{"id":1021,"date":"2025-09-01T13:53:54","date_gmt":"2025-09-01T08:23:54","guid":{"rendered":"https:\/\/codeanddebug.in\/blog\/?p=1021"},"modified":"2025-09-01T13:53:55","modified_gmt":"2025-09-01T08:23:55","slug":"balanced-binary-tree","status":"publish","type":"post","link":"https:\/\/codeanddebug.in\/blog\/balanced-binary-tree\/","title":{"rendered":"Balanced Binary Tree | Leetcode 110 | Optimal and Slightly Optimal Solutions"},"content":{"rendered":"\n<p>You are given the root of a binary tree. Your task is to determine whether the tree is <strong>height-balanced<\/strong>.<\/p>\n\n\n\n<p>A binary tree is considered <strong>height-balanced<\/strong> if, for every node in the tree:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The height difference between its left and right subtrees is at most 1.<\/li>\n\n\n\n<li>Both left and right subtrees are also height-balanced.<\/li>\n<\/ul>\n\n\n\n<p>Here&#8217;s the [<strong><a href=\"https:\/\/leetcode.com\/problems\/balanced-binary-tree\/description\/\" target=\"_blank\" rel=\"noreferrer noopener\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\"><span style=\"text-decoration: underline;\">Problem Link<\/span><\/mark><\/a><\/strong>] to begin with.<\/p>\n\n\n\n<p><strong>Example 1<\/strong><\/p>\n\n\n\n<div class=\"wp-block-kevinbatdorf-code-block-pro cbp-has-line-numbers\" data-code-block-pro-font-family=\"Code-Pro-JetBrains-Mono\" style=\"font-size:.875rem;font-family:Code-Pro-JetBrains-Mono,ui-monospace,SFMono-Regular,Menlo,Monaco,Consolas,monospace;--cbp-line-number-color:#D4D4D4;--cbp-line-number-width:calc(1 * 0.6 * .875rem);line-height:1.5rem;--cbp-tab-width:2;tab-size:var(--cbp-tab-width, 2)\"><span style=\"display:block;padding:16px 0 0 16px;margin-bottom:-1px;width:100%;text-align:left;background-color:#1E1E1E\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"54\" height=\"14\" viewBox=\"0 0 54 14\"><g fill=\"none\" fill-rule=\"evenodd\" transform=\"translate(1 1)\"><circle cx=\"6\" cy=\"6\" r=\"6\" fill=\"#FF5F56\" stroke=\"#E0443E\" stroke-width=\".5\"><\/circle><circle cx=\"26\" cy=\"6\" r=\"6\" fill=\"#FFBD2E\" stroke=\"#DEA123\" stroke-width=\".5\"><\/circle><circle cx=\"46\" cy=\"6\" r=\"6\" fill=\"#27C93F\" stroke=\"#1AAB29\" stroke-width=\".5\"><\/circle><\/g><\/svg><\/span><span role=\"button\" tabindex=\"0\" data-code=\"Input: root = [3,9,20,null,null,15,7]\n\n        3\n       \/ \\\n      9   20\n         \/  \\\n        15   7\n\nOutput: true\" style=\"color:#D4D4D4;display:none\" aria-label=\"Copy\" class=\"code-block-pro-copy-button\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" style=\"width:24px;height:24px\" fill=\"none\" viewBox=\"0 0 24 24\" stroke=\"currentColor\" stroke-width=\"2\"><path class=\"with-check\" stroke-linecap=\"round\" stroke-linejoin=\"round\" d=\"M9 5H7a2 2 0 00-2 2v12a2 2 0 002 2h10a2 2 0 002-2V7a2 2 0 00-2-2h-2M9 5a2 2 0 002 2h2a2 2 0 002-2M9 5a2 2 0 012-2h2a2 2 0 012 2m-6 9l2 2 4-4\"><\/path><path class=\"without-check\" stroke-linecap=\"round\" stroke-linejoin=\"round\" d=\"M9 5H7a2 2 0 00-2 2v12a2 2 0 002 2h10a2 2 0 002-2V7a2 2 0 00-2-2h-2M9 5a2 2 0 002 2h2a2 2 0 002-2M9 5a2 2 0 012-2h2a2 2 0 012 2\"><\/path><\/svg><\/span><pre class=\"shiki dark-plus\" style=\"background-color: #1E1E1E\" tabindex=\"0\"><code><span class=\"line\"><span style=\"color: #569CD6\">Input<\/span><span style=\"color: #D4D4D4\">: <\/span><span style=\"color: #CE9178\">root = [3,9,20,null,null,15,7]<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">        <\/span><span style=\"color: #B5CEA8\">3<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">       <\/span><span style=\"color: #CE9178\">\/ \\<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">      <\/span><span style=\"color: #CE9178\">9   20<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">         <\/span><span style=\"color: #CE9178\">\/  \\<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">        <\/span><span style=\"color: #CE9178\">15   7<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #569CD6\">Output<\/span><span style=\"color: #D4D4D4\">: <\/span><span style=\"color: #569CD6\">true<\/span><\/span><\/code><\/pre><\/div>\n\n\n\n<p><strong>Example 2<\/strong><\/p>\n\n\n\n<div class=\"wp-block-kevinbatdorf-code-block-pro cbp-has-line-numbers\" data-code-block-pro-font-family=\"Code-Pro-JetBrains-Mono\" style=\"font-size:.875rem;font-family:Code-Pro-JetBrains-Mono,ui-monospace,SFMono-Regular,Menlo,Monaco,Consolas,monospace;--cbp-line-number-color:#D4D4D4;--cbp-line-number-width:calc(2 * 0.6 * .875rem);line-height:1.5rem;--cbp-tab-width:2;tab-size:var(--cbp-tab-width, 2)\"><span style=\"display:block;padding:16px 0 0 16px;margin-bottom:-1px;width:100%;text-align:left;background-color:#1E1E1E\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"54\" height=\"14\" viewBox=\"0 0 54 14\"><g fill=\"none\" fill-rule=\"evenodd\" transform=\"translate(1 1)\"><circle cx=\"6\" cy=\"6\" r=\"6\" fill=\"#FF5F56\" stroke=\"#E0443E\" stroke-width=\".5\"><\/circle><circle cx=\"26\" cy=\"6\" r=\"6\" fill=\"#FFBD2E\" stroke=\"#DEA123\" stroke-width=\".5\"><\/circle><circle cx=\"46\" cy=\"6\" r=\"6\" fill=\"#27C93F\" stroke=\"#1AAB29\" stroke-width=\".5\"><\/circle><\/g><\/svg><\/span><span role=\"button\" tabindex=\"0\" data-code=\"Input: root = [1,2,2,3,3,null,null,4,4]\n\n        1\n       \/ \\\n      2   2\n     \/ \\\n    3   3\n   \/ \\\n  4   4\n\nOutput: false\nExplanation: The left subtree has height 3 more than the right subtree, so it is unbalanced.\" style=\"color:#D4D4D4;display:none\" aria-label=\"Copy\" class=\"code-block-pro-copy-button\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" style=\"width:24px;height:24px\" fill=\"none\" viewBox=\"0 0 24 24\" stroke=\"currentColor\" stroke-width=\"2\"><path class=\"with-check\" stroke-linecap=\"round\" stroke-linejoin=\"round\" d=\"M9 5H7a2 2 0 00-2 2v12a2 2 0 002 2h10a2 2 0 002-2V7a2 2 0 00-2-2h-2M9 5a2 2 0 002 2h2a2 2 0 002-2M9 5a2 2 0 012-2h2a2 2 0 012 2m-6 9l2 2 4-4\"><\/path><path class=\"without-check\" stroke-linecap=\"round\" stroke-linejoin=\"round\" d=\"M9 5H7a2 2 0 00-2 2v12a2 2 0 002 2h10a2 2 0 002-2V7a2 2 0 00-2-2h-2M9 5a2 2 0 002 2h2a2 2 0 002-2M9 5a2 2 0 012-2h2a2 2 0 012 2\"><\/path><\/svg><\/span><pre class=\"shiki dark-plus\" style=\"background-color: #1E1E1E\" tabindex=\"0\"><code><span class=\"line\"><span style=\"color: #569CD6\">Input<\/span><span style=\"color: #D4D4D4\">: <\/span><span style=\"color: #CE9178\">root = [1,2,2,3,3,null,null,4,4]<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">        <\/span><span style=\"color: #B5CEA8\">1<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">       <\/span><span style=\"color: #CE9178\">\/ \\<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">      <\/span><span style=\"color: #CE9178\">2   2<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">     <\/span><span style=\"color: #CE9178\">\/ \\<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">    <\/span><span style=\"color: #CE9178\">3   3<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">   <\/span><span style=\"color: #CE9178\">\/ \\<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">  <\/span><span style=\"color: #CE9178\">4   4<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #569CD6\">Output<\/span><span style=\"color: #D4D4D4\">: <\/span><span style=\"color: #569CD6\">false<\/span><\/span>\n<span class=\"line\"><span style=\"color: #569CD6\">Explanation<\/span><span style=\"color: #D4D4D4\">: <\/span><span style=\"color: #CE9178\">The left subtree has height 3 more than the right subtree, so it is unbalanced.<\/span><\/span><\/code><\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Intuition and Approach<\/h2>\n\n\n\n<p>To check if a tree is balanced:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Compute the height of left and right subtrees for each node.