{"id":8825,"date":"2025-08-01T12:44:46","date_gmt":"2025-08-01T07:14:46","guid":{"rendered":"https:\/\/namastedev.com\/blog\/?p=8825"},"modified":"2025-08-01T12:48:16","modified_gmt":"2025-08-01T07:18:16","slug":"diameter-of-a-binary-tree","status":"publish","type":"post","link":"https:\/\/namastedev.com\/blog\/diameter-of-a-binary-tree\/","title":{"rendered":"Diameter of a Binary Tree"},"content":{"rendered":"\n<!-- Diameter of a 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  --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 <code>root<\/code> of a binary tree, return <i>the length of the <strong>diameter<\/strong> of the tree<\/i>.<\/p> \n\n       <p>The <strong>diameter<\/strong> of a binary tree is the <strong>length<\/strong> of the longest path between any two nodes in a tree. This path may or may not pass through the <code>root<\/code>.<\/p>\n\n       <p>The <strong>length<\/strong> of a path between two nodes is represented by the number of edges between them.<\/p>\n        <h2>Examples:<\/h2>\n\n                <h3>Example 1:<\/h3>\n                <img decoding=\"async\" src=\"https:\/\/namastedev.com\/blog\/wp-content\/uploads\/2025\/08\/Screenshot-2025-08-01-at-12.46.15\u202fPM.png\" alt=\"\">\n                <p><strong>Input:<\/strong> root = [1,2,3,4,5]<\/p>\n                <p><strong>Output:<\/strong> 3<\/p>\n                <p><strong>Explanation: <\/strong>3 is the length of the path [4,2,1,3] or [5,2,1,3].<\/p>\n\n                <h3>Example 2:<\/h3>\n                <p><strong>Input:<\/strong> root = [1,2]<\/p>\n                <p><strong>Output:<\/strong> 1<\/p>\n\n                    <h2>Constraints:<\/h2>\n                    <ul>\n                        <li>The number of nodes in the tree is in the range [1, 10<sup>4<\/sup>]<\/li>\n                        <li><code>-100 <= Node.val <= 100<\/code><\/li>\n                    <\/ul>\n\n                <h2>Approach<\/h2>\n             <ul>\n                <li><strong>Use DFS (Depth-First Search)<\/strong> to calculate the depth of each node.<\/li>\n                <li>At each node: \n                    <ul>\n                        <li>Calculate the <strong>left<\/strong> and <strong>right<\/strong> subtree depths.<\/li>\n                        <li>The <strong>diameter through that node<\/strong> = <code>leftDepth + rightDepth<\/code>.<\/li>\n                        <li>Update <code>maxDiameter<\/code> if this is the largest so far.<\/li>\n                    <\/ul>\n                <\/li>\n                <li>Return the maximum diameter found during the traversal.<\/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>\n<div style=\"background: #f9f9f9; padding: 10px; border: 1px solid #ccc; font-family: monospace;\">\n<b>Function Call:<\/b> diameterOfBinaryTree(root) where<br>\nroot = TreeNode(1)<br>\n\u251c\u2500\u2500 left: TreeNode(2)<br>\n\u2502\u00a0\u00a0 \u251c\u2500\u2500 left: TreeNode(4)<br>\n\u2502\u00a0\u00a0 \u2514\u2500\u2500 right: TreeNode(5)<br>\n\u2514\u2500\u2500 right: TreeNode(3)<br><br>\n\n<b>Step 1:<\/b><br>\n\u2192 Call findDepth(1)<br><br>\n\n<b>Step 2:<\/b><br>\n\u2192 Call findDepth(2)<br><br>\n\n<b>Step 3:<\/b><br>\n\u2192 Call findDepth(4)<br><br>\n\n<b>Step 4:<\/b><br>\n\u2192 Call findDepth(null) \u2192 return 0<br>\n\u2192 Call findDepth(null) \u2192 return 0<br>\n\u2192 Node 4 \u2192 leftDepth = 0, rightDepth = 0<br>\n\u2192 currDiameter = 0<br>\n\u2192 maxDiameter = max(0, 0) = 0<br>\n\u2192 Return depth = 1<br><br>\n\n<b>Step 5:<\/b><br>\n\u2192 Back to Node 2<br>\n\u2192 leftDepth = 1<br>\n\u2192 Call findDepth(5)<br><br>\n\n<b>Step 6:<\/b><br>\n\u2192 Call findDepth(null) \u2192 return 0<br>\n\u2192 Call findDepth(null) \u2192 return 0<br>\n\u2192 Node 5 \u2192 leftDepth = 0, rightDepth = 0<br>\n\u2192 currDiameter = 0<br>\n\u2192 maxDiameter = max(0, 0) = 0<br>\n\u2192 Return depth = 1<br><br>\n\n<b>Step 7:<\/b><br>\n\u2192 Back to Node 2<br>\n\u2192 rightDepth = 1<br>\n\u2192 Node 2 \u2192 leftDepth = 1, rightDepth = 1<br>\n\u2192 currDiameter = 2<br>\n\u2192 maxDiameter = max(0, 2) = 2<br>\n\u2192 Return depth = 2<br><br>\n\n<b>Step 8:<\/b><br>\n\u2192 Back to Node 1<br>\n\u2192 leftDepth = 2<br>\n\u2192 Call findDepth(3)<br><br>\n\n<b>Step 9:<\/b><br>\n\u2192 Call findDepth(null) \u2192 return 0<br>\n\u2192 Call findDepth(null) \u2192 return 0<br>\n\u2192 Node 3 \u2192 leftDepth = 0, rightDepth = 0<br>\n\u2192 currDiameter = 0<br>\n\u2192 maxDiameter = max(2, 0) = 2<br>\n\u2192 Return depth = 1<br><br>\n\n<b>Step 10:<\/b><br>\n\u2192 