{"id":9011,"date":"2025-08-06T16:48:28","date_gmt":"2025-08-06T11:18:28","guid":{"rendered":"https:\/\/namastedev.com\/blog\/?p=9011"},"modified":"2025-08-06T16:49:43","modified_gmt":"2025-08-06T11:19:43","slug":"lowest-common-ancestor-of-a-bst","status":"publish","type":"post","link":"https:\/\/namastedev.com\/blog\/lowest-common-ancestor-of-a-bst\/","title":{"rendered":"Lowest Common Ancestor of a BST"},"content":{"rendered":"\n<!-- Lowest: 6 -->\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: #f8c291;\n  --light-bg: #fef9f4;\n  --text-dark: #2d2d2d;\n  --tab-radius: 12px;\n  --shadow: 0 4px 12px rgba(0, 0, 0, 0.08);\n  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0;\n  padding: 1.5rem;\n  font-size: 1rem;\n  overflow-x: auto;\n  background: var(--code-bg);\n  border-radius: var(--tab-radius);\n  color: var(--code-text);\n}\n<\/style>\n\n<div class=\"wp_blog_container wp_blog_theme\"> \n    <h1 class=\"wp_blog_main-heading\"><\/h1>\n    <div class=\"wp_blog_explanation\">\n        <h2>Problem Statement:<\/h2>\n        <p>Given a binary search tree (BST), find the lowest common ancestor (LCA) node of two given nodes in the BST.<\/p>\n        <p>According to the definition of LCA on Wikipedia: \u201cThe lowest common ancestor is defined between two nodes <code>p<\/code> and <code>q<\/code> as the lowest node in <code>T<\/code> that has both <code>p<\/code> and <code>q<\/code> as descendants (where we allow <strong>a node to be a descendant of itself)<\/strong>.\u201d<\/p>\n\n        <h2>Examples:<\/h2>\n                <h3>Example 1:<\/h3>\n                <img decoding=\"async\" src=\"https:\/\/namastedev.com\/blog\/wp-content\/uploads\/2025\/08\/Screenshot-2025-08-06-at-4.26.12\u202fPM.png\" alt=\"\">\n                <p><strong>Input:<\/strong> root = [6,2,8,0,4,7,9,null,null,3,5], p = 2, q = 8<\/p>\n                <p><strong>Output:<\/strong> 6<\/p>\n                <p><strong>Explanation:<\/strong> The LCA of nodes 2 and 8 is 6.<\/p>\n            \n                <h3>Example 2:<\/h3>\n                <img decoding=\"async\" src=\"https:\/\/namastedev.com\/blog\/wp-content\/uploads\/2025\/08\/Screenshot-2025-08-06-at-4.26.12\u202fPM.png\" alt=\"\">\n                <p><strong>Input:<\/strong> root = [6,2,8,0,4,7,9,null,null,3,5], p = 2, q = 4<\/p>\n                <p><strong>Output:<\/strong> 2<\/p>\n                <p><strong>Explanation:<\/strong> The LCA of nodes 2 and 4 is 2, since a node can be a descendant of itself according to the LCA definition.<\/p>\n\n                <h3>Example 3:<\/h3>\n                <p><strong>Input:<\/strong> root = [2,1], p = 2, q = 1<\/p>\n                <p><strong>Output:<\/strong> 2<\/p>\n\n                    <h2>Constraints:<\/h2>\n                    <ul>\n                        <li>The number of nodes in the tree is in the range <code>[2, 10<sup>5<\/sup>]<\/code>.<\/li>\n                        <li><code>-10<sup>9<\/sup> <= Node.val <= 10<sup>9<\/sup><\/code><\/li>\n                        <li>All <code>Node.val<\/code> are <strong>unique<\/strong>.<\/li>\n                        <li><code>p != q<\/code><\/li>\n                        <li><code>p<\/code> and <code>q<\/code> will exist in the BST.<\/li>\n                    <\/ul>\n                <h2>Approach<\/h2>\n               <ul>\n                <li>If both <code>p<\/code> and <code>q<\/code> are <strong>less than root<\/strong>, LCA lies in the <code>left subtree \u2192 recurse left<\/code>.<\/li>\n                <li>If both <code>p<\/code> and <code>q<\/code> are <strong>greater than root<\/strong>, LCA lies in the <code>right subtree \u2192 recurse right<\/code>.