{"id":8934,"date":"2025-08-04T15:44:00","date_gmt":"2025-08-04T10:14:00","guid":{"rendered":"https:\/\/namastedev.com\/blog\/?p=8934"},"modified":"2025-08-04T15:45:25","modified_gmt":"2025-08-04T10:15:25","slug":"binary-tree-maximum-path-sum","status":"publish","type":"post","link":"https:\/\/namastedev.com\/blog\/binary-tree-maximum-path-sum\/","title":{"rendered":"Binary Tree Maximum Path Sum"},"content":{"rendered":"\n<!-- Max Path: 26 -->\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>A <strong>path<\/strong> in a binary tree is a sequence of nodes where each pair of adjacent nodes in the sequence has an edge connecting them. A node can only appear in the sequence <strong>at most once<\/strong>. Note that the path does not need to pass through the root.<\/p>\n\n        <p>The <strong>path sum<\/strong> of a path is the sum of the node&#8217;s values in the path.<\/p>\n\n        <p>Given the <code>root<\/code> of a binary tree, return the <i>maximum <strong>path sum<\/strong> of any <strong>non-empty<\/strong> path.<\/i><\/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-2025-08-04-at-3.38.01\u202fPM.png\" alt=\"\">\n                <p><strong>Input:<\/strong> root = [1,2,3]<\/p>\n                <p><strong>Output:<\/strong> 6<\/p>\n                <p><strong>Explanation:<\/strong> The optimal path is 2 -> 1 -> 3 with a path sum of 2 + 1 + 3 = 6.<\/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-3.38.56\u202fPM.png\" alt=\"\">\n                <p><strong>Input:<\/strong> root = [-10,9,20,null,null,15,7]<\/p>\n                <p><strong>Output:<\/strong> 42<\/p>\n                <p><strong>Explanation:<\/strong> The optimal path is 15 -> 20 -> 7 with a path sum of 15 + 20 + 7 = 42.<\/p>\n\n                    <h2>Constraints:<\/h2>\n                    <ul>\n                        <li>The number of nodes in the tree is in the range <code>[1, 3 * 10<sup>4<\/sup>]<\/code>.<\/li>\n                        <li><code>-1000 <= Node.val <= 1000<\/code><\/li>\n                    <\/ul>\n\n                <h2>Approach<\/h2>\n               <ul>\n                <li>At each node, calculate:\n                    <ul>\n                        <li><code>maxLeft<\/code>: max gain from the left subtree (0 if negative)<\/li>\n                        <li><code>maxRight<\/code>: max gain from the right subtree (0 if negative)<\/li>\n                    <\/ul>\n                <\/li>\n\n                <li>The <strong>local max path<\/strong> passing through current node is: <code>curr.val + maxLeft + maxRight<\/code><\/li>\n                <li>Update the <strong>global max sum<\/strong> (<code>maxSumPath<\/code>) with the local max.<\/li>\n                <li>Return the <strong>max gain<\/strong> to the parent node: <code>curr.val + max(maxLeft, maxRight)<\/code><\/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>(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> maxPathSum(root) where<br> root = Node(1)<br> \u251c\u2500\u2500 left: Node(2)<br> \u2502\u00a0\u00a0 \u251c\u2500\u2500 left: Node(4)<br> \u2502\u00a0\u00a0 \u2514\u2500\u2500 right: Node(5)<br> \u2514\u2500\u2500 right: Node(3)<br> &nbsp;&nbsp;&nbsp;&nbsp;\u251c\u2500\u2500 left: Node(6)<br> &nbsp;&nbsp;&nbsp;&nbsp;\u2514\u2500\u2500 right: Node(7)<br><br>\n<b>Step 1:<\/b><br>\n\u2192 Call traversal(curr = 1)<br>\n\u2192 Call traversal(curr = 2)<br>\n\u2192 Call traversal(curr = 4)<br>\n\u2192 traversal(curr.left) = 0 (null)<br>\n\u2192 traversal(curr.right) = 0 (null)<br>\n\u2192 currMax = 4 + 0 + 0 = 4<br>\n\u2192 maxSumPath = max(-Infinity, 4) = 4<br>\n\u2192 return 4<br><br>\n\u2192 Call traversal(curr = 5)<br>\n\u2192 traversal(curr.left) = 0 (null)<br>\n\u2192 traversal(curr.right) = 0 (null)<br>\n\u2192 currMax = 5 + 0 + 0 = 5<br>\n\u2192 maxSumPath = max(4, 5) = 5<br>\n\u2192 return 5<br><br>\n\n\u2192 Now at curr = 2<br>\n\u2192 maxLeft = 4, maxRight = 5<br>\n\u2192 currMax = 2 + 4 + 5 = 11<br>\n\u2192 maxSumPath = max(5, 11) = 11<br>\n\u2192 return 2 + max(4, 5) = 7<br><br>\n\n\u2192 Call traversal(curr = 3)<br>\n\u2192 Call traversal(curr = 6)<br>\n\u2192 traversal(curr.left) = 0 (null)<br>\n\u2192 traversal(curr.right) = 0 (null)<br>\n\u2192 currMax = 6 + 0 + 0 = 6<br>\n\u2192 maxSumPath = max(11, 6) = 11<br>\n\u2192 return 6<br><br>\n\n\u2192 Call traversal(curr = 7)<br>\n\u2192 traversal(curr.left) = 0 (null)<br>\n\u2192 traversal(curr.right) = 0 (null)<br>\n\u2192 currMax = 7 + 0 + 0 = 7<br>\n\u2192 maxSumPath = max(11, 7) = 11<br>\n\u2192 return 7<br><br>\n\n\u2192 Now at curr = 3<br>\n\u2192 maxLeft = 6, maxRight = 7<br>\n\u2192 currMax = 3 + 6 + 7 = 16<br>\n\u2192 maxSumPath = max(11, 16) = 16<br>\n\u2192 return 3 + max(6, 7) = 10<br><br>\n\n\u2192 Back at root = 1<br>\n\u2192 maxLeft = 7, maxRight = 10<br>\n\u2192 currMax = 1 + 7 + 10 = 18<br>\n\u2192 maxSumPath = max(16, 18) = 18<br>\n\u2192 return 1 + max(7, 10) = 11<br><br>\n\n<b>Final Result:<\/b> 18 is the maximum path sum in the binary tree.