{"id":8957,"date":"2025-08-05T10:52:53","date_gmt":"2025-08-05T05:22:53","guid":{"rendered":"https:\/\/namastedev.com\/blog\/?p=8957"},"modified":"2025-08-05T10:55:22","modified_gmt":"2025-08-05T05:25:22","slug":"valid-bst","status":"publish","type":"post","link":"https:\/\/namastedev.com\/blog\/valid-bst\/","title":{"rendered":"Valid Binary Search Tree"},"content":{"rendered":"\n<!-- Valid Binary 1 -->\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: #d4f1ff;\n}\n\n.wp_blog_container {\n  font-family: 'Segoe UI', sans-serif;\n  background: var(--light-bg);\n  margin: 0;\n  padding: 0;\n  color: var(--text-dark);\n}\n\n\/* Heading *\/\n.wp_blog_main-heading {\n  text-align: center;\n  font-size: 2.4rem;\n  color: var(--primary);\n  margin-top: 2.5rem;\n  font-weight: bold;\n}\n\n\/* Explanation Card *\/\n.wp_blog_explanation,\n.wp_blog_code-tabs-container {\n  max-width: 940px;\n  margin: 2rem auto;\n  padding: 2rem;\n  background: white;\n  border-radius: var(--tab-radius);\n  box-shadow: var(--shadow);\n}\n\n\/* Text and Visuals *\/\n.wp_blog_explanation h2{\n  font-size: 1.4rem;\n  color: var(--primary);\n  margin-bottom: 0.5rem;\n}\n.wp_blog_explanation h5{\n  color: var(--primary);\n}\n\n.wp_blog_explanation p,\n.wp_blog_explanation li {\n  font-size: 1.05rem;\n  line-height: 1.7;\n  margin: 0.5rem 0;\n}\n.wp_blog_explanation code {\n  background: #f9cea6;\n  color: #2d2d2d;\n  padding: 3px 6px;\n  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>Given the root of a binary tree, <i>determine if it is a valid binary search tree (BST)<\/i>.<\/p>\n        <p>A <strong>valid BST<\/strong> is defined as follows: <\/p>\n        <ul>\n            <li>The left subtree of a node contains only nodes with keys strictly less than the node&#8217;s key.<\/li>\n            <li>The right subtree of a node contains only nodes with keys strictly greater than the node&#8217;s key.<\/li>\n            <li>Both the left and right subtrees must also be binary search trees.<\/li>\n        <\/ul>\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-2025-08-05-at-10.49.08\u202fAM.png\" alt=\"\">\n                <p><strong>Input:<\/strong> root = [2,1,3]<\/p>\n                <p><strong>Output:<\/strong> true<\/p>\n            \n                <h3>Example 2:<\/h3>\n                <img decoding=\"async\" src=\"https:\/\/namastedev.com\/blog\/wp-content\/uploads\/2025\/08\/Screenshot-2025-08-05-at-10.50.16\u202fAM.png\" alt=\"\">\n                <p><strong>Input:<\/strong> root = [5,1,4,null,null,3,6]<\/p>\n                <p><strong>Output:<\/strong> false<\/p>\n                <p><strong>Explanation:<\/strong> The root node&#8217;s value is 5 but its right child&#8217;s value is 4.<\/p>\n\n                    <h2>Constraints:<\/h2>\n                    <ul>\n                        <li>The number of nodes in the tree is in the range <code>[1, 10<sup>4<\/sup>]<\/code>.<\/li>\n                        <li><code>-2<sup>31<\/sup> <= Node.val <= 2<sup>31<\/sup> - 1<\/code><\/li>\n                    <\/ul>\n\n                <h2>Approach<\/h2>\n                <ul>\n                    <li><strong>Base Case:<\/strong> If the current node is <code>null<\/code>, return <code>true<\/code>.<\/li>\n                    <li><strong>Violation Check:<\/strong>\n                        <ul>\n                            <li>If <code>curr.val<\/code> \u2264 <code>lo<\/code> or \u2265 <code>hi<\/code>, it violates BST rules, so return <code>false<\/code>.<\/li>\n                        <\/ul>\n                    <\/li>\n\n                    <li><strong>Recursive Check:<\/strong>\n                        <ul>\n                            <li>Left subtree must be in range <code>(lo, curr.val)<\/code><\/li>\n                            <li>Right subtree must be in range <code>(curr.val, hi)<\/code><\/li>\n                        <\/ul>\n                    <\/li>\n\n                    <li>Return <code>true<\/code> only if both left and right subtrees are valid.<\/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>\n<div style=\"background: #f9f9f9; padding: 10px; border: 1px solid #ccc; font-family: monospace;\">\n<b>Function Call:<\/b> isValidBST(root) where<br>\nroot = Node(5)<br>\n\u251c\u2500\u2500 left: Node(3)<br>\n\u2502\u00a0\u00a0 \u251c\u2500\u2500 left: Node(2)<br>\n\u2502\u00a0\u00a0 \u2514\u2500\u2500 right: Node(4)<br>\n\u2514\u2500\u2500 right: Node(7)<br>\n&nbsp;&nbsp;&nbsp;&nbsp;\u251c\u2500\u2500 left: Node(6)<br>\n&nbsp;&nbsp;&nbsp;&nbsp;\u2514\u2500\u2500 right: Node(8)<br><br>\n\n<b>Step 1:<\/b><br>\n\u2192 Call isValidBST(curr = 5, lo = null, hi = null)<br>\n\u2192 5 is valid (no bounds)<br>\n\u2192 Call isValidBST(curr = 3, lo = null, hi = 5)<br>\n\u2192 3 is valid (less than 5)<br>\n\u2192 Call isValidBST(curr = 2, lo = null, hi = 3)<br>\n\u2192 