{"id":8687,"date":"2025-07-31T16:20:10","date_gmt":"2025-07-31T10:50:10","guid":{"rendered":"https:\/\/namastedev.com\/blog\/?p=8687"},"modified":"2025-07-31T17:00:51","modified_gmt":"2025-07-31T11:30:51","slug":"symmetric-tree-recursive-approach","status":"publish","type":"post","link":"https:\/\/namastedev.com\/blog\/symmetric-tree-recursive-approach\/","title":{"rendered":"Symmetric Tree Recursive Approach"},"content":{"rendered":"\n<!--Symmtery: Recursive -->\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>check whether it is a mirror of itself<\/i>(i.e., symmetric around its center).<\/p>\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-4.54.38\u202fPM.png\" alt=\"\">\n                <p><strong>Input:<\/strong> root = [1,2,2,3,4,4,3]<\/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\/07\/Screenshot-2025-07-31-at-4.57.54\u202fPM.png\" alt=\"\">\n                <p><strong>Input:<\/strong> root = [1,2,2,null,3,null,3]<\/p>\n                <p><strong>Output:<\/strong> false<\/p>\n\n                    <h2>Constraints:<\/h2>\n                    <ul>\n                      <li>The number of nodes in the tree is in the range <code>[1, 1000]<\/code>.<\/li>\n                      <li><code>-100 <= Node.val <= 100<\/code><\/li>\n                    <\/ul>\n\n                <h2>Approach: Bottom Up<\/h2>\n              <ul>\n                <li>Use a <strong>helper function<\/strong> <code>isMirror(left, right)<\/code> to compare two nodes.<\/li>\n                <li>The tree is symmetric if:\n                    <ul>\n                        <li>Both left and right subtrees are <code>null<\/code> \u2192 return <code>true<\/code>.<\/li>\n                        <li>Only one is <code>null<\/code> \u2192 return <code>false<\/code>.<\/li>\n                        <li>Their values match <strong>and<\/strong>:\n\n                            <ul>\n                                <li>Left\u2019s left subtree mirrors Right\u2019s right subtree.<\/li>\n                                <li>Left\u2019s right subtree mirrors Right\u2019s left subtree.<\/li>\n                            <\/ul>\n                        <\/li>\n                    <\/ul>\n                <\/li>\n                <li>Start the comparison with <code>root.left<\/code> and <code>root.right<\/code>.<\/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                <\/li>\n\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    Tree Structure: \n        1 \n       \/ \\ \n      2   3 \n       \\\n        4\nFunction call: isSymmetric(root)\n\u2192 Calls isMirror(root.left, root.right)\n\u2192 isMirror(2, 3)\n- Both are not null \u2192 OK\n- Compare values: 2 === 3 \u2192 false\n\u2192 Return false\nFunction returns false (not symmetric)\n<\/pre>\n<p><strong>Output:<\/strong> <code>Result: false<\/code><\/p> <\/div>\n\n        <!-- <h2>Visualisation:<\/h2>\n        <img decoding=\"async\" src=\"https:\/\/namastedev.com\/blog\/wp-content\/uploads\/2025\/07\/Screenshot-2025-07-19-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 isSymmetric = function(root) {\n    let isMirror = (left, right) => {\n        if(!left && !right) return true;\n        if(!left || !right) return false;\n        return left.val === right.val &&\n                        isMirror(left.left, right.right) &&\n                        isMirror(left.right, right.left);      \n    }\n    return isMirror(root.left, root.right);\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 isMirror(left, right):\n    if not left and not right:\n        return True\n    if not left or not right:\n        return False\n    return (left.val == right.val and\n            isMirror(left.left, right.right) and\n            isMirror(left.right, right.left))\n\ndef isSymmetric(root):\n    return isMirror(root.left, root.right)\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\">\npublic boolean isMirror(TreeNode left, TreeNode right) {\n    if (left == null && right == null) return true;\n    if (left == null || right == null) return false;\n    return (left.val == right.val) &&\n           isMirror(left.left, right.right) &&\n           isMirror(left.right, right.left);\n}\n\npublic boolean isSymmetric(TreeNode root) {\n    return isMirror(root.left, root.right);\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 isMirror(TreeNode* left, TreeNode* right) {\n    if (!left && !right) return true;\n    if (!left || !right) return false;\n    return (left->val == right->val) &&\n           isMirror(left->left, right->right) &&\n           isMirror(left->right, right->left);\n}\n\nbool isSymmetric(TreeNode* root) {\n    return isMirror(root->left, root->right);\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\">\nbool isMirror(struct TreeNode* left, struct TreeNode* right) {\n    if (!left && !right) return true;\n    if (!left || !right) return false;\n    return (left->val == right->val) &&\n           isMirror(left->left, right->right) &&\n           isMirror(left->right, right->left);\n}\n\nbool isSymmetric(struct TreeNode* root) {\n    return isMirror(root->left, root->right);\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 bool IsMirror(TreeNode left, TreeNode right) {\n    if (left == null && right == null) return true;\n    if (left == null || right == null) return false;\n    return left.val == right.val &&\n           IsMirror(left.left, right.right) &&\n           IsMirror(left.right, right.left);\n}\n\npublic bool IsSymmetric(TreeNode root) {\n    return IsMirror(root.left, root.right);\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, check whether it is a mirror of itself(i.e., symmetric around its center). Examples: Example 1: Input: root = [1,2,2,3,4,4,3] Output: true Example 2: Input: root = [1,2,2,null,3,null,3] Output: false Constraints: The number of nodes in the tree is in the range [1, 1000]. -100 val ==<\/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":[322,176,175,211,811,810,174,172,173],"tags":[],"class_list":["post-8687","post","type-post","status-publish","format-standard","category-algorithms-and-data-structures","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\/8687","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=8687"}],"version-history":[{"count":2,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/8687\/revisions"}],"predecessor-version":[{"id":8785,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/8687\/revisions\/8785"}],"wp:attachment":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/media?parent=8687"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/categories?post=8687"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/tags?post=8687"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}