\n\n<\/div>\n\n\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 maxPathSum = function(root) {\n    let maxSumPath = -Infinity;\n    let traversal = (curr) => {\n        if(!curr) return 0;\n        let maxLeft = Math.max(0, traversal(curr.left));\n        let maxRight = Math.max(0, traversal(curr.right));\n        currMax = curr.val + maxLeft + maxRight;\n        maxSumPath = Math.max(currMax, maxSumPath);\n\n        return curr.val + Math.max(maxLeft, maxRight);\n    }\n    traversal(root);\n    return maxSumPath;\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 maxPathSum(self, root):\n        self.maxSumPath = float('-inf')       \n        def traversal(node):\n            if not node:\n                return 0\n            maxLeft = max(0, traversal(node.left))\n            maxRight = max(0, traversal(node.right))\n            currMax = node.val + maxLeft + maxRight\n            self.maxSumPath = max(self.maxSumPath, currMax)\n            return node.val + max(maxLeft, maxRight)\n        traversal(root)\n        return self.maxSumPath\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    private int maxSumPath = Integer.MIN_VALUE;\n    private int traversal(TreeNode root) {\n        if (root == null) return 0;\n        int maxLeft = Math.max(0, traversal(root.left));\n        int maxRight = Math.max(0, traversal(root.right));\n        int currMax = root.val + maxLeft + maxRight;\n        maxSumPath = Math.max(maxSumPath, currMax);\n        return root.val + Math.max(maxLeft, maxRight);\n    }\n    public int maxPathSum(TreeNode root) {\n        traversal(root);\n        return maxSumPath;\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 maxSumPath = INT_MIN;\n    int traversal(TreeNode* root) {\n        if (!root) return 0;\n        int maxLeft = max(0, traversal(root->left));\n        int maxRight = max(0, traversal(root->right));\n        int currMax = root->val + maxLeft + maxRight;\n        maxSumPath = max(maxSumPath, currMax);\n        return root->val + max(maxLeft, maxRight);\n    }\n    int maxPathSum(TreeNode* root) {\n        traversal(root);\n        return maxSumPath;\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\">\nstruct TreeNode {\n    int val;\n    struct TreeNode *left;\n    struct TreeNode *right;\n};\nint maxSumPath;\nint max(int a, int b) {\n    return (a > b) ? a : b;\n}\nint traversal(struct TreeNode* root) {\n    if (!root) return 0;\n    int maxLeft = max(0, traversal(root->left));\n    int maxRight = max(0, traversal(root->right));\n    int currMax = root->val + maxLeft + maxRight;\n    if (currMax > maxSumPath) maxSumPath = currMax;\n    return root->val + max(maxLeft, maxRight);\n}\nint maxPathSum(struct TreeNode* root) {\n    maxSumPath = INT_MIN;\n    traversal(root);\n    return maxSumPath;\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    private int maxSumPath = int.MinValue;\n    private int Traversal(TreeNode root) {\n        if (root == null) return 0;\n        int maxLeft = Math.Max(0, Traversal(root.left));\n        int maxRight = Math.Max(0, Traversal(root.right));\n        int currMax = root.val + maxLeft + maxRight;\n        maxSumPath = Math.Max(maxSumPath, currMax);\n        return root.val + Math.Max(maxLeft, maxRight);\n    }\n    public int MaxPathSum(TreeNode root) {\n        Traversal(root);\n        return maxSumPath;\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                    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A node can only appear in the sequence at most once. Note that the path does not need to pass through the root. The path sum of a<\/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":{"0":"post-8934","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-algorithms","7":"category-csharp","8":"category-cplusplus","9":"category-data-structures","10":"category-data-structures-and-algorithms","11":"category-dsa","12":"category-java","13":"category-javascript","14":"category-python"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/8934","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=8934"}],"version-history":[{"count":1,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/8934\/revisions"}],"predecessor-version":[{"id":8935,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/8934\/revisions\/8935"}],"wp:attachment":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/media?parent=8934"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/categories?post=8934"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/tags?post=8934"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}