{"id":10245,"date":"2025-10-13T10:57:38","date_gmt":"2025-10-13T05:27:38","guid":{"rendered":"https:\/\/namastedev.com\/blog\/?p=10245"},"modified":"2025-10-13T10:57:39","modified_gmt":"2025-10-13T05:27:39","slug":"lowest-common-ancestor-of-a-binary-search-tree","status":"publish","type":"post","link":"https:\/\/namastedev.com\/blog\/lowest-common-ancestor-of-a-binary-search-tree\/","title":{"rendered":"Lowest Common Ancestor of a Binary Search Tree"},"content":{"rendered":"\n<!-- Prism.js CSS and JS -->\n<link href=\"https:\/\/cdn.jsdelivr.net\/npm\/prismjs@1.29.0\/themes\/prism-tomorrow.css\" rel=\"stylesheet\" \/>\n<script src=\"https:\/\/cdn.jsdelivr.net\/npm\/prismjs@1.29.0\/prism.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_code-tabs-container {\n    font-family: \"Segoe UI\", sans-serif !important;\n    max-width: 900px !important;\n    margin: 2rem auto !important;\n    border: 1px solid #ddd !important;\n    border-radius: 8px !important;\n    overflow: hidden !important;\n    background-color: white !important;\n  }\n\n  .wp_blog_code-tabs-header {\n    background: #f7f7f7 !important;\n    display: flex !important;\n    border-bottom: 1px solid #ddd !important;\n  }\n\n  .wp_blog_code-tab-button {\n    flex: 1 !important;\n    padding: 10px 15px !important;\n    border: none !important;\n    background: transparent !important;\n    cursor: pointer !important;\n    font-weight: bold !important;\n    transition: background 0.2s !important;\n    color: #242b33 !important;\n  }\n\n  .wp_blog_code-tab-button.active {\n    background: white !important;\n    border-bottom: 3px solid #0073aa !important;\n  }\n\n  .wp_blog_code-tab-content {\n    display: none !important;\n    padding: 20px !important;\n    background: #242b33 !important;\n  }\n\n  .wp_blog_code-tab-content > pre {\n    background: #242b33 !important;\n  }\n\n  .wp_blog_code-tab-content.active {\n    display: block !important;\n  }\n\n  .wp_blog_code-tab-content pre {\n    margin: 0 !important;\n    overflow-x: auto !important;\n  }\n\n  .wp_blog_explanation {\n    max-width: 900px !important;\n    margin: 2rem auto !important;\n    font-family: \"Segoe UI\", sans-serif !important;\n    line-height: 1.6 !important;\n    background: white !important;\n    color: black !important;\n    padding: 1rem !important;\n    border-radius: 8px !important;\n  }\n\n  .wp_blog_explanation h2 {\n    color: #0073aa !important;\n    font-size: 1.5rem !important;\n    margin-bottom: 0.5rem !important;\n  }\n\n  .wp_blog_explanation code {\n    background: #f1f1f1 !important;\n    padding: 2px 6px !important;\n    border-radius: 4px !important;\n    font-family: monospace !important;\n  }\n\n  .wp_blog_explanation h1,\n  .wp_blog_explanation h2,\n  .wp_blog_explanation h3,\n  .wp_blog_explanation h4,\n  .wp_blog_explanation h5,\n  .wp_blog_explanation h6,\n  .wp_blog_explanation p {\n    margin-top: 10px !important;\n    margin-bottom: 10px !important;\n  }\n<\/style>\n\n<div class=\"wp_blog_explanation\">\n    <p>Given a binary search tree (BST), find the lowest common ancestor (LCA) of two given nodes <code>p<\/code> and <code>q<\/code>.<\/p>\n  \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 the tree that has both <code>p<\/code> and <code>q<\/code> as descendants (where we allow a node to be a descendant of itself).\u201d<\/p>\n  \n    <h2>Examples<\/h2>\n    <p><strong>Input:<\/strong> <code>root = [6,2,8,0,4,7,9,null,null,3,5], p = 2, q = 8<\/code><\/p>\n    <p><strong>Output:<\/strong> <code>6<\/code><\/p>\n  \n    <p><strong>Input:<\/strong> <code>root = [6,2,8,0,4,7,9,null,null,3,5], p = 2, q = 4<\/code><\/p>\n    <p><strong>Output:<\/strong> <code>2<\/code><\/p>\n  \n    <p><strong>Input:<\/strong> <code>root = [2,1], p = 2, q = 1<\/code><\/p>\n    <p><strong>Output:<\/strong> <code>2<\/code><\/p>\n  \n    <h2>Approach<\/h2>\n    <ul>\n      <li>Since it&#8217;s a BST, the left subtree contains smaller values and right subtree contains larger values.