4, 5, 5, 10, 20, 20, 30, 10] Insert value = 0 <\/pre> <p><strong>State Transitions:<\/strong><\/p> <pre> Step 1: Call insert(0) \u2192 push(0) \u2192 heap = [1, 4, 5, 5, 10, 20, 20, 30, 10, 0] \u2192 lastIndex = 9\nStep 2: heapifyUp(9)\ni = 9 \u2192 parentIndex = 4 \u2192 Compare 0 < 10 \u2192 swap \u2192 [1, 4, 5, 5, 0, 20, 20, 30, 10, 10]\ni = 4 \u2192 parentIndex = 1 \u2192 Compare 0 < 4 \u2192 swap \u2192 [1, 0, 5, 5, 4, 20, 20, 30, 10, 10]\ni = 1 \u2192 parentIndex = 0 \u2192 Compare 0 < 1 \u2192 swap \u2192 [0, 1, 5, 5, 4, 20, 20, 30, 10, 10]\ni = 0 \u2192 loop ends\n<\/pre>\n<p><strong>Final Output:<\/strong> <code>[0, 1, 5, 5, 4, 20, 20, 30, 10, 10]<\/code><\/p> <p><strong>Final State:<\/strong> <code>heap = [0, 1, 5, 5, 4, 20, 20, 30, 10, 10]<\/code><\/p> <!-- Peek --> <p><strong>Operation:<\/strong> <code>peek()<\/code><\/p> <p>Output = <code>0<\/code><\/p> <!-- Extract 1 --> <p><strong>Operation:<\/strong> <code>extract()<\/code><\/p> <pre> Initial heap = [0, 1, 5, 5, 4, 20, 20, 30, 10, 10] Swap heap[0] with heap[9] \u2192 [10, 1, 5, 5, 4, 20, 20, 30, 10, 0] Pop \u2192 heap = [10, 1, 5, 5, 4, 20, 20, 30, 10]\nheapifyDown(0):\n\u2192 left = 1, right = 2, smallest = 1 \u2192 swap \u2192 [1, 10, 5, 5, 4, 20, 20, 30, 10]\n\u2192 i = 1: left = 3, right = 4, smallest = 4 \u2192 swap \u2192 [1, 4, 5, 5, 10, 20, 20, 30, 10]\n\u2192 i = 4: left = 9, right = 10 \u2192 out of range \u2192 stop\n<\/pre>\n<p><strong>Extracted:<\/strong> <code>0<\/code><\/p> <p><strong>Final heap:<\/strong> <code>[1, 4, 5, 5, 10, 20, 20, 30, 10]<\/code><\/p> <!-- Extract 2 --> <p><strong>Operation:<\/strong> <code>extract()<\/code><\/p> <pre> Initial heap = [1, 4, 5, 5, 10, 20, 20, 30, 10] Swap heap[0] with heap[8] \u2192 [10, 4, 5, 5, 10, 20, 20, 30, 1] Pop \u2192 heap = [10, 4, 5, 5, 10, 20, 20, 30]\nheapifyDown(0):\n\u2192 left = 1, right = 2, smallest = 1 \u2192 swap \u2192 [4, 10, 5, 5, 10, 20, 20, 30]\n\u2192 i = 1: left = 3, right = 4, smallest = 3 \u2192 swap \u2192 [4, 5, 5, 10, 10, 20, 20, 30]\n\u2192 i = 3: left = 7, right = 8 \u2192 out of range \u2192 stop\n<\/pre>\n<p><strong>Extracted:<\/strong> <code>1<\/code><\/p> <p><strong>Final heap:<\/strong> <code>[4, 5, 5, 10, 10, 20, 20, 30]<\/code><\/p> <\/div>\n\n    <\/div>\n<\/div>\n\n<script>\ndocument.addEventListener(\"DOMContentLoaded\", () => {\n  const buttons = document.querySelectorAll(\".wp_blog_code-tab-button\");\n  const contents = document.querySelectorAll(\".wp_blog_code-tab-content\");\n\n  buttons.forEach((button) => {\n    button.addEventListener(\"click\", () => {\n      const lang = button.getAttribute(\"data-lang\");\n\n      buttons.forEach((btn) => btn.classList.remove(\"active\"));\n      contents.forEach((content) => content.classList.remove(\"active\"));\n\n      button.classList.add(\"active\");\n      document\n        .querySelector(`.wp_blog_code-tab-content[data-lang=\"${lang}\"]`)\n        .classList.add(\"active\");\n    });\n  });\n\n  const themeToggle = document.getElementById(\"blogNotesThemeToggle\");\n  const themeContainer = document.querySelector(\".wp_blog_theme\");\n\n  themeToggle.addEventListener(\"click\", () => {\n    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Heapify down is the process of restoring the heap property after removing the root element (or moving an element downwards). MinHeap is formed. Practice: Solution: Min Heap is formed. Code class MinHeap { constructor() { this.heap = [5,<\/p>\n","protected":false},"author":108,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[176,175,211,811,810,174,172,173],"tags":[],"class_list":["post-9167","post","type-post","status-publish","format-standard","category-csharp","category-cplusplus","category-data-structures","category-data-structures-and-algorithms","category-dsa","category-java","category-javascript","category-python"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/9167","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/users\/108"}],"replies":[{"embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/comments?post=9167"}],"version-history":[{"count":3,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/9167\/revisions"}],"predecessor-version":[{"id":10339,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/9167\/revisions\/10339"}],"wp:attachment":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/media?parent=9167"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/categories?post=9167"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/tags?post=9167"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}