<\/li>\n\n\n\n<li>If the absolute difference of heights is greater than 1, the tree is not balanced.<\/li>\n\n\n\n<li>To make this efficient, use a special return value <code>-1<\/code> to signal imbalance. This allows early termination, avoiding unnecessary work.<\/li>\n<\/ol>\n\n\n\n<p>We\u2019ll look at two versions:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Optimal solution<\/strong> \u2013 Computes left and right heights, then checks balance.<\/li>\n\n\n\n<li><strong>Slightly optimal solution<\/strong> \u2013 Adds a pruning step by checking left first, and only if it is balanced proceeds to check right.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Optimal Solution<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Code Implementation<\/h3>\n\n\n\n<div class=\"wp-block-kevinbatdorf-code-block-pro cbp-has-line-numbers\" data-code-block-pro-font-family=\"Code-Pro-JetBrains-Mono\" style=\"font-size:.875rem;font-family:Code-Pro-JetBrains-Mono,ui-monospace,SFMono-Regular,Menlo,Monaco,Consolas,monospace;--cbp-line-number-color:#D4D4D4;--cbp-line-number-width:calc(2 * 0.6 * .875rem);line-height:1.5rem;--cbp-tab-width:2;tab-size:var(--cbp-tab-width, 2)\"><span style=\"display:block;padding:16px 0 0 16px;margin-bottom:-1px;width:100%;text-align:left;background-color:#1E1E1E\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"54\" height=\"14\" viewBox=\"0 0 54 14\"><g fill=\"none\" fill-rule=\"evenodd\" transform=\"translate(1 1)\"><circle cx=\"6\" cy=\"6\" r=\"6\" fill=\"#FF5F56\" stroke=\"#E0443E\" stroke-width=\".5\"><\/circle><circle cx=\"26\" cy=\"6\" r=\"6\" fill=\"#FFBD2E\" stroke=\"#DEA123\" stroke-width=\".5\"><\/circle><circle cx=\"46\" cy=\"6\" r=\"6\" fill=\"#27C93F\" stroke=\"#1AAB29\" stroke-width=\".5\"><\/circle><\/g><\/svg><\/span><span role=\"button\" tabindex=\"0\" data-code=\"class Solution:\n    def solve(self, node):\n        if node is None:\n            return 0\n        leftH = self.solve(node.left)\n        rightH = self.solve(node.right)\n        if leftH == -1 or rightH == -1:\n            return -1\n        if abs(leftH - rightH) &gt; 1:\n            return -1\n        return 1 + max(leftH, rightH)\n\n    def isBalanced(self, root: Optional[TreeNode]) -&gt; bool:\n        height = self.solve(root)\n        if height == -1:\n            return False\n        return True\" style=\"color:#D4D4D4;display:none\" aria-label=\"Copy\" class=\"code-block-pro-copy-button\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" style=\"width:24px;height:24px\" fill=\"none\" viewBox=\"0 0 24 24\" stroke=\"currentColor\" stroke-width=\"2\"><path class=\"with-check\" stroke-linecap=\"round\" stroke-linejoin=\"round\" d=\"M9 5H7a2 2 0 00-2 2v12a2 2 0 002 2h10a2 2 0 002-2V7a2 2 0 00-2-2h-2M9 5a2 2 0 002 2h2a2 2 0 002-2M9 5a2 2 0 012-2h2a2 2 0 012 2m-6 9l2 2 4-4\"><\/path><path class=\"without-check\" stroke-linecap=\"round\" stroke-linejoin=\"round\" d=\"M9 5H7a2 2 0 00-2 2v12a2 2 0 002 2h10a2 2 0 002-2V7a2 2 0 00-2-2h-2M9 5a2 2 0 002 2h2a2 2 0 002-2M9 5a2 2 0 012-2h2a2 2 0 012 2\"><\/path><\/svg><\/span><pre class=\"shiki dark-plus\" style=\"background-color: #1E1E1E\" tabindex=\"0\"><code><span class=\"line\"><span style=\"color: #569CD6\">class<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #4EC9B0\">Solution<\/span><span style=\"color: #D4D4D4\">:<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">    <\/span><span style=\"color: #569CD6\">def<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #DCDCAA\">solve<\/span><span style=\"color: #D4D4D4\">(<\/span><span style=\"color: #9CDCFE\">self<\/span><span style=\"color: #D4D4D4\">, <\/span><span style=\"color: #9CDCFE\">node<\/span><span style=\"color: #D4D4D4\">):<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">        <\/span><span style=\"color: #C586C0\">if<\/span><span style=\"color: #D4D4D4\"> node <\/span><span style=\"color: #569CD6\">is<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #569CD6\">None<\/span><span style=\"color: #D4D4D4\">:<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">            <\/span><span style=\"color: #C586C0\">return<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #B5CEA8\">0<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">        leftH = <\/span><span style=\"color: #569CD6\">self<\/span><span style=\"color: #D4D4D4\">.solve(node.left)<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">        rightH = <\/span><span style=\"color: #569CD6\">self<\/span><span style=\"color: #D4D4D4\">.solve(node.right)<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">        <\/span><span style=\"color: #C586C0\">if<\/span><span style=\"color: #D4D4D4\"> leftH == -<\/span><span style=\"color: #B5CEA8\">1<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #569CD6\">or<\/span><span style=\"color: #D4D4D4\"> rightH == -<\/span><span style=\"color: #B5CEA8\">1<\/span><span style=\"color: #D4D4D4\">:<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">            <\/span><span style=\"color: #C586C0\">return<\/span><span style=\"color: #D4D4D4\"> -<\/span><span style=\"color: #B5CEA8\">1<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">        <\/span><span style=\"color: #C586C0\">if<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #DCDCAA\">abs<\/span><span style=\"color: #D4D4D4\">(leftH - rightH) &gt; <\/span><span style=\"color: #B5CEA8\">1<\/span><span style=\"color: #D4D4D4\">:<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">            <\/span><span style=\"color: #C586C0\">return<\/span><span style=\"color: #D4D4D4\"> -<\/span><span style=\"color: #B5CEA8\">1<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">        <\/span><span style=\"color: #C586C0\">return<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #B5CEA8\">1<\/span><span style=\"color: #D4D4D4\"> + <\/span><span style=\"color: #DCDCAA\">max<\/span><span style=\"color: #D4D4D4\">(leftH, rightH)<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">    <\/span><span style=\"color: #569CD6\">def<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #DCDCAA\">isBalanced<\/span><span style=\"color: #D4D4D4\">(<\/span><span style=\"color: #9CDCFE\">self<\/span><span style=\"color: #D4D4D4\">, <\/span><span style=\"color: #9CDCFE\">root<\/span><span style=\"color: #D4D4D4\">: Optional[TreeNode]) -&gt; <\/span><span style=\"color: #4EC9B0\">bool<\/span><span style=\"color: #D4D4D4\">:<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">        height = <\/span><span style=\"color: #569CD6\">self<\/span><span style=\"color: #D4D4D4\">.solve(root)<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">        <\/span><span style=\"color: #C586C0\">if<\/span><span style=\"color: #D4D4D4\"> height == -<\/span><span style=\"color: #B5CEA8\">1<\/span><span style=\"color: #D4D4D4\">:<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">            <\/span><span style=\"color: #C586C0\">return<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #569CD6\">False<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">        <\/span><span style=\"color: #C586C0\">return<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #569CD6\">True<\/span><\/span><\/code><\/pre><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Code Explanation<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Base case: If the node is <code>None<\/code>, its height is 0.<\/li>\n\n\n\n<li>Recursively compute <code>leftH<\/code> and <code>rightH<\/code>.<\/li>\n\n\n\n<li>If either subtree is unbalanced (returns <code>-1<\/code>), propagate <code>-1<\/code> upwards.