{"id":9001,"date":"2025-08-06T16:15:35","date_gmt":"2025-08-06T10:45:35","guid":{"rendered":"https:\/\/namastedev.com\/blog\/?p=9001"},"modified":"2025-08-06T16:18:24","modified_gmt":"2025-08-06T10:48:24","slug":"kth-smallestelement","status":"publish","type":"post","link":"https:\/\/namastedev.com\/blog\/kth-smallestelement\/","title":{"rendered":"Kth Smallest Element"},"content":{"rendered":"\n<!-- kth 5 -->\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: #001f3f;\n  --code-text: 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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 the <code>root<\/code> of a binary search tree, and an integer <code>k<\/code>, return the <code><sup>th<\/sup><\/code> <i>smallest value (1-indexed) of all the values of the nodes in the tree<\/i>.\n\n<\/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-2025-08-06-at-3.23.19\u202fPM.png\" alt=\"\">\n                <p><strong>Input:<\/strong> root = [3,1,4,null,2], k = 1<\/p>\n                <p><strong>Output:<\/strong> 1<\/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-3.22.48\u202fPM.png\" alt=\"\">\n                <p><strong>Input:<\/strong> root = [5,3,6,2,4,null,null,1], k = 3<\/p>\n                <p><strong>Output:<\/strong> 3<\/p>\n\n                <h3>Example 3:<\/h3>\n                <p><strong>Input:<\/strong> root = [4,2,7,1,3,null,null,null,null,null,null], val = 5<\/p>\n                <p><strong>Output:<\/strong> [4,2,7,1,3,5]<\/p>\n\n                    <h2>Constraints:<\/h2>\n                    <ul>\n                        <li>The number of nodes in the tree is <code>n<\/code>.<\/li>\n                        <li><code>1 <= k <= n <= 10<sup>4<\/sup><\/code><\/li>\n                        <li><code>0 <= Node.val <= 10<sup>4<\/sup><\/code><\/li>\n                    <\/ul>\n                <h2>Approach<\/h2>\n                <ul>\n                    <li><strong>In-order Traversal of BST<\/strong> gives sorted order of elements.<\/li>\n                    <li>Use a <strong>counter<\/strong> <code>count = k<\/code> to track how many elements we&#8217;ve visited.<\/li>\n                    <li><strong>Traverse left subtree<\/strong>, decrement <code>count<\/code>.<\/li>\n                    <li>When <code>count === 0<\/code>, current node is the <strong>kth smallest \u2192 store<\/strong> it in <code>ans<\/code>.<\/li>\n                    <li>Stop traversal once we find the answer.<\/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> kthSmallest(root, 3) where<br> root = Node(5)<br> \u251c\u2500\u2500 left: Node(3)<br> \u2502\u00a0\u00a0 \u251c\u2500\u2500 left: Node(2)<br> \u2502\u00a0\u00a0 \u2502\u00a0\u00a0 \u2514\u2500\u2500 left: Node(1)<br> \u2502\u00a0\u00a0 \u2514\u2500\u2500 right: Node(4)<br> \u2514\u2500\u2500 right: Node(7)<br> \u00a0\u00a0\u00a0\u00a0\u251c\u2500\u2500 left: Node(6)<br> \u00a0\u00a0\u00a0\u00a0\u2514\u2500\u2500 right: Node(8)<br><br>\n<b>Initial State:<\/b><br>\n\u2192 ans = null<br>\n\u2192 count = 3<br><br>\n<b>Step 1:<\/b><br>\n\u2192 traversal(curr = 5)<br>\n\u2192 curr.left exists \u2192 traversal(curr = 3)<br><br>\n\n<b>Step 2:<\/b><br>\n\u2192 traversal(curr = 3)<br>\n\u2192 curr.left exists \u2192 traversal(curr = 2)<br><br>\n\n<b>Step 3:<\/b><br>\n\u2192 traversal(curr = 2)<br>\n\u2192 curr.left exists \u2192 traversal(curr = 1)<br><br>\n\n<b>Step 4:<\/b><br>\n\u2192 traversal(curr = 1)<br>\n\u2192 curr.left is null \u2192 skip<br>\n\u2192 &#8211;count \u2192 count = 2<br>\n\u2192 count \u2260 0 \u2192 skip setting ans<br>\n\u2192 curr.right is null \u2192 skip<br>\n\u2192 return<br><br>\n\n<b>Step 5:<\/b><br>\n\u2192 Back to traversal(curr = 2)<br>\n\u2192 &#8211;count \u2192 count = 1<br>\n\u2192 count \u2260 0 \u2192 skip setting ans<br>\n\u2192 curr.right is null \u2192 skip<br>\n\u2192 return<br><br>\n\n<b>Step 6:<\/b><br>\n\u2192 Back to traversal(curr = 3)<br>\n\u2192 &#8211;count \u2192 count = 0<br>\n\u2192 count == 0 \u2192 