<\/li>\n                <li>Otherwise, split happens at root (one node on each side or one is the root itself) \u2192 <code>this root is the LCA<\/code>.<\/li>\n               <\/ul> \n\n                <h2>Time Complexity:<\/h2>\n                <li>\n                  <p><strong>Time Complexity = O(n)<\/strong>\n                  <\/li>\n                <h2>Space Complexity:<\/h2>\n                <li>\n                  <p><strong>Space Complexity = O(h)<\/strong>(h=tree height)<\/p>\n                <\/li>\n<h2>Dry Run<\/h2> <div style=\"background: #f9f9f9; padding: 10px; border: 1px solid #ccc; font-family: monospace;\"> <b>Function Call:<\/b> lowestCommonAncestor(root, p=Node(2), q=Node(8)) where<br> root = Node(6)<br> \u251c\u2500\u2500 left: Node(2)<br> \u2502\u00a0\u00a0 \u251c\u2500\u2500 left: Node(0)<br> \u2502\u00a0\u00a0 \u2514\u2500\u2500 right: Node(4)<br> \u2502\u00a0\u00a0 \u00a0\u00a0\u00a0 \u251c\u2500\u2500 left: Node(3)<br> \u2502\u00a0\u00a0 \u00a0\u00a0\u00a0 \u2514\u2500\u2500 right: Node(5)<br> \u2514\u2500\u2500 right: Node(8)<br> \u00a0\u00a0\u00a0\u251c\u2500\u2500 left: Node(7)<br> \u00a0\u00a0\u00a0\u2514\u2500\u2500 right: Node(9)<br><br>\n<b>Initial State:<\/b><br>\n\u2192 root = Node(6)<br>\n\u2192 p = Node(2)<br>\n\u2192 q = Node(8)<br><br>\n<b>Step 1:<\/b><br>\n\u2192 p.val = 2, q.val = 8<br>\n\u2192 Since p.val < root.val and q.val > root.val \u2192 Nodes lie on different sides<br>\n\u2192 Return current root \u2192 Node(6) is the Lowest Common Ancestor<br><br>\n\n<b>Final Result:<\/b><br>\nLCA = Node(6) \u2192 The lowest common ancestor of Node(2) and Node(8)\n\n<\/div>\n    <!-- <h2>Visualisation:<\/h2>\n        <img decoding=\"async\" src=\"https:\/\/namastedev.com\/blog\/wp-content\/uploads\/2025\/07\/Screenshot-2025-07-19-at-5.23.43\u202fPM.png\" alt=\"longest\" \/> -->\n    <\/div>\n    \n\n    <div class=\"wp_blog_code-tabs-container\">\n        <div class=\"wp_blog_code-tabs-header\">\n            <button class=\"wp_blog_code-tab-button active\" data-lang=\"js\">JavaScript<\/button>\n            <button class=\"wp_blog_code-tab-button\" data-lang=\"py\">Python<\/button>\n            <button class=\"wp_blog_code-tab-button\" data-lang=\"java\">Java<\/button>\n            <button class=\"wp_blog_code-tab-button\" data-lang=\"cpp\">C++<\/button>\n            <button class=\"wp_blog_code-tab-button\" data-lang=\"c\">C<\/button>\n            <button class=\"wp_blog_code-tab-button\" data-lang=\"cs\">C#<\/button>\n        <\/div>\n\n        <!-- JavaScript -->\n        <div class=\"wp_blog_code-tab-content active\" data-lang=\"js\">\n            <pre><code class=\"language-javascript\">\nvar lowestCommonAncestor = function(root, p, q) {\n    if(p.val < root.val &#038;&#038; q.val < root.val){\n        return lowestCommonAncestor(root.left, p, q);\n    } else if(p.val > root.val && q.val > root.val){\n        return lowestCommonAncestor(root.right, p,q);\n    } else {\n        return root;\n    }\n};\n  <\/code><\/pre>\n        <\/div>\n\n        <!-- Python -->\n        <div class=\"wp_blog_code-tab-content\" data-lang=\"py\">\n            <pre><code class=\"language-python\">\ndef lowestCommonAncestor(root, p, q):\n    if p.val < root.val and q.val < root.val:\n        return lowestCommonAncestor(root.left, p, q)\n    elif p.val > root.val and q.val > root.val:\n        return lowestCommonAncestor(root.right, p, q)\n    else:\n        return root\n          <\/code><\/pre>\n        <\/div>\n\n        <!