<\/li>\n\n\n\n<li>If the absolute difference of <code>leftH<\/code> and <code>rightH<\/code> exceeds 1, return <code>-1<\/code> to mark unbalance.<\/li>\n\n\n\n<li>Otherwise, return the actual height <code>1 + max(leftH, rightH)<\/code>.<\/li>\n\n\n\n<li><code>isBalanced(root)<\/code> checks the root result. If <code>-1<\/code>, return <code>False<\/code>, else return <code>True<\/code>.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Slightly Optimal Solution<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Code Implementation<\/h3>\n\n\n\n<div class=\"wp-block-kevinbatdorf-code-block-pro cbp-has-line-numbers\" data-code-block-pro-font-family=\"Code-Pro-JetBrains-Mono\" style=\"font-size:.875rem;font-family:Code-Pro-JetBrains-Mono,ui-monospace,SFMono-Regular,Menlo,Monaco,Consolas,monospace;--cbp-line-number-color:#D4D4D4;--cbp-line-number-width:calc(2 * 0.6 * .875rem);line-height:1.5rem;--cbp-tab-width:2;tab-size:var(--cbp-tab-width, 2)\"><span style=\"display:block;padding:16px 0 0 16px;margin-bottom:-1px;width:100%;text-align:left;background-color:#1E1E1E\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"54\" height=\"14\" viewBox=\"0 0 54 14\"><g fill=\"none\" fill-rule=\"evenodd\" transform=\"translate(1 1)\"><circle cx=\"6\" cy=\"6\" r=\"6\" fill=\"#FF5F56\" stroke=\"#E0443E\" stroke-width=\".5\"><\/circle><circle cx=\"26\" cy=\"6\" r=\"6\" fill=\"#FFBD2E\" stroke=\"#DEA123\" stroke-width=\".5\"><\/circle><circle cx=\"46\" cy=\"6\" r=\"6\" fill=\"#27C93F\" stroke=\"#1AAB29\" stroke-width=\".5\"><\/circle><\/g><\/svg><\/span><span role=\"button\" tabindex=\"0\" data-code=\"class Solution:\n    def solve(self, node):\n        if node is None:\n            return 0\n        leftH = self.solve(node.left)\n        if leftH == -1:\n            return -1\n        rightH = self.solve(node.right)\n        if rightH == -1:\n            return -1\n        if abs(leftH - rightH) &gt; 1:\n            return -1\n        return 1 + max(leftH, rightH)\n\n    def isBalanced(self, root: Optional[TreeNode]) -&gt; bool:\n        height = self.solve(root)\n        if height == -1:\n            return False\n        return True\" style=\"color:#D4D4D4;display:none\" aria-label=\"Copy\" class=\"code-block-pro-copy-button\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" style=\"width:24px;height:24px\" fill=\"none\" viewBox=\"0 0 24 24\" stroke=\"currentColor\" stroke-width=\"2\"><path class=\"with-check\" stroke-linecap=\"round\" stroke-linejoin=\"round\" d=\"M9 5H7a2 2 0 00-2 2v12a2 2 0 002 2h10a2 2 0 002-2V7a2 2 0 00-2-2h-2M9 5a2 2 0 002 2h2a2 2 0 002-2M9 5a2 2 0 012-2h2a2 2 0 012 2m-6 9l2 2 4-4\"><\/path><path class=\"without-check\" stroke-linecap=\"round\" stroke-linejoin=\"round\" d=\"M9 5H7a2 2 0 00-2 2v12a2 2 0 002 2h10a2 2 0 002-2V7a2 2 0 00-2-2h-2M9 5a2 2 0 002 2h2a2 2 0 002-2M9 5a2 2 0 012-2h2a2 2 0 012 2\"><\/path><\/svg><\/span><pre class=\"shiki dark-plus\" style=\"background-color: #1E1E1E\" tabindex=\"0\"><code><span class=\"line\"><span style=\"color: #569CD6\">class<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #4EC9B0\">Solution<\/span><span style=\"color: #D4D4D4\">:<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">    <\/span><span style=\"color: #569CD6\">def<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #DCDCAA\">solve<\/span><span style=\"color: #D4D4D4\">(<\/span><span style=\"color: #9CDCFE\">self<\/span><span style=\"color: #D4D4D4\">, <\/span><span style=\"color: #9CDCFE\">node<\/span><span style=\"color: #D4D4D4\">):<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">        <\/span><span style=\"color: #C586C0\">if<\/span><span style=\"color: #D4D4D4\"> node <\/span><span style=\"color: #569CD6\">is<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #569CD6\">None<\/span><span style=\"color: #D4D4D4\">:<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">            <\/span><span style=\"color: #C586C0\">return<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #B5CEA8\">0<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">        leftH = <\/span><span style=\"color: #569CD6\">self<\/span><span style=\"color: #D4D4D4\">.solve(node.left)<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">        <\/span><span style=\"color: #C586C0\">if<\/span><span style=\"color: #D4D4D4\"> leftH == -<\/span><span style=\"color: #B5CEA8\">1<\/span><span style=\"color: #D4D4D4\">:<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">            <\/span><span style=\"color: #C586C0\">return<\/span><span style=\"color: #D4D4D4\"> -<\/span><span style=\"color: #B5CEA8\">1<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">        rightH = <\/span><span style=\"color: #569CD6\">self<\/span><span style=\"color: #D4D4D4\">.solve(node.right)<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">        <\/span><span style=\"color: #C586C0\">if<\/span><span style=\"color: #D4D4D4\"> rightH == -<\/span><span style=\"color: #B5CEA8\">1<\/span><span style=\"color: #D4D4D4\">:<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">            <\/span><span style=\"color: #C586C0\">return<\/span><span style=\"color: #D4D4D4\"> -<\/span><span style=\"color: #B5CEA8\">1<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">        <\/span><span style=\"color: #C586C0\">if<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #DCDCAA\">abs<\/span><span style=\"color: #D4D4D4\">(leftH - rightH) &gt; <\/span><span style=\"color: #B5CEA8\">1<\/span><span style=\"color: #D4D4D4\">:<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">            <\/span><span style=\"color: #C586C0\">return<\/span><span style=\"color: #D4D4D4\"> -<\/span><span style=\"color: #B5CEA8\">1<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">        <\/span><span style=\"color: #C586C0\">return<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #B5CEA8\">1<\/span><span style=\"color: #D4D4D4\"> + <\/span><span style=\"color: #DCDCAA\">max<\/span><span style=\"color: #D4D4D4\">(leftH, rightH)<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">    <\/span><span style=\"color: #569CD6\">def<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #DCDCAA\">isBalanced<\/span><span style=\"color: #D4D4D4\">(<\/span><span style=\"color: #9CDCFE\">self<\/span><span style=\"color: #D4D4D4\">, <\/span><span style=\"color: #9CDCFE\">root<\/span><span style=\"color: #D4D4D4\">: Optional[TreeNode]) -&gt; <\/span><span style=\"color: #4EC9B0\">bool<\/span><span style=\"color: #D4D4D4\">:<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">        height = <\/span><span style=\"color: #569CD6\">self<\/span><span style=\"color: #D4D4D4\">.solve(root)<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">        <\/span><span style=\"color: #C586C0\">if<\/span><span style=\"color: #D4D4D4\"> height == -<\/span><span style=\"color: #B5CEA8\">1<\/span><span style=\"color: #D4D4D4\">:<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">            <\/span><span style=\"color: #C586C0\">return<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #569CD6\">False<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">        <\/span><span style=\"color: #C586C0\">return<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #569CD6\">True<\/span><\/span><\/code><\/pre><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Code Explanation<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>This version prunes earlier.<\/li>\n\n\n\n<li>If the left subtree is already unbalanced (<code>-1<\/code>), it does not bother computing the right subtree.<\/li>\n\n\n\n<li>Similarly, if the right is unbalanced, it exits early.<\/li>\n\n\n\n<li>This saves unnecessary recursive calls when imbalance is found in large trees.