{"id":10191,"date":"2025-09-30T15:03:24","date_gmt":"2025-09-30T09:33:24","guid":{"rendered":"https:\/\/namastedev.com\/blog\/?p=10191"},"modified":"2025-09-30T15:48:06","modified_gmt":"2025-09-30T10:18:06","slug":"maximum-subarray-kadanes-algorithm","status":"publish","type":"post","link":"https:\/\/namastedev.com\/blog\/maximum-subarray-kadanes-algorithm\/","title":{"rendered":"Maximum Subarray Kadane&#8217;s Algorithm"},"content":{"rendered":"\n<!-- PrismJS for Syntax Highlighting -->\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: #030302;\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\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\n.wp_blog_explanation code {\n  background: #fef9f4; 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\/* makes it the reference for absolute children *\/\n}\n\n.wp_blog_toggle-btn {\n  position: absolute;\n  top: 1rem;\n  right: 1rem;\n  z-index: 9999;\n  padding: 0.5rem 0.8rem;\n  border-radius: 10%;\n  background: var(--primary);\n  color: white;\n  font-weight: bold;\n  cursor: pointer;\n  border: none;\n  box-shadow: var(--shadow);\n  transition: background 0.3s, transform 0.2s;\n}\n\n.wp_blog_toggle-btn:hover {\n  background: #cc772e;\n}\n\n.wp_blog_theme.dark-mode .wp_blog_code-tabs-container {\n  background: #1e1e1e;\n}\n<\/style>\n\n<div class=\"wp_blog_container wp_blog_theme\">\n  <button id=\"blogNotesThemeToggle\" class=\"wp_blog_toggle-btn\">\ud83c\udf19<\/button>\n  <h1 class=\"wp_blog_main-heading\"><\/h1>\n\n  <div class=\"wp_blog_explanation\">\n    <h2>Use Kadane&#8217;s Algorithms<\/h2>\n    <h2>Problem Statement:<\/h2>\n    <p>\n        Given an integer array <code>nums<\/code>, find the subarray with the largest sum, and return <i>its sum<\/i>.\n    <\/p>\n\n    <h3>Example 1:<\/h2>\n    <p><strong>Input:<\/strong> nums = [-2,1,-3,4,-1,2,1,-5,4]<\/p>\n    <p><strong>Output:<\/strong> 6<\/p>\n    <p><strong>Explanation:<\/strong> The subarray [4,-1,2,1] has the largest sum 6.<\/p>\n\n    <h3>Example 2:<\/h2>\n    <p><strong>Input:<\/strong> nums = [1]<\/p>\n    <p><strong>Output:<\/strong> 1<\/p>\n    <p><strong>Explanation:<\/strong> The subarray [1] has the largest sum 1.<\/p>\n\n    <h3>Example 3:<\/h2>\n    <p><strong>Input:<\/strong> nums = [5,4,-1,7,8]<\/p>\n    <p><strong>Output:<\/strong> 23<\/p>\n    <p><strong>Explanation:<\/strong> The subarray [5,4,-1,7,8] has the largest sum 23.<\/p>\n\n    <h3>Constraints<\/h3>\n    <ul>\n       <li><code>1 <= nums.length <= 10<sup>5<\/sup><\/code><\/li>\n        <li><code>-10<sup>4<\/sup> <= nums[i] <= 10<sup>4<\/sup><\/code><\/li>\n    <\/ul>\n    \n<h2>Approach:<\/h2>\n<ul>\n  <li><strong>Initialize two variables:<\/strong>\n  <ul>\n    <li><code>currSum = arr[0]<\/code> \u2192 keeps track of the maximum subarray sum ending at the <strong>current index<\/strong>.<\/li>\n    <li><code>maxSum = arr[0]<\/code> \u2192 keeps track of the <strong>global maximum subarray sum<\/strong> found so far.<\/li>\n  <\/ul>\n  <\/li>\n\n  <li><strong>Iterate through the array starting from index 1:<\/strong>\n    <ul>\n      <li>For each element <code>arr[i]:<\/code>\n        <ul>\n          <li>Decide whether to <strong>extend the previous subarray<\/strong> <code>(currSum + arr[i])<\/code>\nor start a new subarray from this element <code>(arr[i])<\/code>.\n\u2192 currSum = <code>Math.max(currSum + arr[i], arr[i])<\/code>;<\/li>\n        <\/ul>\n\n      <\/li>\n    <\/ul>\n  <\/li>\n\n  <li><strong>Update the global maximum:<\/strong>\n  <ul>\n    <li>After updating <code>currSum<\/code>, compare it with the <strong>global maximum<\/strong> and update if larger:\n\u2192 <code>maxSum = Math.max(maxSum, currSum)<\/code>;<\/li>\n  <\/ul>\n  <\/li>\n\n  <li><strong>After traversing the entire array<\/strong>, maxSum will contain the <code>largest sum of any contiguous subarray<\/code>.