{"id":8909,"date":"2025-08-04T10:41:03","date_gmt":"2025-08-04T05:11:03","guid":{"rendered":"https:\/\/namastedev.com\/blog\/?p=8909"},"modified":"2025-08-04T10:43:16","modified_gmt":"2025-08-04T05:13:16","slug":"count-good-nodes-in-binary-tree","status":"publish","type":"post","link":"https:\/\/namastedev.com\/blog\/count-good-nodes-in-binary-tree\/","title":{"rendered":"Count Good Nodes in Binary Tree"},"content":{"rendered":"\n<!-- Count Good Node: 24-->\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 a binary tree <code>root<\/code>, a node X in the tree is named <strong>good<\/strong> if in the path from root to X there are no nodes with a value greater than X.\n        <\/p>  \n        \n        <p>\n            Return the number of <strong>good<\/strong> nodes in the binary tree.\n        <\/p>\n        <h2>Examples:<\/h2>\n                <h3>Example 1:<\/h3>\n                <img decoding=\"async\" src=\"https:\/\/namastedev.com\/blog\/wp-content\/uploads\/2025\/08\/Screenshot-2025-08-04-at-10.35.57\u202fAM.png\" alt=\"\">\n                <p><strong>Input:<\/strong>  root = [3,1,4,3,null,1,5]<\/p>\n                <p><strong>Output:<\/strong> 4<\/p>\n                <p><strong>Explanation:<\/strong>\n                    <pre>\n                    Nodes in blue are good.\n                    Root Node (3) is always a good node.\n                    Node 4 -> (3,4) is the maximum value in the path starting from the root.\n                    Node 5 -> (3,4,5) is the maximum value in the path\n                    Node 3 -> (3,1,3) is the maximum value in the path.\n                    <\/pre>\n                <\/p>\n\n               <h3>Example 2:<\/h3>\n               <img decoding=\"async\" src=\"https:\/\/namastedev.com\/blog\/wp-content\/uploads\/2025\/08\/Screenshot-2025-08-04-at-10.39.03\u202fAM.png\" alt=\"\">\n                <p><strong>Input:<\/strong>  root = [3,3,null,4,2]<\/p>\n                <p><strong>Output:<\/strong> 3<\/p>\n                <p><strong>Explanation:<\/strong> Node 2 -> (3, 3, 2) is not good, because &#8220;3&#8221; is higher than it.\n                <\/p>\n                \n                <h3>Example 3:<\/h3>\n                <p><strong>Input:<\/strong> root = [1]<\/p>\n                <p><strong>Output:<\/strong> 1<\/p>\n                <p><strong>Explanation:<\/strong> Root is considered as <strong>good<\/strong>.<\/p>\n\n                    <h2>Constraints:<\/h2>\n                    <ul>\n                        <li>The number of nodes in the binary tree is in the range <code>[1, 10<sup>5<\/sup>]<\/code>.<\/li>\n                        <li>Each node&#8217;s value is between <code>-10<sup>4<\/sup>, 10<sup>4<\/sup><\/code><\/li>\n                    <\/ul>\n\n                <h2>Approach<\/h2>\n                <ul>\n                    <li>Use <strong>DFS traversal<\/strong> starting from the root.<\/li>\n                    <li>Keep track of the <strong>maximum value seen so far<\/strong> (<code>maxSeenSoFar<\/code>) along the path.<\/li>\n                    <li>For each node:\n                        <ul>\n                            <li>If <code>node.val >= maxSeenSoFar<\/code>, it&#8217;s a <strong>good node<\/strong> \u2192 increment count.<\/li>\n                            <li>Update <code>maxSeenSoFar<\/code> to <code>Math.max(curr.val, maxSeenSoFar)<\/code>.<\/li>\n                        <\/ul>\n                    <\/li>\n                    <li>Recurse for left and right children.<\/li>\n                    <li>Return the total count of good nodes.<\/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(n)<\/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> goodNodes(root) where<br>\nroot = TreeNode(3)<br>\n\u251c\u2500\u2500 left: TreeNode(1)<br>\n\u2502\u00a0\u00a0 \u2514\u2500\u2500 left: TreeNode(3)<br>\n\u2514\u2500\u2500 right: TreeNode(4)<br>\n \u00a0\u00a0 \u2514\u2500\u2500 right: TreeNode(5)<br><br>\n\n<b>Step 1:<\/b><br>\n\u2192 Initialize ans = 0<br>\n\u2192 Call traversal(root, -Infinity)<br><br>\n\n<b>Step 2:<\/b><br>\n\u2192 curr = 3, maxSeenSoFar = -Infinity<br>\n\u2192 3 >= -Infinity \u2192 ans++ \u2192 ans = 1<br>\n\u2192 currMax = max(-Infinity, 3) = 3<br>\n\u2192 Call traversal(curr.left = 1, currMax = 3)<br><br>\n\n<b>Step 3:<\/b><br>\n\u2192 curr = 1, maxSeenSoFar = 3<br>\n\u2192 1 >= 3 \u2192 false \u2192 ans unchanged<br>\n\u2192 currMax = max(3, 1) = 3<br>\n\u2192 Call traversal(curr.left = 3, currMax = 3)<br><br>\n\n<b>Step 4:<\/b><br>\n\u2192 curr = 3, maxSeenSoFar = 3<br>\n\u2192 3 >= 3 \u2192 ans++ \u2192 ans = 2<br>\n\u2192 currMax = max(3, 3) = 3<br>\n\u2192 curr.left = null \u2192 skip<br>\n\u2192 curr.right = null \u2192 skip<br>\n\u2192 return<br><br>\n\n<b>Step 5:<\/b><br>\n\u2192 curr.right = null for node 1 \u2192 skip<br>\n\u2192 return<br><br>\n\n<b>Step 6:<\/b><br>\n\u2192 Back to root, call traversal(curr.right = 4, currMax = 3)<br><br>\n\n<b>Step 7:<\/b><br>\n\u2192 curr = 4, maxSeenSoFar = 3<br>\n\u2192 4 >= 3 \u2192 ans++ \u2192 ans = 3<br>\n\u2192 currMax = max(3, 4) = 4<br>\n\u2192 curr.left = null \u2192 skip<br>\n\u2192 Call traversal(curr.right = 5, currMax = 4)<br><br>\n\n<b>Step 8:<\/b><br>\n\u2192 curr = 5, maxSeenSoFar = 4<br>\n\u2192 5 >= 4 \u2192 ans++ \u2192 ans = 4<br>\n\u2192 curr.left = null \u2192 skip<br>\n\u2192 curr.right = null \u2192 skip<br>\n\u2192 return<br><br>\n\n<b>Step 9:<\/b><br>\n\u2192 All calls done \u2192 return ans = 4<br><br>\n\n<b>Final Result:<\/b> 4\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 goodNodes = function(root) {\n    let ans = 0;\n    let traversal = (curr, maxSeenSoFar) =>{\n        if(curr.val >= maxSeenSoFar){\n            ++ans;\n        }\n        let currMax = Math.max(maxSeenSoFar, curr.val);\n        curr.left && traversal(curr.left, currMax);\n        curr.right && traversal(curr.right, currMax);\n    }\n    traversal(root, -Infinity);\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 goodNodes(self, root):\n        self.ans = 0\n        \n        def traversal(curr, max_seen_so_far):\n            if not curr:\n                return\n            if curr.val >= max_seen_so_far:\n                self.ans += 1\n            curr_max = max(max_seen_so_far, curr.val)\n            traversal(curr.left, curr_max)\n            traversal(curr.right, curr_max)\n        \n        traversal(root, float('-inf'))\n        return self.ans\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 ans = 0;  \n    public void traversal(TreeNode curr, int maxSeenSoFar) {\n        if (curr == null) return;\n        if (curr.val >= maxSeenSoFar) ans++;\n        int currMax = Math.max(maxSeenSoFar, curr.val);\n        traversal(curr.left, currMax);\n        traversal(curr.right, currMax);\n    }\n    public int goodNodes(TreeNode root) {\n        traversal(root, Integer.MIN_VALUE);\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    int ans = 0;\n    void traversal(TreeNode* curr, int maxSeenSoFar) {\n        if (!curr) return;\n        if (curr->val >= maxSeenSoFar) ans++;\n        int currMax = max(maxSeenSoFar, curr->val);\n        traversal(curr->left, currMax);\n        traversal(curr->right, currMax);\n    }  \n    int goodNodes(TreeNode* root) {\n        traversal(root, INT_MIN);\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\">\nint ans = 0;\nvoid traversal(struct TreeNode* curr, int maxSeenSoFar) {\n    if (curr == NULL) return;\n\n    if (curr->val >= maxSeenSoFar) {\n        ans++;\n    }\n    int currMax = (curr->val > maxSeenSoFar) ? curr->val : maxSeenSoFar;\n    traversal(curr->left, currMax);\n    traversal(curr->right, currMax);\n}\nint goodNodes(struct TreeNode* root) {\n    ans = 0;\n    traversal(root, INT_MIN);\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    int ans = 0;\n    public void Traversal(TreeNode curr, int maxSeenSoFar) {\n        if (curr == null) return;\n        if (curr.val >= maxSeenSoFar) ans++;\n        int currMax = Math.Max(maxSeenSoFar, curr.val);\n        Traversal(curr.left, currMax);\n        Traversal(curr.right, currMax);\n    }\n    public int GoodNodes(TreeNode root) {\n        ans = 0;\n        Traversal(root, int.MinValue);\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 root, a node X in the tree is named good if in the path from root to X there are no nodes with a value greater than X. Return the number of good nodes in the binary tree. Examples: Example 1: Input: root = [3,1,4,3,null,1,5] Output: 4 Explanation: Nodes<\/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":[322,260,176,175,211,811,810,174,172,173],"tags":[],"class_list":["post-8909","post","type-post","status-publish","format-standard","category-algorithms-and-data-structures","category-c-c-plus-plus","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\/8909","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=8909"}],"version-history":[{"count":1,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/8909\/revisions"}],"predecessor-version":[{"id":8911,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/8909\/revisions\/8911"}],"wp:attachment":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/media?parent=8909"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/categories?post=8909"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/tags?post=8909"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}