{"id":8455,"date":"2025-07-30T23:04:44","date_gmt":"2025-07-30T17:34:44","guid":{"rendered":"https:\/\/namastedev.com\/blog\/?p=8455"},"modified":"2025-07-30T23:06:43","modified_gmt":"2025-07-30T17:36:43","slug":"maximum-depth-of-binary-tree","status":"publish","type":"post","link":"https:\/\/namastedev.com\/blog\/maximum-depth-of-binary-tree\/","title":{"rendered":"Maximum Depth of Binary Tree"},"content":{"rendered":"\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  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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 tree, return <i>its maximum depth.<\/i><\/p>\n        <p>A binary tree&#8217;s <strong>maximum depth<\/strong> is the number of nodes along the longest path from the root node down to the farthest leaf node.<\/p>\n\n                <h2>Examples:<\/h2>\n\n                <h3>Example 1:<\/h3>\n                <img decoding=\"async\" src=\"https:\/\/namastedev.com\/blog\/wp-content\/uploads\/2025\/07\/Screenshot-2025-07-30-at-11.00.28\u202fPM.png\" alt=\"\">\n\n                <p><strong>Input:<\/strong> root = [3,9,20,null,null,15,7]<\/p>\n                <p><strong>Output:<\/strong> 3<\/p>\n\n                <h3>Example 2:<\/h3>\n                <p><strong>Input:<\/strong> root = [1,null,2]<\/p>\n                <p><strong>Output:<\/strong> 2<\/p>\n\n                    <h2>Constraints:<\/h2>\n                    <ul>\n                      <li>The number of nodes in the tree is in the range [0, 10<sup>4<\/sup>].<\/li>\n                      <li><code>-100 <= Node.val <= 100<\/code><\/li>\n                    <\/ul>\n\n                <h2>Approach 1: (Top-Down)<\/h2>\n                <ul>\n                  <li>Start with the root node at depth <code>1<\/code>.<\/li> \n                  <li><code>Traverse left<\/code> and right children, increasing depth at each level.<\/li>\n                  <li>Keep track of the <strong>maximum depth<\/strong> encountered during traversal.<\/li>\n                  <li><strong>Edge Case: <\/strong>If tree is empty (root is null), <code>return 0<\/code>.<\/li>\n                <\/ul>\n\n                <h2>Time Complexity:<\/h2>\n                <li>\n                  <p><strong>Time Complexity = O(n)<\/strong>\n            \n                  <\/li>\n                <h2>Space Complexity:<\/h2>\n                <li>\n                  <p><strong>Space Complexity = O(n)<\/strong>\n                  <\/p>\n                <\/li>\n<h2>Dry Run<\/h2> <div style=\"background: #f9f9f9; border-left: 4px solid var(--primary); padding: 1rem; border-radius: var(--tab-radius); margin: 1rem 0;\"> <p><strong>Input:<\/strong> <code>root = [1, 2, 3, null, 4]<\/code><\/p> <pre style=\"white-space: pre-wrap; background: #fff5ea; padding: 1rem; border-radius: 8px; overflow-x: auto;\"> \n      \n        1\n       \/ \\\n      2   3\n       \\\n        4\n\nInitialize:\nmaxDepth = 0\nCall traversal(root, 1)\n\u2192 curr = 1, depth = 1\n\u2192 maxDepth = max(0, 1) = 1\n\u2192 curr.left = 2 \u2192 call traversal(2, 2)\n\u2192 curr = 2, depth = 2\n\u2192 maxDepth = max(1, 2) = 2\n\u2192 curr.left = null \u2192 no call\n\u2192 curr.right = 4 \u2192 call traversal(4, 3)\n<pre>\n\u2192 curr = 4, depth = 3\n\u2192 maxDepth = max(2, 3) = 3\n\u2192 curr.left = null \u2192 no call\n\u2192 curr.right = null \u2192 no call\n<\/pre>\n\u2192 Back to curr = 2 \u2192 done\n\u2192 Back to curr = 1\n\u2192 curr.right = 3 \u2192 call traversal(3, 2)\n\u2192 curr = 3, depth = 2\n\u2192 maxDepth = max(3, 2) = 3\n\u2192 curr.left = null \u2192 no call\n\u2192 curr.right = null \u2192 no call\n\u2192 Back to curr = 1 \u2192 done\nTraversal complete.