{"id":8920,"date":"2025-08-04T11:46:56","date_gmt":"2025-08-04T06:16:56","guid":{"rendered":"https:\/\/namastedev.com\/blog\/?p=8920"},"modified":"2025-08-04T11:52:43","modified_gmt":"2025-08-04T06:22:43","slug":"subtree-of-another-tree","status":"publish","type":"post","link":"https:\/\/namastedev.com\/blog\/subtree-of-another-tree\/","title":{"rendered":"Subtree of another Tree"},"content":{"rendered":"\n<!-- SubTree Another: 21 -->\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>\n            Given the roots of two binary trees <code>root<\/code> and <code>subRoot<\/code>, return <code>true<\/code> if there is a subtree of <code>root<\/code> with the same structure and node values of <code>subRoot<\/code> and <code>false<\/code> otherwise.\n        <\/p>\n        <p>A subtree of a binary <code>tree<\/code> tree is a tree that consists of a node in <code>tree<\/code> and all of this node&#8217;s descendants. The tree <code>tree<\/code> could also be considered as a subtree of itself.<\/p>\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-2025-08-02-at-5.40.25\u202fPM.png\" alt=\"\">\n                <p><strong>Input:<\/strong> root = [3,4,5,1,2], subRoot = [4,1,2]<\/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-2025-08-02-at-5.43.18\u202fPM.png\" alt=\"\">\n                <p><strong>Input:<\/strong> root = [3,4,5,1,2,null,null,null,null,0], subRoot = [4,1,2]<\/p>\n                <p><strong>Output:<\/strong> false<\/p>\n\n                    <h2>Constraints:<\/h2>\n                    <ul>\n                        <li>The number of nodes in the <code>root<\/code> tree is in the range <code>[1, 2000]<\/code>.<\/li>\n                        <li>The number of nodes in the <code>subRoot<\/code> tree is in the range <code>[1, 1000]<\/code>.<\/li>\n                        <li><code>-10<sup>4<\/sup> <= root.val <= 10<sup>4<\/sup><\/code><\/li>\n                        <li><code>-10<sup>4<\/sup> <= subRoot.val <= 10<sup>4<\/sup><\/code><\/li>\n                    <\/ul>\n\n                <h2>Approach<\/h2>\n                <ul>\n                    <li><strong>Serialize both trees<\/strong> using <code>preorder traversal<\/code> (with null markers) into strings.<\/li>\n                    <li>Check if <code>subRoot's<\/code> serialized string is a substring of <code>root's<\/code> serialized string.<\/li>\n                    <li>If yes, subRoot is a subtree of root; return <code>true<\/code>, else <code>false<\/code>.<\/li>\n                <\/ul>\n\n                <h2>Time Complexity:<\/h2>\n                <li>\n                  <p><strong>Time Complexity = O(n * m)<\/strong>\n                  <\/li>\n                <h2>Space Complexity:<\/h2>\n                <li>\n                  <p><strong>Space Complexity = O(n + m)<\/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> isSubtree(root, subRoot) where<br> root = TreeNode(3)<br> \u251c\u2500\u2500 left: TreeNode(4)<br> \u2502\u00a0\u00a0 \u251c\u2500\u2500 left: TreeNode(1)<br> \u2502\u00a0\u00a0 \u2514\u2500\u2500 right: TreeNode(2)<br> \u2514\u2500\u2500 right: TreeNode(5)<br><br>\nsubRoot = TreeNode(4)<br>\n\u251c\u2500\u2500 left: TreeNode(1)<br>\n\u2514\u2500\u2500 right: TreeNode(2)<br><br>\n<b>Step 1:<\/b><br>\n\u2192 Call serialize(root)<br><br>\n\n<b>Serializing root:<\/b><br>\n\u2192 curr = 3 \u2192 hash = &#8220;-3&#8221;<br>\n\u2192 curr.left = 4 \u2192 hash = &#8220;-3-4&#8221;<br>\n\u2192 curr.left.left = 1 \u2192 hash = &#8220;-3-4-1&#8221;<br>\n\u2192 curr.left.left.left = null \u2192 hash = &#8220;-3-4-1-#&#8221;<br>\n\u2192 