<\/li>\n      <li>If both <code>p<\/code> and <code>q<\/code> are less than the root, search left.<\/li>\n      <li>If both are greater than the root, search right.<\/li>\n      <li>Otherwise, root is the lowest common ancestor.<\/li>\n    <\/ul>\n  \n    <h2>Time &#038; Space Complexity<\/h2>\n    <ul>\n      <li><strong>Time Complexity:<\/strong> O(h), where h is the height of the tree<\/li>\n      <li><strong>Space Complexity:<\/strong> O(h) due to recursive stack<\/li>\n    <\/ul>\n  <\/div>\n\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=\"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=\"java\">Java<\/button>\n      <button class=\"wp_blog_code-tab-button\" data-lang=\"py\">Python<\/button>\n      <button class=\"wp_blog_code-tab-button\" data-lang=\"c#\">C#<\/button>\n    <\/div>\n  \n    <div class=\"wp_blog_code-tab-content active\" data-lang=\"js\">\n      <pre><code class=\"language-javascript\">\n  var 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    <div class=\"wp_blog_code-tab-content\" data-lang=\"cpp\">\n      <pre><code class=\"language-cpp\">\n  TreeNode* 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      <\/code><\/pre>\n    <\/div>\n  \n    <div class=\"wp_blog_code-tab-content\" data-lang=\"c\">\n      <pre><code class=\"language-c\">\n  struct TreeNode {\n      int val;\n      struct TreeNode* left;\n      struct TreeNode* right;\n  };\n  \n  struct 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      <\/code><\/pre>\n    <\/div>\n  \n    <div class=\"wp_blog_code-tab-content\" data-lang=\"java\">\n      <pre><code class=\"language-java\">\n  public class Solution {\n      public 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    <div class=\"wp_blog_code-tab-content\" data-lang=\"py\">\n      <pre><code class=\"language-python\">\n  def 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    <div class=\"wp_blog_code-tab-content\" data-lang=\"c#\">\n      <pre><code class=\"language-csharp\">\n  public class Solution {\n      public 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  \n\n\n\n  <a href=\"\" target=\"blank\">Solve this problem.<\/a>\n  <script>\n  document.addEventListener(\"DOMContentLoaded\", function () {\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        button.classList.add(\"active\");\n\n        contents.forEach((content) => {\n          content.classList.toggle(\"active\", content.getAttribute(\"data-lang\") === lang);\n        });\n      });\n    });\n  });\n<\/script>\n\n\n","protected":false},"excerpt":{"rendered":"<p>Given a binary search tree (BST), find the lowest common ancestor (LCA) of two given nodes p and q. 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 the tree that has both p and q as descendants (where<\/p>\n","protected":false},"author":1,"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":[811],"tags":[],"class_list":{"0":"post-10245","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-data-structures-and-algorithms"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/10245","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\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/comments?post=10245"}],"version-history":[{"count":1,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/10245\/revisions"}],"predecessor-version":[{"id":10246,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/10245\/revisions\/10246"}],"wp:attachment":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/media?parent=10245"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/categories?post=10245"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/tags?post=10245"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}