\nFinal maxDepth = 3\n<\/pre>\n<p><strong>Output:<\/strong> <code>Result: 3<\/code><\/p> <\/div>\n\n        <!-- <h2>Visualisation:<\/h2>\n        <img decoding=\"async\" src=\"https:\/\/namastedev.com\/blog\/wp-content\/uploads\/2025\/07\/Screenshot-2025-07-15-at-3.36.17\u202fPM.png\" alt=\"Stocks\" \/> -->\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=\"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 maxDepth = function(root) {\n    if(!root) return 0;\n    let maxDepth = 0;\n    let traversal = (curr, depth) => {\n        maxDepth = Math.max(maxDepth, depth);\n        curr.left && traversal(curr.left, depth + 1);\n        curr.right && traversal(curr.right, depth + 1);\n    }\n    traversal(root, 1);\n    return maxDepth;\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 TreeNode:\n    def __init__(self, val=0, left=None, right=None):\n        self.val = val\n        self.left = left\n        self.right = right\n\ndef maxDepth(root):\n    if not root:\n        return 0\n    return max(maxDepth(root.left), maxDepth(root.right)) + 1\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    TreeNode(int val) {\n        this.val = val;\n    }\n}\nclass Solution {\n    public int maxDepth(TreeNode root) {\n        if (root == null) return 0;\n        return Math.max(maxDepth(root.left), maxDepth(root.right)) + 1;\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\">\nstruct TreeNode {\n    int val;\n    TreeNode *left;\n    TreeNode *right;\n    TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}\n};\nint maxDepth(TreeNode* root) {\n    if (!root) return 0;\n    return std::max(maxDepth(root->left), maxDepth(root->right)) + 1;\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#include &lt;stdio.h&gt;\n#include &lt;stdlib.h&gt;\nstruct TreeNode {\n    int val;\n    struct TreeNode *left;\n    struct TreeNode *right;\n};\nint max(int a, int b) {\n    return a > b ? a : b;\n}\nint maxDepth(struct TreeNode* root) {\n    if (!root) return 0;\n    int left = maxDepth(root->left);\n    int right = maxDepth(root->right);\n    return max(left, right) + 1;\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    public TreeNode(int val = 0, TreeNode left = null, TreeNode right = null) {\n        this.val = val;\n        this.left = left;\n        this.right = right;\n    }\n}\npublic class Solution {\n    public int MaxDepth(TreeNode root) {\n        if (root == null) return 0;\n        return Math.Max(MaxDepth(root.left), MaxDepth(root.right)) + 1;\n    }\n}\n            <\/code><\/pre>\n        <\/div>\n    <\/div>\n<\/div>\n\n<!-- Approach 2:  -->\n  <div class=\"wp_blog_container wp_blog_theme\"> \n    <h1 class=\"wp_blog_main-heading\"><\/h1>\n    <div class=\"wp_blog_explanation\">\n\n        <h2>Approach 2: Bottom Up<\/h2>\n            <ul>\n            <li><strong>Base Case:<\/strong> If the node is null, return 0 \u2014 it means we've reached beyond a leaf node.<\/li>\n            <li><strong>Recursive Case:<\/strong>\n            <ul>\n                <li>Recursively find the max depth of the <code>left<\/code> subtree.<\/li> \n                <li>Recursively find the max depth of the <code>right<\/code> subtree.<\/li>\n            <\/ul>\n            <\/li>\n            <li><code>Return 1 + the maximum<\/code> of left and right subtree depths.<\/li>\n            <\/ul>\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(n)<\/strong> <\/p>\n\n                    <\/li>\n\n    <!