{"id":8821,"date":"2025-08-01T12:22:45","date_gmt":"2025-08-01T06:52:45","guid":{"rendered":"https:\/\/namastedev.com\/blog\/?p=8821"},"modified":"2025-08-01T12:24:38","modified_gmt":"2025-08-01T06:54:38","slug":"balanced-binary-tree","status":"publish","type":"post","link":"https:\/\/namastedev.com\/blog\/balanced-binary-tree\/","title":{"rendered":"Balanced Binary Tree"},"content":{"rendered":"\n<!-- Balanced Binary Tree -->\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  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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 a binary tree, determine if it is height-balanced.<\/p>\n        \n        <h2>Examples:<\/h2>\n                <h3>Example 1:<\/h3>\n                <img decoding=\"async\" src=\"https:\/\/namastedev.com\/blog\/wp-content\/uploads\/2025\/07\/Screenshot-2025-07-31-at-11.07.53\u202fPM.png\" alt=\"\">\n                <p><strong>Input:<\/strong> root = [3,9,20,null,null,15,7]<\/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\/07\/Screenshot-2025-07-31-at-11.11.30\u202fPM.png\" alt=\"\">\n                <p><strong>Input:<\/strong> root = [1,2,2,3,3,null,null,4,4]<\/p>\n                <p><strong>Output:<\/strong> false<\/p>\n\n                <h3>Example 3:<\/h3>\n                <p><strong>Input: <\/strong> root = []<\/p>\n                <p><strong>Output: <\/strong>true<\/p>\n\n                    <h2>Constraints:<\/h2>\n                    <ul>\n                      <li>The number of nodes in the tree is in the range <code>[0, 100]<\/code>.<\/li>\n                      <li><code>-10<sup>4<\/sup> <= Node.val <= 10<sup>4<\/sup><\/code><\/li>\n                    <\/ul>\n\n                <h2>Approach<\/h2>\n              <ul>\n                <li>Use <code>post-order traversal<\/code> to compute the height of left and right subtrees.<\/li>\n                <li>At each node, check if the height difference is more than 1.<\/li>\n                <li>If yes, set a global flag <code>(ans = false)<\/code>.<\/li>\n                <li>Return height = <code>1 + max(leftHeight, rightHeight)<\/code> at each step.<\/li>\n                <li>Finally, return the <code>ans<\/code> flag<\/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> recursion stack space (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> isBalanced(root) where<br> root = TreeNode(1)<br> \u251c\u2500\u2500 left: TreeNode(2)<br> \u2502\u00a0\u00a0 \u2514\u2500\u2500 left: TreeNode(4)<br> \u2514\u2500\u2500 right: TreeNode(3)<br><br>\n<b>Step 1:<\/b><br>\n\u2192 Call calculateHeight(1)<br><br>\n<b>Step 2:<\/b><br>\n\u2192 Call calculateHeight(2)<br><br>\n<b>Step 3:<\/b><br>\n\u2192 Call calculateHeight(4)<br><br>\n<b>Step 4:<\/b><br>\n\u2192 Call calculateHeight(null) \u2192 return 0<br>\n\u2192 Call calculateHeight(null) \u2192 return 0<br>\n\u2192 Node 4 \u2192 leftHeight = 0, rightHeight = 0<br>\n\u2192 |0 &#8211; 0| = 0 \u2192 OK<br>\n\u2192 Return height = 1<br><br>\n<b>Step 5:<\/b><br>\n\u2192 Back to Node 2<br>\n\u2192 leftHeight = 1<br>\n\u2192 Call calculateHeight(null) \u2192 return 0<br>\n\u2192 rightHeight = 0<br>\n\u2192 |1 &#8211; 0| = 1 \u2192 OK<br>\n\u2192 Return height = 2<br><br>\n<b>Step 6:<\/b><br>\n\u2192 Back to Node 1<br>\n\u2192 leftHeight = 2<br>\n\u2192 Call calculateHeight(3)<br><br>\n<b>Step 7:<\/b><br>\n\u2192 Call calculateHeight(null) \u2192 return 0<br>\n\u2192 Call calculateHeight(null) \u2192 return 0<br>\n\u2192 Node 3 \u2192 leftHeight = 0, rightHeight = 0<br>\n\u2192 |0 &#8211; 0| = 0 \u2192 OK<br>\n\u2192 Return height = 1<br><br>\n<b>Step 8:<\/b><br>\n\u2192 Back to Node 1<br>\n\u2192 rightHeight = 1<br>\n\u2192 |2 &#8211; 1| = 1 \u2192 OK<br>\n\u2192 Return height = 3<br><br>\n<b>Final Check:<\/b><br>\n\u2192 Variable <code>ans<\/code> is still true \u2192 Tree is balanced<br><br>\n<b>Final Result:<\/b> true\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 isBalanced = function(root) {\n    let ans = true;\n    let calculateHeight = (curr) => {\n        