-- Java -->\n        <div class=\"wp_blog_code-tab-content\" data-lang=\"java\">\n            <pre><code class=\"language-java\">\npublic TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {\n    if(p.val < root.val &#038;&#038; q.val < root.val) {\n        return lowestCommonAncestor(root.left, p, q);\n    } else if(p.val > root.val && q.val > root.val) {\n        return lowestCommonAncestor(root.right, p, q);\n    } else {\n        return root;\n    }\n}\n     <\/code><\/pre>\n        <\/div>\n\n        <!-- C++ -->\n        <div class=\"wp_blog_code-tab-content\" data-lang=\"cpp\">\n            <pre><code class=\"language-cpp\">\nTreeNode* lowestCommonAncestor(TreeNode* root, TreeNode* p, TreeNode* q) {\n    if(p->val < root->val && q->val < root->val) {\n        return lowestCommonAncestor(root->left, p, q);\n    } else if(p->val > root->val && q->val > root->val) {\n        return lowestCommonAncestor(root->right, p, q);\n    } else {\n        return root;\n    }\n}\n   <\/code><\/pre>\n        <\/div>\n\n        <!-- C -->\n        <div class=\"wp_blog_code-tab-content\" data-lang=\"c\">\n            <pre><code class=\"language-c\">\nstruct TreeNode {\n    int val;\n    struct TreeNode *left;\n    struct TreeNode *right;\n};\n\nstruct TreeNode* lowestCommonAncestor(struct TreeNode* root, struct TreeNode* p, struct TreeNode* q) {\n    if (p->val < root->val && q->val < root->val) {\n        return lowestCommonAncestor(root->left, p, q);\n    } else if (p->val > root->val && q->val > root->val) {\n        return lowestCommonAncestor(root->right, p, q);\n    } else {\n        return root;\n    }\n}\n            <\/code><\/pre>\n        <\/div>\n\n        <!-- C# -->\n        <div class=\"wp_blog_code-tab-content\" data-lang=\"cs\">\n            <pre><code class=\"language-csharp\">\npublic TreeNode LowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {\n    if (p.val < root.val &#038;&#038; q.val < root.val) {\n        return LowestCommonAncestor(root.left, p, q);\n    } else if (p.val > root.val && q.val > root.val) {\n        return LowestCommonAncestor(root.right, p, q);\n    } else {\n        return root;\n    }\n}\n            <\/code><\/pre>\n        <\/div>\n    <\/div>\n<\/div>\n\n<script>\n    document.addEventListener(\"DOMContentLoaded\", () => {\n        const buttons = 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According to the definition of LCA on Wikipedia: \u201cThe lowest common ancestor is defined between two nodes p and q as the lowest node in T that has both p and q as<\/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":[210,176,175,211,811,810,174,172,173],"tags":[],"class_list":{"0":"post-9011","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-algorithms","7":"category-csharp","8":"category-cplusplus","9":"category-data-structures","10":"category-data-structures-and-algorithms","11":"category-dsa","12":"category-java","13":"category-javascript","14":"category-python"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/9011","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=9011"}],"version-history":[{"count":1,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/9011\/revisions"}],"predecessor-version":[{"id":9012,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/9011\/revisions\/9012"}],"wp:attachment":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/media?parent=9011"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/categories?post=9011"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/tags?post=9011"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}