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Time and Space Complexity<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Time Complexity (both versions):<\/strong><br>Each node is visited once, and at each node we do constant work.<br>So time is <strong>O(N)<\/strong>, where <code>N<\/code> is the number of nodes.<\/li>\n\n\n\n<li><strong>Space Complexity:<\/strong><br>The space is due to recursion depth. In the worst case (skewed tree), it can be <strong>O(N)<\/strong>.<br>In the best case (balanced tree), it is <strong>O(log N)<\/strong>.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Conclusion<\/h2>\n\n\n\n<p>The <strong>Balanced Binary Tree<\/strong> problem is solved by combining height calculation with an early unbalance detection mechanism:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The <strong>optimal solution<\/strong> calculates both left and right subtree heights first.<\/li>\n\n\n\n<li>The <strong>slightly optimal solution<\/strong> improves efficiency by pruning unnecessary checks as soon as imbalance is detected.<\/li>\n<\/ul>\n\n\n\n<p>Both approaches run in <strong>O(N)<\/strong> time and ensure early stopping when imbalance is found, making them efficient in practice.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<div class=\"wp-block-buttons is-content-justification-center is-layout-flex wp-container-core-buttons-is-layout-16018d1d wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link wp-element-button\" href=\"https:\/\/codeanddebug.in\/course\/zero-to-hero-python-dsa\" target=\"_blank\" rel=\"noreferrer noopener\">Join our Advance DSA COURSE<\/a><\/div>\n<\/div>\n\n\n\n<p><em>For any changes to the article, kindly email at <a href=\"mailto:code@codeanddebug.in\" target=\"_blank\" rel=\"noreferrer noopener\">code@codeanddebug.in<\/a> or contact us at <a href=\"tel:+91-9712928220\" target=\"_blank\" rel=\"noreferrer noopener\">+91-9712928220<\/a>.<\/em><\/p>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>You are given the root of a binary tree. Your task is to determine whether the tree is height-balanced. A binary tree is considered height-balanced if, for every node in the tree: Here&#8217;s the [Problem Link] to begin with. Example 1 Example 2 Intuition and Approach To check if a tree is balanced: We\u2019ll look<\/p>\n","protected":false},"author":1,"featured_media":1022,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3,4],"tags":[14,8],"class_list":{"0":"post-1021","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-data-structures-and-algorithm","8":"category-beginner","9":"tag-binary-trees","10":"tag-easy"},"featured_image_src":"https:\/\/codeanddebug.in\/blog\/wp-content\/uploads\/2025\/09\/balanced-binary-tree-featured-image.png","author_info":{"display_name":"codeanddebug","author_link":"https:\/\/codeanddebug.in\/blog\/author\/codeanddebug\/"},"_links":{"self":[{"href":"https:\/\/codeanddebug.in\/blog\/wp-json\/wp\/v2\/posts\/1021","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/codeanddebug.in\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/codeanddebug.in\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/codeanddebug.in\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/codeanddebug.in\/blog\/wp-json\/wp\/v2\/comments?post=1021"}],"version-history":[{"count":2,"href":"https:\/\/codeanddebug.in\/blog\/wp-json\/wp\/v2\/posts\/1021\/revisions"}],"predecessor-version":[{"id":1024,"href":"https:\/\/codeanddebug.in\/blog\/wp-json\/wp\/v2\/posts\/1021\/revisions\/1024"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/codeanddebug.in\/blog\/wp-json\/wp\/v2\/media\/1022"}],"wp:attachment":[{"href":"https:\/\/codeanddebug.in\/blog\/wp-json\/wp\/v2\/media?parent=1021"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/codeanddebug.in\/blog\/wp-json\/wp\/v2\/categories?post=1021"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/codeanddebug.in\/blog\/wp-json\/wp\/v2\/tags?post=1021"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}