{"id":8914,"date":"2025-08-04T11:33:57","date_gmt":"2025-08-04T06:03:57","guid":{"rendered":"https:\/\/namastedev.com\/blog\/?p=8914"},"modified":"2026-03-17T20:08:33","modified_gmt":"2026-03-17T14:38:33","slug":"lowest-common-ancestor","status":"publish","type":"post","link":"https:\/\/namastedev.com\/blog\/lowest-common-ancestor\/","title":{"rendered":"Lowest Common Ancestor"},"content":{"rendered":"\n<!-- Lowest Common Ancestor: 22 -->\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  --code-bg: 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border-radius: 4px;\n  font-family: 'Courier New', monospace;\n}\n.wp_blog_explanation img {\n  max-width: 100%;\n  border-radius: var(--tab-radius);\n  margin-top: 1rem;\n  box-shadow: 0 2px 12px rgba(0,0,0,0.06);\n}\n\n\/* Tab Buttons *\/\n.wp_blog_code-tabs-header {\n  display: flex;\n  flex-wrap: wrap;\n  gap: 0.5rem;\n  margin-bottom: 1rem;\n}\n.wp_blog_code-tab-button {\n  padding: 0.6rem 1.2rem;\n  border: 1px solid var(--primary);\n  background: white;\n  color: var(--primary);\n  border-radius: 50px;\n  font-weight: 600;\n  cursor: pointer;\n  transition: all 0.3s ease;\n}\n.wp_blog_code-tab-button:hover {\n  background: var(--secondary);\n}\n.wp_blog_code-tab-button.active {\n  background: var(--primary);\n  color: white;\n}\n\n\/* Code Content *\/\n.wp_blog_code-tab-content {\n  display: none;\n  background: var(--code-bg);\n  border-radius: var(--tab-radius);\n}\n.wp_blog_code-tab-content.active {\n  display: block;\n}\n.wp_blog_code-tab-content pre {\n  margin: 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>\n            Given a binary tree, find the lowest common ancestor (LCA) of two given nodes in the tree.\n        <\/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        <h2>Examples:<\/h2>\n                <h3>Example 1:<\/h3>\n                <img decoding=\"async\" src=\"https:\/\/namastedev.com\/blog\/wp-content\/uploads\/2025\/08\/Screenshot-2025-08-04-at-11.25.56\u202fAM.png\" alt=\"\">\n                <p><strong>Input:<\/strong> root = [3,5,1,6,2,0,8,null,null,7,4], p = 5, q = 1<\/p>\n                <p><strong>Output:<\/strong> 3<\/p>\n                <p><strong>Explanation:<\/strong> The LCA of nodes 5 and 1 is 3.<\/p>\n\n                <h3>Example 2:<\/h3>\n                <img decoding=\"async\" src=\"https:\/\/namastedev.com\/blog\/wp-content\/uploads\/2025\/08\/Screenshot-2025-08-04-at-11.25.56\u202fAM.png\" alt=\"\">\n                <p><strong>Input:<\/strong> root = [3,5,1,6,2,0,8,null,null,7,4], p = 5, q = 4<\/p>\n                <p><strong>Output:<\/strong> 5<\/p>\n                <p><strong>Explanation: <\/strong>The LCA of nodes 5 and 4 is 5, 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 = [1,2], p = 1, q = 2<\/p>\n                <p><strong>Output:<\/strong> 1<\/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><\/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 tree.<\/li>\n                    <\/ul> \n\n                <h2>Approach<\/h2>\n                <ul>\n                    <li><strong>Use post-order traversal to explore the tree.<\/strong><\/li>\n                    <li>Recursively count how many of the target nodes (<code>p<\/code> or <code>q<\/code>) are found in the left and right subtrees.<\/li>\n                    <li>If the current node is either <code>p<\/code> or <code>q<\/code>, increment the count.<\/li>\n                    <li>When the total count from <code>left + right + current node<\/code> becomes 2, this node is the Lowest Common Ancestor.<\/li>\n                    <li><strong>Return<\/strong> the stored lca node after traversal.