ans = 3<br>\n\u2192 curr.right = Node(4), but ans is already found \u2192 return<br><br>\n\n<b>Final Result:<\/b>\nans = 3 \u2192 the 3rd smallest element in the BST\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 kthSmallest = function(root, k) {\n    let ans = null;\n    let count = k;\n    let traversal = (curr) => {\n        if(ans != null) return;\n        curr.left && traversal(curr.left);\n        --count;\n        if(count == 0){\n            ans = curr.val;\n        }\n        curr.right && traversal(curr.right);\n    }\n    traversal(root);\n    return ans;\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\">\nclass Solution:\n    def kthSmallest(self, root, k):\n        self.count = k\n        self.ans = None\n\n        def inorder(node):\n            if not node or self.ans is not None:\n                return\n            inorder(node.left)\n            self.count -= 1\n            if self.count == 0:\n                self.ans = node.val\n                return\n            inorder(node.right)\n        inorder(root)\n        return self.ans\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 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    private void inorder(TreeNode node) {\n        if (node == null || count == 0) return;\n        inorder(node.left);\n        count--;\n        if (count == 0) {\n            result = node.val;\n            return;\n        }\n        inorder(node.right);\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\">\nclass Solution {\npublic:\n    int count;\n    int ans;\n    void inorder(TreeNode* root) {\n        if (!root || count == 0) return;\n        inorder(root->left);\n        count--;\n        if (count == 0) {\n            ans = root->val;\n            return;\n        }\n        inorder(root->right);\n    }\n    int kthSmallest(TreeNode* root, int k) {\n        count = k;\n        inorder(root);\n        return ans;\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};\nvoid inorder(struct TreeNode* root, int* count, int* result) {\n    if (!root || *result != -1) return;\n    inorder(root->left, count, result);\n    (*count)--;\n    if (*count == 0) {\n        *result = root->val;\n        return;\n    }\n    inorder(root->right, count, result);\n}\nint 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        <!-- C# -->\n        <div class=\"wp_blog_code-tab-content\" data-lang=\"cs\">\n            <pre><code class=\"language-csharp\">\npublic 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    private void InOrder(TreeNode node) {\n        if (node == null || count == 0) return;\n        InOrder(node.left);\n        count--;\n        if (count == 0) {\n            result = node.val;\n            return;\n        }\n        InOrder(node.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                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Examples: Example 1: Input: root = [3,1,4,null,2], k = 1 Output: 1 Example 2: Input: root = [5,3,6,2,4,null,null,1], k = 3 Output: 3 Example 3:<\/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":["post-9001","post","type-post","status-publish","format-standard","category-algorithms","category-algorithms-and-data-structures","category-csharp","category-cplusplus","category-data-structures","category-java","category-javascript","category-python"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/9001","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=9001"}],"version-history":[{"count":3,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/9001\/revisions"}],"predecessor-version":[{"id":9009,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/9001\/revisions\/9009"}],"wp:attachment":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/media?parent=9001"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/categories?post=9001"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/tags?post=9001"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}