2 is valid (less than 3)<br>\n\u2192 Call isValidBST(curr = null, lo = null, hi = 2) \u2192 returns true<br>\n\u2192 Call isValidBST(curr = null, lo = 2, hi = 3) \u2192 returns true<br>\n\u2192 return true for Node(2)<br><br>\n\n\u2192 Call isValidBST(curr = 4, lo = 3, hi = 5)<br>\n\u2192 4 is valid (between 3 and 5)<br>\n\u2192 Call isValidBST(curr = null, lo = 3, hi = 4) \u2192 returns true<br>\n\u2192 Call isValidBST(curr = null, lo = 4, hi = 5) \u2192 returns true<br>\n\u2192 return true for Node(4)<br><br>\n\n\u2192 return true for Node(3)<br><br>\n\n\u2192 Call isValidBST(curr = 7, lo = 5, hi = null)<br>\n\u2192 7 is valid (greater than 5)<br>\n\u2192 Call isValidBST(curr = 6, lo = 5, hi = 7)<br>\n\u2192 6 is valid (between 5 and 7)<br>\n\u2192 Call isValidBST(curr = null, lo = 5, hi = 6) \u2192 returns true<br>\n\u2192 Call isValidBST(curr = null, lo = 6, hi = 7) \u2192 returns true<br>\n\u2192 return true for Node(6)<br><br>\n\n\u2192 Call isValidBST(curr = 8, lo = 7, hi = null)<br>\n\u2192 8 is valid (greater than 7)<br>\n\u2192 Call isValidBST(curr = null, lo = 7, hi = 8) \u2192 returns true<br>\n\u2192 Call isValidBST(curr = null, lo = 8, hi = null) \u2192 returns true<br>\n\u2192 return true for Node(8)<br><br>\n\n\u2192 return true for Node(7)<br><br>\n\n\u2192 return true for root Node(5)<br><br>\n\n<b>Final Result:<\/b> true \u2013 the binary tree is a valid BST.\n<\/div>\n\n\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 isValidBST = function(curr, lo = null, hi = null) {\n    if (!curr) return true;\n    if ((lo !== null && curr.val <= lo) || (hi !== null &#038;&#038; curr.val >= hi))\n        return false;\n    let isLeftBST = isValidBST(curr.left, lo, curr.val);\n    let isRightBST = isValidBST(curr.right, curr.val, hi);\n    return isLeftBST && isRightBST;\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 isValidBST(curr, lo=float('-inf'), hi=float('inf')):\n    if not curr:\n        return True\n    if curr.val <= lo or curr.val >= hi:\n        return False\n    return isValidBST(curr.left, lo, curr.val) and isValidBST(curr.right, curr.val, hi)\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}\nclass Solution {\n    public boolean isValidBST(TreeNode curr) {\n        return isValid(curr, Long.MIN_VALUE, Long.MAX_VALUE);\n    }\n    private boolean isValid(TreeNode curr, long lo, long hi) {\n        if (curr == null) return true;\n        if (curr.val <= lo || curr.val >= hi) return false;\n        return isValid(curr.left, lo, curr.val) && isValid(curr.right, curr.val, hi);\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\">\nbool isValidBST(TreeNode* curr, long long lo = LLONG_MIN, long long hi = LLONG_MAX) {\n    if (!curr) return true;\n    if (curr->val <= lo || curr->val >= hi) return false;\n    return isValidBST(curr->left, lo, curr->val) && isValidBST(curr->right, curr->val, hi);\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};\nbool isValidBST(struct TreeNode* curr, long long lo, long long hi) {\n    if (!curr) return true;\n    if (curr->val <= lo || curr->val >= hi) return false;\n    return isValidBST(curr->left, lo, curr->val) && isValidBST(curr->right, curr->val, hi);\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}\npublic class Solution {\n    public bool IsValidBST(TreeNode curr, long lo = long.MinValue, long hi = long.MaxValue) {\n        if (curr == null) return true;\n        if (curr.val <= lo || curr.val >= hi) return false;\n        return IsValidBST(curr.left, lo, curr.val) && IsValidBST(curr.right, curr.val, hi);\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                    .querySelector(`.wp_blog_code-tab-content[data-lang=\"${lang}\"]`)\n                    .classList.add(\"active\");\n            });\n        });\n    });\n<\/script>\n","protected":false},"excerpt":{"rendered":"<p>Problem Statement: Given the root of a binary tree, determine if it is a valid binary search tree (BST). A valid BST is defined as follows: The left subtree of a node contains only nodes with keys strictly less than the node&#8217;s key. The right subtree of a node contains only nodes with keys strictly<\/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-8957","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\/8957","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=8957"}],"version-history":[{"count":2,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/8957\/revisions"}],"predecessor-version":[{"id":8959,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/8957\/revisions\/8959"}],"wp:attachment":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/media?parent=8957"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/categories?post=8957"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/tags?post=8957"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}