Back to Node 1<br>\n\u2192 rightDepth = 1<br>\n\u2192 Node 1 \u2192 leftDepth = 2, rightDepth = 1<br>\n\u2192 currDiameter = 3<br>\n\u2192 maxDiameter = max(2, 3) = 3<br>\n\u2192 Return depth = 3<br><br>\n\n<b>Final Result:<\/b> 3\n<\/div>\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 diameterOfBinaryTree = function(root) {\n    let maxDiameter = 0;\n    let findDepth = (curr) => {\n        if(!curr) return 0;\n        let leftDepth = findDepth(curr.left);\n        let rightDepth = findDepth(curr.right);      \n        let currDiameter = leftDepth + rightDepth;\n        maxDiameter = Math.max(currDiameter, maxDiameter);\n        return 1+Math.max(leftDepth, rightDepth);\n    }\n    findDepth(root);\n    return maxDiameter;\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 diameterOfBinaryTree(self, root):\n        self.maxDiameter = 0\n\n        def findDepth(node):\n            if not node:\n                return 0\n            left = findDepth(node.left)\n            right = findDepth(node.right)\n            self.maxDiameter = max(self.maxDiameter, left + right)\n            return 1 + max(left, right)\n        findDepth(root)\n        return self.maxDiameter\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    int maxDiameter = 0;\n\n    public int diameterOfBinaryTree(TreeNode root) {\n        findDepth(root);\n        return maxDiameter;\n    }\n    private int findDepth(TreeNode node) {\n        if (node == null) return 0;\n        int left = findDepth(node.left);\n        int right = findDepth(node.right);\n        maxDiameter = Math.max(maxDiameter, left + right);\n        return 1 + Math.max(left, 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 maxDiameter = 0;\n\n    int findDepth(TreeNode* node) {\n        if (!node) return 0;\n        int left = findDepth(node->left);\n        int right = findDepth(node->right);\n        maxDiameter = std::max(maxDiameter, left + right);\n        return 1 + std::max(left, right);\n    }\n\n    int diameterOfBinaryTree(TreeNode* root) {\n        findDepth(root);\n        return maxDiameter;\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\">\n<i>\/\/ C doesn't support OOP, so we assume TreeNode is defined and a helper is used.<\/i>\n\nint maxDiameter = 0;\nint findDepth(struct TreeNode* node) {\n    if (node == NULL) return 0;\n    int left = findDepth(node->left);\n    int right = findDepth(node->right);\n    int currDiameter = left + right;\n    if (currDiameter > maxDiameter) maxDiameter = currDiameter;\n    return 1 + (left > right ? left : right);\n}\nint diameterOfBinaryTree(struct TreeNode* root) {\n    maxDiameter = 0; \/\/ reset global variable\n    findDepth(root);\n    return maxDiameter;\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    int maxDiameter = 0;\n\n    public int DiameterOfBinaryTree(TreeNode root) {\n        FindDepth(root);\n        return maxDiameter;\n    }\n    private int FindDepth(TreeNode node) {\n        if (node == null) return 0;\n        int left = FindDepth(node.left);\n        int right = FindDepth(node.right);\n        maxDiameter = Math.Max(maxDiameter, left + right);\n        return 1 + Math.Max(left, 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                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, return the length of the diameter of the tree. The diameter of a binary tree is the length of the longest path between any two nodes in a tree. This path may or may not pass through the root. The length of a path between two<\/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":[210,176,175,211,811,810,174,172,173],"tags":[],"class_list":["post-8825","post","type-post","status-publish","format-standard","category-algorithms","category-csharp","category-cplusplus","category-data-structures","category-data-structures-and-algorithms","category-dsa","category-java","category-javascript","category-python"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/8825","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=8825"}],"version-history":[{"count":2,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/8825\/revisions"}],"predecessor-version":[{"id":8828,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/8825\/revisions\/8828"}],"wp:attachment":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/media?parent=8825"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/categories?post=8825"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/tags?post=8825"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}