if(!curr) return 0;\n        let leftHeight = calculateHeight(curr.left);\n        let rightHeight = calculateHeight(curr.right);\n        if(Math.abs(leftHeight - rightHeight) > 1){\n            ans = ans && false;\n        }\n        return 1 + Math.max(leftHeight, rightHeight);\n    }\n    calculateHeight(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 isBalanced(self, root):\n        self.ans = True\n\n        def calculateHeight(node):\n            if not node:\n                return 0\n            left = calculateHeight(node.left)\n            right = calculateHeight(node.right)\n            if abs(left - right) > 1:\n                self.ans = False\n            return 1 + max(left, right)\n        calculateHeight(root)\n        return self.ans\n\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 boolean ans = true;\n    private int calculateHeight(TreeNode root) {\n        if (root == null) return 0;\n        int left = calculateHeight(root.left);\n        int right = calculateHeight(root.right);\n        if (Math.abs(left - right) > 1) {\n            ans = false;\n        }\n        return 1 + Math.max(left, right);\n    }\n    public boolean isBalanced(TreeNode root) {\n        calculateHeight(root);\n        return ans;\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    bool ans = true;\n    int calculateHeight(TreeNode* root) {\n        if (!root) return 0;\n        int leftHeight = calculateHeight(root->left);\n        int rightHeight = calculateHeight(root->right);\n        if (abs(leftHeight - rightHeight) > 1) {\n            ans = false;\n        }\n        return 1 + max(leftHeight, rightHeight);\n    }\n    bool isBalanced(TreeNode* root) {\n        calculateHeight(root);\n        return ans;\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\">\ntypedef struct TreeNode {\n    int val;\n    struct TreeNode* left;\n    struct TreeNode* right;\n} TreeNode;\nint max(int a, int b) {\n    return (a > b) ? a : b;\n}\nint calculateHeight(TreeNode* root, bool* ans) {\n    if (!root) return 0;\n    int left = calculateHeight(root->left, ans);\n    int right = calculateHeight(root->right, ans);\n    if (abs(left - right) > 1) {\n        *ans = false;\n    }\n    return 1 + max(left, right);\n}\nbool isBalanced(TreeNode* root) {\n    bool ans = true;\n    calculateHeight(root, &ans);\n    return ans;\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 bool ans = true;\n    private int CalculateHeight(TreeNode root) {\n        if (root == null) return 0;\n        int left = CalculateHeight(root.left);\n        int right = CalculateHeight(root.right);\n        if (Math.Abs(left - right) > 1) {\n            ans = false;\n        }\n        return 1 + Math.Max(left, right);\n    }\n    public bool IsBalanced(TreeNode root) {\n        CalculateHeight(root);\n        return ans;\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 a binary tree, determine if it is height-balanced. Examples: Example 1: Input: root = [3,9,20,null,null,15,7] Output: true Example 2: Input: root = [1,2,2,3,3,null,null,4,4] Output: false Example 3: Input: root = [] Output: true Constraints: The number of nodes in the tree is in the range [0, 100]. -104 1){ ans = ans<\/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":[322,176,175,211,174,172,173],"tags":[],"class_list":["post-8821","post","type-post","status-publish","format-standard","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\/8821","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=8821"}],"version-history":[{"count":1,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/8821\/revisions"}],"predecessor-version":[{"id":8822,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/8821\/revisions\/8822"}],"wp:attachment":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/media?parent=8821"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/categories?post=8821"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/tags?post=8821"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}