<\/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> isSubtree(root, subRoot) where<br> root = TreeNode(3)<br> \u251c\u2500\u2500 left: TreeNode(4)<br> \u2502\u00a0\u00a0 \u251c\u2500\u2500 left: TreeNode(1)<br> \u2502\u00a0\u00a0 \u2514\u2500\u2500 right: TreeNode(2)<br> \u2514\u2500\u2500 right: TreeNode(5)<br><br>\nsubRoot = TreeNode(4)<br>\n\u251c\u2500\u2500 left: TreeNode(1)<br>\n\u2514\u2500\u2500 right: TreeNode(2)<br><br>\n<b>Step 1:<\/b><br>\n\u2192 Call serialize(root)<br><br>\n\n<b>Serializing root:<\/b><br>\n\u2192 curr = 3 \u2192 hash = &#8220;-3&#8221;<br>\n\u2192 curr.left = 4 \u2192 hash = &#8220;-3-4&#8221;<br>\n\u2192 curr.left.left = 1 \u2192 hash = &#8220;-3-4-1&#8221;<br>\n\u2192 curr.left.left.left = null \u2192 hash = &#8220;-3-4-1-#&#8221;<br>\n\u2192 curr.left.left.right = null \u2192 hash = &#8220;-3-4-1-#-#&#8221;<br>\n\u2192 curr.left.right = 2 \u2192 hash = &#8220;-3-4-1-#-#-2&#8221;<br>\n\u2192 curr.left.right.left = null \u2192 hash = &#8220;-3-4-1-#-#-2-#&#8221;<br>\n\u2192 curr.left.right.right = null \u2192 hash = &#8220;-3-4-1-#-#-2-#-#&#8221;<br>\n\u2192 curr.right = 5 \u2192 hash = &#8220;-3-4-1-#-#-2-#-#-5&#8221;<br>\n\u2192 curr.right.left = null \u2192 hash = &#8220;-3-4-1-#-#-2-#-#-5-#&#8221;<br>\n\u2192 curr.right.right = null \u2192 hash = &#8220;-3-4-1-#-#-2-#-#-5-#-#&#8221;<br><br>\n\n<b>Serialized root:<\/b><br>\n\u2192 hashRoot = &#8220;-3-4-1-#-#-2-#-#-5-#-#&#8221;<br><br>\n\n<b>Step 2:<\/b><br>\n\u2192 Call serialize(subRoot)<br><br>\n\n<b>Serializing subRoot:<\/b><br>\n\u2192 curr = 4 \u2192 hash = &#8220;-4&#8221;<br>\n\u2192 curr.left = 1 \u2192 hash = &#8220;-4-1&#8221;<br>\n\u2192 curr.left.left = null \u2192 hash = &#8220;-4-1-#&#8221;<br>\n\u2192 curr.left.right = null \u2192 hash = &#8220;-4-1-#-#&#8221;<br>\n\u2192 curr.right = 2 \u2192 hash = &#8220;-4-1-#-#-2&#8221;<br>\n\u2192 curr.right.left = null \u2192 hash = &#8220;-4-1-#-#-2-#&#8221;<br>\n\u2192 curr.right.right = null \u2192 hash = &#8220;-4-1-#-#-2-#-#&#8221;<br><br>\n\n<b>Serialized subRoot:<\/b><br>\n\u2192 hashSubRoot = &#8220;-4-1-#-#-2-#-#&#8221;<br><br>\n\n<b>Step 3:<\/b><br>\n\u2192 Check if hashRoot includes hashSubRoot:<br>\n\u2192 &#8220;-3-4-1-#-#-2-#-#-5-#-#&#8221; includes &#8220;-4-1-#-#-2-#-#&#8221; \u2192 true<br><br>\n\n<b>Final Result:<\/b> true\n\n<\/div>\n\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    let lca = null;\n    let traversal = (curr) => {\n        let count = 0;\n        if(!curr) return 0;\n        let ansOnLeft = traversal(curr.left);\n        let ansOnRight = traversal(curr.right);\n        if(curr.val === p.val || curr.val === q.val) {\n            ++count;\n        } \n        count = count + ansOnLeft + ansOnRight;\n        if(count === 2 && !lca) {\n            lca = curr;\n        }\n        return count;\n    }\n    traversal(root);\n    return lca;\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\">\nclass TreeNode:\n    def __init__(self, val=0, left=None, right=None):\n        self.val = val\n        self.left = left\n        self.right = right\n\nclass Solution:\n    def lowestCommonAncestor(self, root, p, q):\n        # Base case\n        if not root or root == p or root == q:\n            return root\n\n        # Search in left and right subtree\n        left = self.lowestCommonAncestor(root.left, p, q)\n        right = self.lowestCommonAncestor(root.right, p, q)\n\n        # If both sides return non-null \u2192 current node is LCA\n        if left and right:\n            return root\n\n        # Otherwise return the non-null side\n        return left if left else right\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\">\nclass TreeNode {\n    int val;\n    TreeNode left;\n    TreeNode right;\n\n    TreeNode(int x) {\n        val = x;\n    }\n}\n\nclass Solution {\n    public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {\n        \/\/ Base case\n        if (root == null || root == p || root == q) {\n            return root;\n        }\n\n        \/\/ Search in left and right subtree\n        TreeNode left = lowestCommonAncestor(root.left, p, q);\n        TreeNode right = lowestCommonAncestor(root.right, p, q);\n\n        \/\/ If both sides are non-null \u2192 LCA found\n        if (left != null && right != null) {\n            return root;\n        }\n\n        \/\/ Return non-null side\n        return (left != null) ? left : right;\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\">\nclass TreeNode {\npublic:\n    int val;\n    TreeNode* left;\n    TreeNode* right;\n\n    TreeNode(int x) {\n        val = x;\n        left = right = NULL;\n    }\n};\n\nclass Solution {\npublic:\n    TreeNode* lowestCommonAncestor(TreeNode* root, TreeNode* p, TreeNode* q) {\n        \/\/ Base case\n        if (root == NULL || root == p || root == q)\n            return root;\n\n        TreeNode* left = lowestCommonAncestor(root->left, p, q);\n        TreeNode* right = lowestCommonAncestor(root->right, p, q);\n\n        \/\/ If both sides return non-null \u2192 LCA\n        if (left != NULL && right != NULL)\n            return root;\n\n        \/\/ Otherwise return non-null side\n        return (left != NULL) ? left : right;\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    \/\/ Base case\n    if (root == NULL || root == p || root == q)\n        return root;\n\n    struct TreeNode* left = lowestCommonAncestor(root->left, p, q);\n    struct TreeNode* right = lowestCommonAncestor(root->right, p, q);\n\n    \/\/ If both sides are non-null \u2192 LCA\n    if (left != NULL && right != NULL)\n        return root;\n\n    \/\/ Return non-null side\n    return (left != NULL) ? left : right;\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 class TreeNode {\n    public int val;\n    public TreeNode left;\n    public TreeNode right;\n\n    public TreeNode(int x) {\n        val = x;\n    }\n}\n\npublic class Solution {\n    public TreeNode LowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {\n        \/\/ Base case\n        if (root == null || root == p || root == q)\n            return root;\n\n        TreeNode left = LowestCommonAncestor(root.left, p, q);\n        TreeNode right = LowestCommonAncestor(root.right, p, q);\n\n        \/\/ If both sides return non-null \u2192 LCA\n        if (left != null && right != null)\n            return root;\n\n        \/\/ Otherwise return non-null side\n        return (left != null) ? left : right;\n    }\n}\n            <\/code><\/pre>\n        <\/div>\n    <\/div>\n<\/div>\n\n<script>\n    document.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) =>\n                    content.classList.remove(\"active\")\n                );\n\n                button.classList.add(\"active\");\n                document\n                    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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 descendants (where we<\/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":[210,322,176,175,211,174,172,173],"tags":[],"class_list":{"0":"post-8914","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-algorithms","7":"category-algorithms-and-data-structures","8":"category-csharp","9":"category-cplusplus","10":"category-data-structures","11":"category-java","12":"category-javascript","13":"category-python"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/8914","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=8914"}],"version-history":[{"count":5,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/8914\/revisions"}],"predecessor-version":[{"id":11861,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/8914\/revisions\/11861"}],"wp:attachment":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/media?parent=8914"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/categories?post=8914"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/tags?post=8914"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}