{"id":8404,"date":"2025-07-29T12:02:40","date_gmt":"2025-07-29T06:32:40","guid":{"rendered":"https:\/\/namastedev.com\/blog\/?p=8404"},"modified":"2026-06-16T12:53:28","modified_gmt":"2026-06-16T07:23:28","slug":"level-order-traversal-queue-bfs","status":"publish","type":"post","link":"https:\/\/namastedev.com\/blog\/level-order-traversal-queue-bfs\/","title":{"rendered":"Level Order Traversal Queue BFS"},"content":{"rendered":"\n<!-- Level Order Traversal - Queue - BFS -->\n<link href=\"https:\/\/cdn.jsdelivr.net\/npm\/prismjs@1.29.0\/themes\/prism-tomorrow.min.css\" rel=\"stylesheet\">\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 &lt;= Node.val &lt;= 100<\/code><\/li>\n                    <\/ul>\n\n                <h2>Approach<\/h2>\n              <ul>\n                <li><strong>Base Case: <\/strong> If the tree is empty (root == null), return an empty array.<\/li>\n                <li><strong>Initialize Queue: <\/strong>Use a queue to process nodes level by level. Start by pushing the root node.<\/li>\n                <li><strong>Process Each Level:<\/strong>\n                  <ul>\n                    <li>For each level, store the number of nodes (levelSize) currently in the queue.<\/li>\n                    <li>Process levelSize nodes by:\n                      <ul>\n                        <li>Removing each node from the front of the queue.<\/li>\n                        <li>Adding its value to the current level array.<\/li>\n                        <li>Enqueue its left and right children if they exist.<\/li>\n                      <\/ul>\n                    <\/li>\n                  <\/ul>\n                <\/li>\n                <li><strong>Add Level to Result: <\/strong>After processing one level, push the level array to the final result.<\/li>\n                <li><strong>Repeat:<\/strong> Continue until the queue is empty.<\/li>\n                <li><strong>Return Result:<\/strong> Return the array containing node values level by level.<\/li>\n              <\/ul>\n                <h2>Time Complexity:<\/h2>\n                <li>\n                  <p><strong>Time Complexity = O(n)<\/strong>\n                  <\/p><\/li>\n                <h2>Space Complexity:<\/h2>\n                <li>\n                  <p><strong>Space Complexity = O(n)<\/strong><\/p>\n                <\/li>\n<h2>Dry Run<\/h2> <div style=\"background: #f9f9f9; border-left: 4px solid var(--primary); padding: 1rem; border-radius: var(--tab-radius); margin: 1rem 0;\"> <p><strong>Input:<\/strong> <code>root = [1, 2, 3, null, 4]<\/code><\/p> <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 = []\nq = [1] (root)\nMain loop starts (while q.length):\n\u2192 Level 0:\nlevelArr = []\nlevelSize = 1\n\u2192 i = 0:\ncurr = 1\nq = []\ncurr.left (2) \u2192 q = [2]\ncurr.right (3) \u2192 q = [2, 3]\nlevelArr.push(1) \u2192 levelArr = [1]\n\u2192 ans.push([1]) \u2192 ans = [[1]]\n\u2192 Level 1:\nlevelArr = []\nlevelSize = 2\n\u2192 i = 0:\ncurr = 2\nq = [3]\ncurr.left = null\ncurr.right (4) \u2192 q = [3, 4]\nlevelArr.push(2) \u2192 levelArr = [2]\n\u2192 i = 1:\ncurr = 3\nq = [4]\ncurr.left = null\ncurr.right = null\nlevelArr.push(3) \u2192 levelArr = [2, 3]\n\u2192 ans.push([2, 3]) \u2192 ans = [[1], [2, 3]]\n\u2192 Level 2:\nlevelArr = []\nlevelSize = 1\n\u2192 i = 0:\ncurr = 4\nq = []\ncurr.left = null\ncurr.right = null\nlevelArr.push(4) \u2192 levelArr = [4]\n\u2192 ans.push([4]) \u2192 ans = [[1], [2, 3], [4]]\nMain loop ends (q is empty)\nTraversal complete.\nFinal ans: [[1], [2, 3], [4]]\n<\/pre>\n<p><strong>Output:<\/strong> <code>Result: [[1], [2, 3], [4]]<\/code><\/p> <\/div>\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 levelOrder = function (root) {\n    if (!root) return [];\n\n    let q = [root];\n    let ans = [];\n\n    while (q.length) {\n        let levelArr = [];\n        let levelSize = q.length;\n\n        for (let i = 0; i < levelSize; i++) {\n            let curr = q.shift();\n\n            curr.left &#038;&#038; q.push(curr.left);\n            curr.right &#038;&#038; q.push(curr.right);\n\n            levelArr.push(curr.val);\n        }\n\n        ans.push(levelArr);\n    }\n\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\">\nfrom collections import deque\n\ndef levelOrder(root):\n    if not root:\n        return []\n\n    q = deque([root])\n    ans = []\n\n    while q:\n        levelArr = []\n        levelSize = len(q)\n\n        for i in range(levelSize):\n            curr = q.popleft()\n\n            if curr.left:\n                q.append(curr.left)\n\n            if curr.right:\n                