{"id":8419,"date":"2025-07-29T21:38:06","date_gmt":"2025-07-29T16:08:06","guid":{"rendered":"https:\/\/namastedev.com\/blog\/?p=8419"},"modified":"2025-07-29T21:40:30","modified_gmt":"2025-07-29T16:10:30","slug":"level-order-traversal-recursive","status":"publish","type":"post","link":"https:\/\/namastedev.com\/blog\/level-order-traversal-recursive\/","title":{"rendered":"Level Order Traversal Recursive"},"content":{"rendered":"\n<!-- Level Order Traversal - REcursive Approach -->\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\n        <p>Given the <code>root<\/code> of a binary tree, return <i>the level order traversal of its nodes&#8217; values.<\/i>. (i.e., from left to right, level by level).\n        <\/p>\n                <h2>Examples:<\/h2>\n                <h3>Example 1:<\/h3>\n                <p>\n                  <img decoding=\"async\" src=\"https:\/\/namastedev.com\/blog\/wp-content\/uploads\/2025\/07\/Screenshot-2025-07-29-at-11.55.37\u202fAM.png\" alt=\"\">\n                <\/p>\n                <p><strong>Input:<\/strong> root = [3,9,20,null,null,15,7]<\/p>\n                <p><strong>Output:<\/strong> [[3],[9,20],[15,7]]<\/p>\n\n                <h3>Example 2:<\/h3>\n                <p><strong>Input:<\/strong> root = [1]<\/p>\n                <p><strong>Output:<\/strong> [[1]]<\/p>\n                <strong>Explanation:<\/strong>\n                <h3>Example 3:<\/h3>\n                <p><strong>Input:<\/strong> root = []<\/p>\n                <p><strong>Output:<\/strong> []<\/p>\n\n                    <h2>Constraints:<\/h2>\n                    <ul>\n                      <li>The number of nodes in the tree is in the range <code>[0, 100]<\/code>.<\/li>\n                      <li><code>-100 <= Node.val <= 100<\/code><\/li>\n                    <\/ul>\n\n                <h2>Approach<\/h2>\n                <ul>\n                  <li>Use <strong>Depth-First Search<\/strong> (DFS) with <code>recursion<\/code> to traverse the binary tree.<\/li>\n                  <li>Maintain an ans <code>array<\/code> where each index represents a level of the tree.<\/li>\n                  <li><strong>At each node: <\/strong>\n                    <ul>\n                      <li>If the <code>current level<\/code> doesn't exist in <code>ans<\/code>, create a new sub-array.<\/li>\n                      <li>Push the current node's value to the corresponding level in <code>ans<\/code>.<\/li>\n                      <li>Recursively <strong>call the function<\/strong> for the left and right children, increasing the <code>level by 1<\/code>.<\/li>\n                    <\/ul>\n                  <\/li>\n                  <li>Finally, return the <code>ans<\/code> array containing level-wise node values.<\/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   <!-- dry run -->\n <h2>Dry Run<\/h2> \n<div style=\"background: #f9f9f9; border-left: 4px solid var(--primary); padding: 1rem; border-radius: var(--tab-radius); margin: 1rem 0;\"> \n  <p><strong>Input:<\/strong> <code>root = [1, 2, 3, null, 4]<\/code><\/p> \n  <pre style=\"white-space: pre-wrap; background: #fff5ea; padding: 1rem; border-radius: 8px; overflow-x: auto;\"> \nTree Structure: \n        1\n       \/ \\\n      2   3\n       \\\n        4\n\nInitialize:\nans = []\n\nCall traversal(root, 0)\n\u2192 curr = 1, level = 0\n\u2192 ans[0] doesn't exist \u2192 initialize as [] \u2192 ans = [[]]\n\u2192 ans[0].push(1) \u2192 ans = [[1]]\n\u2192 curr.left = 2 \u2192 call traversal(2, 1)\n\n  \u2192 curr = 2, level = 1\n  \u2192 ans[1] doesn't exist \u2192 initialize as [] \u2192 ans = [[1], []]\n  \u2192 ans[1].push(2) \u2192 ans = [[1], [2]]\n  \u2192 curr.left = null \u2192 no call\n  \u2192 curr.right = 4 \u2192 call traversal(4, 2)\n\n    \u2192 curr = 4, level = 2\n    \u2192 ans[2] doesn't exist \u2192 initialize as [] \u2192 ans = [[1], [2], []]\n    \u2192 ans[2].push(4) \u2192 ans = [[1], [2], [4]]\n    \u2192 curr.left = null \u2192 no call\n    \u2192 curr.right = null \u2192 no call\n\n\u2192 Back to curr = 2 \u2192 finished\n\n\u2192 Back to curr = 1\n\u2192 curr.right = 3 \u2192 call traversal(3, 1)\n\n  \u2192 curr = 3, level = 1\n  \u2192 ans[1] exists \u2192 ans[1].push(3) \u2192 ans = [[1], [2, 3], [4]]\n  \u2192 curr.left = null \u2192 no call\n  \u2192 curr.right = null \u2192 no call\n\n\u2192 Back to curr = 1 \u2192 finished\n\nTraversal complete.