curr.left.left.right = null \u2192 hash = &#8220;-3-4-1-#-#&#8221;<br>\n\u2192 curr.left.right = 2 \u2192 hash = &#8220;-3-4-1-#-#-2&#8221;<br>\n\u2192 curr.left.right.left = null \u2192 hash = &#8220;-3-4-1-#-#-2-#&#8221;<br>\n\u2192 curr.left.right.right = null \u2192 hash = &#8220;-3-4-1-#-#-2-#-#&#8221;<br>\n\u2192 curr.right = 5 \u2192 hash = &#8220;-3-4-1-#-#-2-#-#-5&#8221;<br>\n\u2192 curr.right.left = null \u2192 hash = &#8220;-3-4-1-#-#-2-#-#-5-#&#8221;<br>\n\u2192 curr.right.right = null \u2192 hash = &#8220;-3-4-1-#-#-2-#-#-5-#-#&#8221;<br><br>\n\n<b>Serialized root:<\/b><br>\n\u2192 hashRoot = &#8220;-3-4-1-#-#-2-#-#-5-#-#&#8221;<br><br>\n\n<b>Step 2:<\/b><br>\n\u2192 Call serialize(subRoot)<br><br>\n\n<b>Serializing subRoot:<\/b><br>\n\u2192 curr = 4 \u2192 hash = &#8220;-4&#8221;<br>\n\u2192 curr.left = 1 \u2192 hash = &#8220;-4-1&#8221;<br>\n\u2192 curr.left.left = null \u2192 hash = &#8220;-4-1-#&#8221;<br>\n\u2192 curr.left.right = null \u2192 hash = &#8220;-4-1-#-#&#8221;<br>\n\u2192 curr.right = 2 \u2192 hash = &#8220;-4-1-#-#-2&#8221;<br>\n\u2192 curr.right.left = null \u2192 hash = &#8220;-4-1-#-#-2-#&#8221;<br>\n\u2192 curr.right.right = null \u2192 hash = &#8220;-4-1-#-#-2-#-#&#8221;<br><br>\n\n<b>Serialized subRoot:<\/b><br>\n\u2192 hashSubRoot = &#8220;-4-1-#-#-2-#-#&#8221;<br><br>\n\n<b>Step 3:<\/b><br>\n\u2192 Check if hashRoot includes hashSubRoot:<br>\n\u2192 &#8220;-3-4-1-#-#-2-#-#-5-#-#&#8221; includes &#8220;-4-1-#-#-2-#-#&#8221; \u2192 true<br><br>\n\n<b>Final Result:<\/b> true\n\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 isSubtree = function(root, subRoot) {\n    let hashRoot = serialize(root);\n    let hashSubRoot = serialize(subRoot);\n\n    return hashRoot.includes(hashSubRoot);\n};\nlet serialize = function(root) {\n    let hash = \"\";\n    let traversal = (curr) => {\n        if(!curr) {\n            hash = hash + \"-#\";\n            return;\n        }\n        hash = hash + \"-\" + curr.val;\n        traversal(curr.left);\n        traversal(curr.right);\n    }\n    traversal(root);\n    return hash;\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\nclass Solution:\n    def serialize(self, root):\n        hash = []\n        def dfs(node):\n            if not node:\n                hash.append(\"-#\")\n                return\n            hash.append(\"-\" + str(node.val))\n            dfs(node.left)\n            dfs(node.right)\n        dfs(root)\n        return ''.join(hash)\n\n    def isSubtree(self, root, subRoot):\n        hashRoot = self.serialize(root)\n        hashSubRoot = self.serialize(subRoot)\n        return hashSubRoot in hashRoot\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 x) { val = x; }\n}\nclass Solution {\n    public String serialize(TreeNode root) {\n        StringBuilder sb = new StringBuilder();\n        serializeHelper(root, sb);\n        return sb.toString();\n    }\n    private void serializeHelper(TreeNode root, StringBuilder sb) {\n        if (root == null) {\n            sb.append(\"-#\");\n            return;\n        }\n        sb.append(\"-\").append(root.val);\n        serializeHelper(root.left, sb);\n        serializeHelper(root.right, sb);\n    }\n    public boolean isSubtree(TreeNode root, TreeNode subRoot) {\n        String hashRoot = serialize(root);\n        String hashSubRoot = serialize(subRoot);\n        return hashRoot.contains(hashSubRoot);\n    }\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 TreeNode {\npublic:\n    int val;\n    TreeNode* left;\n    TreeNode* right;\n    