<\/li>\n<\/ul>\n\n    <h2>Time &#038; Space Complexity:<\/h2>\n    <p><strong>Time Complexity:<\/strong> <code>O(n)<\/code><\/p>\n    <p><strong>Space Complexity:<\/strong> <code>O(1)<\/code><\/p>\n\n<h2>Dry Run<\/h2> \n<div style=\"background: var(--light-bg); border-left: 4px solid var(--primary); padding: 1rem; border-radius: var(--tab-radius); margin: 1rem 0; color: var(--text-dark);\"> \n  <p><strong>Input:<\/strong> <code>arr = [-2, 1, -3, 4, -1, 2, 1, -5, 4]<\/code><\/p> \n  \n  <pre style=\"white-space: pre-wrap; background: var(--code-bg); padding: 1rem; border-radius: 8px; overflow-x: auto; color: var(--code-text);\">\n\nStep 0: Start Function maxSubArray([-2, 1, -3, 4, -1, 2, 1, -5, 4])\ncurrSum = arr[0] = -2\nmaxSum  = arr[0] = -2\n\nIteration i = 1, arr[1] = 1\ncurrSum = Math.max(currSum + 1, 1)\n        = Math.max(-2 + 1, 1)\n        = Math.max(-1, 1) = 1\nmaxSum  = Math.max(1, -2) = 1\n\nIteration i = 2, arr[2] = -3\ncurrSum = Math.max(1 + (-3), -3)\n        = Math.max(-2, -3) = -2\nmaxSum  = Math.max(-2, 1) = 1\n\nIteration i = 3, arr[3] = 4\ncurrSum = Math.max(-2 + 4, 4)\n        = Math.max(2, 4) = 4\nmaxSum  = Math.max(4, 1) = 4\n\nIteration i = 4, arr[4] = -1\ncurrSum = Math.max(4 + (-1), -1)\n        = Math.max(3, -1) = 3\nmaxSum  = Math.max(3, 4) = 4\n\nIteration i = 5, arr[5] = 2\ncurrSum = Math.max(3 + 2, 2)\n        = Math.max(5, 2) = 5\nmaxSum  = Math.max(5, 4) = 5\n\nIteration i = 6, arr[6] = 1\ncurrSum = Math.max(5 + 1, 1)\n        = Math.max(6, 1) = 6\nmaxSum  = Math.max(6, 5) = 6\n\nIteration i = 7, arr[7] = -5\ncurrSum = Math.max(6 + (-5), -5)\n        = Math.max(1, -5) = 1\nmaxSum  = Math.max(1, 6) = 6\n\nIteration i = 8, arr[8] = 4\ncurrSum = Math.max(1 + 4, 4)\n        = Math.max(5, 4) = 5\nmaxSum  = Math.max(5, 6) = 6\n\nStep 3: End\nReturn maxSum = 6\n  <\/pre> \n  <p><strong>Output:<\/strong> <code>6<\/code> (Maximum subarray is [4, -1, 2, 1])<\/p> \n<\/div>\n        <h2>Visualisation:<\/h2>\n        <img decoding=\"async\" src=\"https:\/\/namastedev.com\/blog\/wp-content\/uploads\/2025\/09\/Screenshot-2025-09-30-at-2.50.41\u202fPM.png\" alt=\"Stocks\" \/>\n   \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    <div class=\"wp_blog_code-tab-content active\" data-lang=\"js\">\n      <pre><code class=\"language-javascript\">\nfunction maxSubArray(arr) {\n    let currSum = arr[0];\n    let maxSum = arr[0];\n\n    for (let i = 1; i < arr.length; i++) {\n        currSum = Math.max(currSum + arr[i], arr[i]);\n        maxSum = Math.max(currSum, maxSum);\n    }\n\n    return maxSum;\n}\n<\/code><\/pre>\n    <\/div>\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"py\">\n      <pre><code class=\"language-python\">\ndef maxSubArray(arr):\n    curr_sum = arr[0]\n    max_sum = arr[0]\n\n    for i in range(1, len(arr)):\n        curr_sum = max(curr_sum + arr[i], arr[i])\n        max_sum = max(max_sum, curr_sum)\n\n    return max_sum\n      <\/code><\/pre>\n    <\/div>\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"java\">\n      <pre><code class=\"language-java\">\npublic class MaxSubArray {\n    public static int maxSubArray(int[] arr) {\n        int currSum = arr[0];\n        int maxSum = arr[0];\n\n        for (int i = 1; i < arr.length; i++) {\n            currSum = Math.max(currSum + arr[i], arr[i]);\n            maxSum = Math.max(maxSum, currSum);\n        }\n\n        return maxSum;\n    }\n\n    public static void main(String[] args) {\n        int[] arr = {-2, 1, -3, 4, -1, 2, 1, -5, 4};\n        System.out.println(maxSubArray(arr)); \/\/ Output: 6\n    }\n}\n\n    <\/code><\/pre>\n    <\/div>\n\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;algorithm&gt;\n\nusing namespace std;\n\nint maxSubArray(vector<int>& arr) {\n    int currSum = arr[0];\n    int maxSum = arr[0];\n\n    for (int i = 1; i < arr.size(); i++) {\n        currSum = max(currSum + arr[i], arr[i]);\n        maxSum = max(maxSum, currSum);\n    }\n\n    return maxSum;\n}\n\nint main() {\n    vector<int> arr = {-2, 1, -3, 4, -1, 2, 1, -5, 4};\n    cout << maxSubArray(arr) << endl; \/\/ Output: 6\n    return 0;\n}\n\n<\/code><\/pre>\n    <\/div>\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"c\">\n      <pre><code class=\"language-c\">\n#include &lt;stdio.h&gt;\nint max(int a, int b) {\n    return (a > b) ? a : b;\n}\n\nint maxSubArray(int arr[], int n) {\n    int currSum = arr[0];\n    int maxSum = arr[0];\n\n    for (int i = 1; i < n; i++) {\n        currSum = max(currSum + arr[i], arr[i]);\n        maxSum = max(maxSum, currSum);\n    }\n\n    return maxSum;\n}\n\nint main() {\n    int arr[] = {-2, 1, -3, 4, -1, 2, 1, -5, 4};\n    int n = sizeof(arr) \/ sizeof(arr[0]);\n\n    printf(\"%d\\n\", maxSubArray(arr, n)); \/\/ Output: 6\n    return 0;\n}\n <\/code><\/pre>\n    <\/div>\n\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"cs\">\n      <pre><code class=\"language-csharp\">\nusing System;\n\nclass Program {\n    public static int MaxSubArray(int[] arr) {\n        int currSum = arr[0];\n        int maxSum = arr[0];\n\n        for (int i = 1; i < arr.Length; i++) {\n            currSum = Math.Max(currSum + arr[i], arr[i]);\n            maxSum = Math.Max(maxSum, currSum);\n        }\n\n        return maxSum;\n    }\n\n    static void Main() {\n        int[] arr = {-2, 1, -3, 4, -1, 2, 1, -5, 4};\n        Console.WriteLine(MaxSubArray(arr)); \/\/ Output: 6\n    }\n}\n\n      <\/code><\/pre>\n    <\/div>\n  <\/div>\n<\/div>\n\n<script>\ndocument.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) => content.classList.remove(\"active\"));\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  const themeToggle = document.getElementById(\"blogNotesThemeToggle\");\n  const themeContainer = document.querySelector(\".wp_blog_theme\");\n\n  themeToggle.addEventListener(\"click\", () => {\n    themeContainer.classList.toggle(\"dark-mode\");\n    themeToggle.textContent =\n      themeContainer.classList.contains(\"dark-mode\") ? \"\u2600\ufe0f\" : \"\ud83c\udf19\";\n  });\n});\n<\/script>\n\n","protected":false},"excerpt":{"rendered":"<p>\ud83c\udf19 Use Kadane&#8217;s Algorithms Problem Statement: Given an integer array nums, find the subarray with the largest sum, and return its sum. Example 1: Input: nums = [-2,1,-3,4,-1,2,1,-5,4] Output: 6 Explanation: The subarray [4,-1,2,1] has the largest sum 6. Example 2: Input: nums = [1] Output: 1 Explanation: The subarray [1] has the largest sum<\/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":[210,322,260,176,175,211,811,810,174,172,173],"tags":[],"class_list":{"0":"post-10191","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-algorithms","7":"category-algorithms-and-data-structures","8":"category-c-c-plus-plus","9":"category-csharp","10":"category-cplusplus","11":"category-data-structures","12":"category-data-structures-and-algorithms","13":"category-dsa","14":"category-java","15":"category-javascript","16":"category-python"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/10191","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=10191"}],"version-history":[{"count":1,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/10191\/revisions"}],"predecessor-version":[{"id":10192,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/10191\/revisions\/10192"}],"wp:attachment":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/media?parent=10191"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/categories?post=10191"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/tags?post=10191"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}