\nFinal ans: [[1], [2, 3], [4]]\n<\/pre> \n  <p><strong>Output:<\/strong> <code>Result: [[1], [2, 3], [4]]<\/code><\/p> \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 levelOrder = function(root) {\n    if(!root) return [];\n    let ans = [];\n    let traversal = (curr, level) => {\n        if(!ans[level]) ans[level] = [];\n        ans[level].push(curr.val);\n        curr.left && traversal(curr.left, level + 1);\n        curr.right && traversal(curr.right, level + 1);\n    }\n    traversal(root, 0);\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 levelOrder(self, root):\n        ans = []\n        def dfs(node, level):\n            if not node:\n                return\n            if len(ans) == level:\n                ans.append([])\n            ans[level].append(node.val)\n            dfs(node.left, level + 1)\n            dfs(node.right, level + 1)\n        dfs(root, 0)\n        return 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    public List<List<Integer>> levelOrder(TreeNode root) {\n        List<List<Integer>> ans = new ArrayList<>();\n        dfs(root, 0, ans);\n        return ans;\n    }\n    private void dfs(TreeNode node, int level, List<List<Integer>> ans) {\n        if (node == null) return;\n        if (ans.size() == level) {\n            ans.add(new ArrayList<>());\n        }\n        ans.get(level).add(node.val);\n        dfs(node.left, level + 1, ans);\n        dfs(node.right, level + 1, 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    void dfs(TreeNode* node, int level, vector<vector<int>>& ans) {\n        if (!node) return;\n        if (ans.size() == level) ans.push_back({});\n        ans[level].push_back(node->val);\n        dfs(node->left, level + 1, ans);\n        dfs(node->right, level + 1, ans);\n    }\n\n    vector<vector<int>> levelOrder(TreeNode* root) {\n        vector<vector<int>> ans;\n        dfs(root, 0, ans);\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\">\n#include &lt;stdio.h&gt;\n#include &lt;stdlib.h&gt;\n#define MAX_LEVELS 100\n#define MAX_NODES_PER_LEVEL 100\ntypedef struct TreeNode {\n    int val;\n    struct TreeNode* left;\n    struct TreeNode* right;\n} TreeNode;\nint ans[MAX_LEVELS][MAX_NODES_PER_LEVEL];\nint count[MAX_LEVELS] = {0};\nvoid dfs(TreeNode* node, int level) {\n    if (!node) return;\n    ans[level][count[level]++] = node->val;\n    dfs(node->left, level + 1);\n    dfs(node->right, level + 1);\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    public void DFS(TreeNode node, int level, List<List<int>> ans) {\n        if (node == null) return;\n        if (ans.Count == level) ans.Add(new List<int>());\n        ans[level].Add(node.val);\n        DFS(node.left, level + 1, ans);\n        DFS(node.right, level + 1, ans);\n    }\n    public IList<IList<int>> LevelOrder(TreeNode root) {\n        var ans = new List<IList<int>>();\n        DFS(root, 0, (List<List<int>>)ans);\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 the root of a binary tree, return the level order traversal of its nodes&#8217; values.. (i.e., from left to right, level by level). Examples: Example 1: Input: root = [3,9,20,null,null,15,7] Output: [[3],[9,20],[15,7]] Example 2: Input: root = [1] Output: [[1]] Explanation: Example 3: Input: root = [] Output: [] Constraints: The number<\/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":[260,176,175,211,811,810,174,172,173],"tags":[],"class_list":["post-8419","post","type-post","status-publish","format-standard","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\/8419","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=8419"}],"version-history":[{"count":1,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/8419\/revisions"}],"predecessor-version":[{"id":8420,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/8419\/revisions\/8420"}],"wp:attachment":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/media?parent=8419"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/categories?post=8419"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/tags?post=8419"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}