TreeNode(int x): val(x), left(nullptr), right(nullptr) {}\n};\n\nclass Solution {\npublic:\n    string serialize(TreeNode* root) {\n        string hash;\n        serializeHelper(root, hash);\n        return hash;\n    }\n    void serializeHelper(TreeNode* root, string& hash) {\n        if (!root) {\n            hash += \"-#\";\n            return;\n        }\n        hash += \"-\" + to_string(root->val);\n        serializeHelper(root->left, hash);\n        serializeHelper(root->right, hash);\n    }\n    bool isSubtree(TreeNode* root, TreeNode* subRoot) {\n        string hashRoot = serialize(root);\n        string hashSubRoot = serialize(subRoot);\n        return hashRoot.find(hashSubRoot) != string::npos;\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\/\/ Pseudo-C style (illustrative only, not complete without memory management and tree setup)\ntypedef struct TreeNode {\n    int val;\n    struct TreeNode* left;\n    struct TreeNode* right;\n} TreeNode;\nvoid serialize(TreeNode* root, char* buffer) {\n    if (!root) {\n        strcat(buffer, \"-#\");\n        return;\n    }\n    char valStr[20];\n    sprintf(valStr, \"-%d\", root->val);\n    strcat(buffer, valStr);\n    serialize(root->left, buffer);\n    serialize(root->right, buffer);\n}\nint isSubtree(TreeNode* root, TreeNode* subRoot) {\n    char hashRoot[1000] = \"\";\n    char hashSubRoot[1000] = \"\";\n    serialize(root, hashRoot);\n    serialize(subRoot, hashSubRoot);\n    return strstr(hashRoot, hashSubRoot) != NULL;\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    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 string Serialize(TreeNode root) {\n        StringBuilder sb = new StringBuilder();\n        SerializeHelper(root, sb);\n        return sb.ToString();\n    }\n    private void SerializeHelper(TreeNode root, StringBuilder sb) {\n        if (root == null) {\n            sb.Append(\"-#\");\n            return;\n        }\n        sb.Append(\"-\" + root.val);\n        SerializeHelper(root.left, sb);\n        SerializeHelper(root.right, sb);\n    }\n    public bool IsSubtree(TreeNode root, TreeNode subRoot) {\n        string hashRoot = Serialize(root);\n        string hashSubRoot = Serialize(subRoot);\n        return hashRoot.Contains(hashSubRoot);\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 roots of two binary trees root and subRoot, return true if there is a subtree of root with the same structure and node values of subRoot and false otherwise. A subtree of a binary tree tree is a tree that consists of a node in tree and all of this node&#8217;s<\/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":[322,176,175,211,810,174,172,173],"tags":[],"class_list":["post-8920","post","type-post","status-publish","format-standard","category-algorithms-and-data-structures","category-csharp","category-cplusplus","category-data-structures","category-dsa","category-java","category-javascript","category-python"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/8920","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=8920"}],"version-history":[{"count":1,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/8920\/revisions"}],"predecessor-version":[{"id":8921,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/8920\/revisions\/8921"}],"wp:attachment":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/media?parent=8920"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/categories?post=8920"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/tags?post=8920"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}