-- dry run -->\n<h2>Dry Run<\/h2> <div style=\"background: #f9f9f9; border-left: 4px solid var(--primary); padding: 1rem; border-radius: var(--tab-radius); margin: 1rem 0;\"> <p><strong>Input:<\/strong> <code>root = [1, 2, 3, null, 4]<\/code><\/p> <pre style=\"white-space: pre-wrap; background: #fff5ea; padding: 1rem; border-radius: 8px; overflow-x: auto;\">\n  1\n \/ \\\n2   3\n \\\n  4\nRecursive Calls:\n\u2192 maxDepth(1)\n\u2192 leftMax = maxDepth(2)\n\u2192 leftMax = maxDepth(null) = 0\n\u2192 rightMax = maxDepth(4)\n\u2192 leftMax = maxDepth(null) = 0\n\u2192 rightMax = maxDepth(null) = 0\n\u2192 return 1 + max(0, 0) = 1\n\u2192 return 1 + max(0, 1) = 2\n\u2192 rightMax = maxDepth(3)\n\u2192 leftMax = maxDepth(null) = 0\n\u2192 rightMax = maxDepth(null) = 0\n\u2192 return 1 + max(0, 0) = 1\n\u2192 return 1 + max(2, 1) = 3\n<\/pre> <p><strong>Output:<\/strong> <code>Result: 3<\/code><\/p> <\/div>\n    \n<\/div>\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 maxDepth = function(root) {\n    if(!root) return 0;\n    let leftMax = maxDepth(root.left);\n    let rightMax = maxDepth(root.right);\n    return 1 + Math.max(leftMax, rightMax);\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 TreeNode:\n    def __init__(self, val=0, left=None, right=None):\n        self.val = val\n        self.left = left\n        self.right = right\n\ndef maxDepth(root):\n    if not root:\n        return 0\n    leftMax = maxDepth(root.left)\n    rightMax = maxDepth(root.right)\n    return 1 + max(leftMax, rightMax)\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}\n\npublic int maxDepth(TreeNode root) {\n    if (root == null) return 0;\n    int leftMax = maxDepth(root.left);\n    int rightMax = maxDepth(root.right);\n    return 1 + Math.max(leftMax, rightMax);\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\">\nstruct TreeNode {\n    int val;\n    TreeNode *left;\n    TreeNode *right;\n};\nint maxDepth(TreeNode* root) {\n    if (!root) return 0;\n    int leftMax = maxDepth(root->left);\n    int rightMax = maxDepth(root->right);\n    return 1 + std::max(leftMax, rightMax);\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};\nint maxDepth(struct TreeNode* root) {\n    if (root == NULL) return 0;\n    int leftMax = maxDepth(root->left);\n    int rightMax = maxDepth(root->right);\n    return 1 + (leftMax > rightMax ? leftMax : rightMax);\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 int MaxDepth(TreeNode root) {\n    if (root == null) return 0;\n    int leftMax = MaxDepth(root.left);\n    int rightMax = MaxDepth(root.right);\n    return 1 + Math.Max(leftMax, rightMax);\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                    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A binary tree&#8217;s maximum depth is the number of nodes along the longest path from the root node down to the farthest leaf node. Examples: Example 1: Input: root = [3,9,20,null,null,15,7] Output: 3 Example 2: Input: root = [1,null,2] Output: 2 Constraints:<\/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":[176,175,211,811,810,174,172,173],"tags":[],"class_list":["post-8455","post","type-post","status-publish","format-standard","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\/8455","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=8455"}],"version-history":[{"count":1,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/8455\/revisions"}],"predecessor-version":[{"id":8462,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/8455\/revisions\/8462"}],"wp:attachment":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/media?parent=8455"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/categories?post=8455"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/tags?post=8455"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}