q.append(curr.right)\n\n            levelArr.append(curr.val)\n\n        ans.append(levelArr)\n\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        if (root == null) return new ArrayList<>();\n\n        Queue<TreeNode> q = new LinkedList<>();\n        q.offer(root);\n\n        List<List<Integer>> ans = new ArrayList<>();\n\n        while (!q.isEmpty()) {\n            List<Integer> levelArr = new ArrayList<>();\n            int levelSize = q.size();\n\n            for (int i = 0; i < levelSize; i++) {\n                TreeNode curr = q.poll();\n\n                if (curr.left != null) q.offer(curr.left);\n                if (curr.right != null) q.offer(curr.right);\n\n                levelArr.add(curr.val);\n            }\n\n            ans.add(levelArr);\n        }\n\n        return ans;\n    }\n}\n     <\/integer><\/treenode><\/list<integer><\/list<integer><\/code><\/pre>\n        <\/div>\n\n        <!-- C++ -->\n        <div class=\"wp_blog_code-tab-content\" data-lang=\"cpp\">\n            <pre><code class=\"language-cpp\">\n#include &lt;iostream&gt;\n#include &lt;vector&gt;\n#include &lt;queue&gt;\nclass Solution {\npublic:\n    vector<vector<int>> levelOrder(TreeNode* root) {\n        if (!root) return {};\n\n        queue<TreeNode*> q;\n        q.push(root);\n\n        vector<vector<int>> ans;\n\n        while (!q.empty()) {\n            vector<int> levelArr;\n            int levelSize = q.size();\n\n            for (int i = 0; i < levelSize; i++) {\n                TreeNode* curr = q.front();\n                q.pop();\n\n                if (curr->left) q.push(curr->left);\n                if (curr->right) q.push(curr->right);\n\n                levelArr.push_back(curr->val);\n            }\n\n            ans.push_back(levelArr);\n        }\n\n        return ans;\n    }\n};\n    <\/int><\/treenode*><\/vector<int><\/vector<int><\/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\nint** levelOrder(struct TreeNode* root, int* returnSize, int** returnColumnSizes) {\n    if (!root) {\n        *returnSize = 0;\n        *returnColumnSizes = NULL;\n        return NULL;\n    }\n\n    struct TreeNode* q[2000];\n    int front = 0, rear = 0;\n\n    q[rear++] = root;\n\n    int** ans = (int**)malloc(2000 * sizeof(int*));\n    *returnColumnSizes = (int*)malloc(2000 * sizeof(int));\n    *returnSize = 0;\n\n    while (front < rear) {\n        int levelSize = rear - front;\n\n        int* levelArr = (int*)malloc(levelSize * sizeof(int));\n\n        for (int i = 0; i < levelSize; i++) {\n            struct TreeNode* curr = q[front++];\n\n            if (curr->left) q[rear++] = curr->left;\n            if (curr->right) q[rear++] = curr->right;\n\n            levelArr[i] = curr->val;\n        }\n\n        ans[*returnSize] = levelArr;\n        (*returnColumnSizes)[*returnSize] = levelSize;\n        (*returnSize)++;\n    }\n\n    return ans;\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 IList<IList<int>> LevelOrder(TreeNode root) {\n        if (root == null) return new List<IList<int>>();\n\n        Queue<TreeNode> q = new Queue<TreeNode>();\n        q.Enqueue(root);\n\n        IList<IList<int>> ans = new List<IList<int>>();\n\n        while (q.Count > 0) {\n            List<int> levelArr = new List<int>();\n            int levelSize = q.Count;\n\n            for (int i = 0; i < levelSize; i++) {\n                TreeNode curr = q.Dequeue();\n\n                if (curr.left != null) q.Enqueue(curr.left);\n                if (curr.right != null) q.Enqueue(curr.right);\n\n                levelArr.Add(curr.val);\n            }\n\n            ans.Add(levelArr);\n        }\n\n        return ans;\n    }\n}\n            <\/int><\/treenode><\/treenode><\/ilist<int><\/ilist<int><\/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":[210,176,175,211,811,810,174,172,173],"tags":[],"class_list":["post-8404","post","type-post","status-publish","format-standard","category-algorithms","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\/8404","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=8404"}],"version-history":[{"count":2,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/8404\/revisions"}],"predecessor-version":[{"id":12252,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/8404\/revisions\/12252"}],"wp:attachment":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/media?parent=8404"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/categories?post=8404"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/tags?post=8404"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}