{"id":10243,"date":"2025-10-13T10:56:30","date_gmt":"2025-10-13T05:26:30","guid":{"rendered":"https:\/\/namastedev.com\/blog\/?p=10243"},"modified":"2025-10-13T10:56:31","modified_gmt":"2025-10-13T05:26:31","slug":"kth-smallest-element-in-a-bst","status":"publish","type":"post","link":"https:\/\/namastedev.com\/blog\/kth-smallest-element-in-a-bst\/","title":{"rendered":"Kth Smallest Element in a BST"},"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    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}\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 the root of a Binary Search Tree (BST) and an integer <code>k<\/code>, return the <code>k<\/code>th smallest value (1-indexed) among all the values of the nodes in the tree.<\/p>\n  \n    <h2>Examples<\/h2>\n    <p><strong>Input:<\/strong> <code>root = [3,1,4,null,2], k = 1<\/code><\/p>\n    <p><strong>Output:<\/strong> <code>1<\/code><\/p>\n  \n    <p><strong>Input:<\/strong> <code>root = [5,3,6,2,4,null,null,1], k = 3<\/code><\/p>\n    <p><strong>Output:<\/strong> <code>3<\/code><\/p>\n  \n    <h2>Approach<\/h2>\n    <ul>\n      <li>Since it&#8217;s a BST, an in-order traversal gives values in ascending order.<\/li>\n      <li>Perform in-order traversal and decrement <code>k<\/code> until it reaches 0.<\/li>\n      <li>Return the node&#8217;s value where <code>k == 0<\/code>.<\/li>\n    <\/ul>\n  \n    <h2>Time &#038; Space Complexity<\/h2>\n    <ul>\n      <li><strong>Time Complexity:<\/strong> O(n) in the worst case (if k is near n)<\/li>\n      <li><strong>Space Complexity:<\/strong> O(n) due to recursion stack<\/li>\n    <\/ul>\n  <\/div>\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 kthSmallest = function(root, k) {\n      let ans = null;\n      let count = k;\n  \n      let traversal = (curr) => {\n          if (ans !== null) return;\n  \n          if (curr.left) traversal(curr.left);\n  \n          count--;\n          if (count === 0) {\n              ans = curr.val;\n              return;\n          }\n  \n          if (curr.right) traversal(curr.right);\n      }\n  \n      traversal(root);\n      return ans;\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  class Solution {\n  public:\n      int kthSmallest(TreeNode* root, int k) {\n          int count = k;\n          int ans = -1;\n          inorder(root, count, ans);\n          return ans;\n      }\n  \n  private:\n      void inorder(TreeNode* node, int &count, int &ans) {\n          if (!node || count == 0) return;\n  \n          inorder(node->left, count, ans);\n  \n          count--;\n          if (count == 0) {\n              ans = node->val;\n              return;\n          }\n  \n          inorder(node->right, count, ans);\n      }\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  void inorder(struct TreeNode* root, int* k, int* result) {\n      if (!root || *k == 0) return;\n  \n      inorder(root->left, k, result);\n  \n      (*k)--;\n      if (*k == 0) {\n          *result = root->val;\n          return;\n      }\n  \n      inorder(root->right, k, result);\n  }\n  \n  int kthSmallest(struct TreeNode* root, int k) {\n      int result = -1;\n      inorder(root, &k, &result);\n      return result;\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  class Solution {\n      private int count;\n      private int result;\n  \n      public int kthSmallest(TreeNode root, int k) {\n          count = k;\n          inorder(root);\n          return result;\n      }\n  \n      private void inorder(TreeNode node) {\n          if (node == null || count == 0) return;\n  \n          inorder(node.left);\n  \n          count--;\n          if (count == 0) {\n              result = node.val;\n              return;\n          }\n  \n          inorder(node.right);\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  class Solution:\n      def kthSmallest(self, root, k):\n          self.k = k\n          self.result = None\n  \n          def inorder(node):\n              if not node or self.result is not None:\n                  return\n  \n              inorder(node.left)\n              self.k -= 1\n              if self.k == 0:\n                  self.result = node.val\n                  return\n              inorder(node.right)\n  \n          inorder(root)\n          return self.result\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      private int count;\n      private int result;\n  \n      public int KthSmallest(TreeNode root, int k) {\n          count = k;\n          InOrder(root);\n          return result;\n      }\n  \n      private void InOrder(TreeNode node) {\n          if (node == null || count == 0) return;\n  \n          InOrder(node.left);\n  \n          count--;\n          if (count == 0) {\n              result = node.val;\n              return;\n          }\n  \n          InOrder(node.right);\n      }\n  }\n      <\/code><\/pre>\n    <\/div>\n  <\/div>\n  \n\n\n\n\n  <a href=\"hhttps:\/\/leetcode.com\/problems\/kth-smallest-element-in-a-bst\/description\/\" target=\"blank\">Solve this problem.<\/a>\n  <script>\n  document.addEventListener(\"DOMContentLoaded\", function () {\n    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Examples Input: root = [3,1,4,null,2], k = 1 Output: 1 Input: root = [5,3,6,2,4,null,null,1], k = 3 Output: 3 Approach Since it&#8217;s a BST, an in-order<\/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":["post-10243","post","type-post","status-publish","format-standard","category-data-structures-and-algorithms"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/10243","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=10243"}],"version-history":[{"count":1,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/10243\/revisions"}],"predecessor-version":[{"id":10244,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/10243\/revisions\/10244"}],"wp:attachment":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/media?parent=10243"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/categories?post=10243"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/tags?post=10243"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}