{"id":10195,"date":"2025-09-30T15:27:32","date_gmt":"2025-09-30T09:57:32","guid":{"rendered":"https:\/\/namastedev.com\/blog\/?p=10195"},"modified":"2025-09-30T15:49:16","modified_gmt":"2025-09-30T10:19:16","slug":"maximum-product-subarray-approach-two","status":"publish","type":"post","link":"https:\/\/namastedev.com\/blog\/maximum-product-subarray-approach-two\/","title":{"rendered":"Maximum Product Subarray Approach 2"},"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>Problem Statement:<\/h2>\n    <p>\n       Given an integer array nums, find a subarray that has the largest product, and return <i> the product.<\/i>\n    <\/p>\n    <p>\n        The test cases are generated so that the answer will fit in a <strong>32-bit integer<\/strong>.\n    <\/p>\n    <h3>Example 1:<\/h2>\n    <p><strong>Input:<\/strong> nums = [2,3,-2,4]<\/p>\n    <p><strong>Output:<\/strong> 6<\/p>\n    <p><strong>Explanation:<\/strong> [2,3] has the largest product 6.<\/p>\n\n    <h3>Example 2:<\/h2>\n    <p><strong>Input:<\/strong> nums = [-2,0,-1]<\/p>\n    <p><strong>Output:<\/strong> 0<\/p>\n    <p><strong>Explanation:<\/strong> The result cannot be 2, because [-2,-1] is not a subarray.<\/p>\n\n    <h3>Constraints<\/h3>\n    <ul>\n       <li><code>1 <= nums.length <= 2 * 10<sup>4<\/sup><\/code><\/li>\n        <li><code>-10 <= nums[i] <= 10<\/code><\/li>\n        <li>The product of any subarray of <code>nums<\/code> is <strong>guaranteed<\/strong> to fit in a <strong>32-bit<\/strong> integer.<\/li>\n    <\/ul>\n    \n<h2>Approach:<\/h2>\n<ul>\n  <li><strong>Initialize Variables<\/strong>\n  <ul>\n    <li><code>ltrProd = 1<\/code> \u2192 product when traversing <strong>left to right<\/strong>.<\/li>\n    <li><code>rtlProd = 1<\/code> \u2192 product when traversing <strong>right to left<\/strong>.<\/li>\n    <li><code>finalMax = -Infinity<\/code> \u2192 to keep track of the <strong>maximum product found<\/strong>.<\/li>\n  <\/ul>\n  <\/li>\n\n  <li><strong>Two-way traversal logic<\/strong>\n  <ul>\n    <li>Since the <code>maximum product subarray<\/code> can break due to negative numbers and zeros, we handle it by multiplying in both directions:\n      <ul>\n        <li><strong>LTR (left-to-right):<\/strong> multiply each element into <code>ltrProd<\/code>.<\/li>\n        <li><strong>RTL (right-to-left):<\/strong> multiply each element from the back into <code>rtlProd<\/code>.<\/li>\n      <\/ul>\n    <\/li>\n  <\/ul>\n  <\/li>\n\n  <li><strong>Update maximum,  <\/strong>After each step, check the maximum value among <code>finalMax<\/code>, <code>ltrProd<\/code>, and <code>rtlProd<\/code>.<\/li>\n\n  <li><strong>Handle zero reset<\/strong>\n    <ul>\n      <li>If at any point the product becomes <code>0<\/code>, reset it to <code>1<\/code>.<\/li>\n      <li>This is because any product involving <code>0<\/code> will be <code>0<\/code>, but a new subarray can start after zero.<\/li>\n    <\/ul>\n  <\/li>\n  <li><strong>After completing the single loop<\/strong>, finalMax will contain the <code>maximum product subarray<\/code>.<\/li>\n<\/ul>\n\n    <h2>Time & 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, 3, -2, 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);\">\nInitial:\nn = 4\nltrProd = 1, rtlProd = 1\nfinalMax = -Infinity\n\ni = 0:\nltrProd = 1 * 2 = 2\nrtlProd = 1 * arr[3] = 1 * 4 = 4\nfinalMax = max(-\u221e, 2, 4) = 4\n\ni = 1:\nltrProd = 2 * 3 = 6\nrtlProd = 4 * arr[2] = 4 * -2 = -8\nfinalMax = max(4, 6, -8) = 6\n\ni = 2:\nltrProd = 6 * -2 = -12\nrtlProd = -8 * arr[1] = -8 * 3 = -24\nfinalMax = max(6, -12, -24) = 6\n\ni = 3:\nltrProd = -12 * 4 = -48\nrtlProd = -24 * arr[0] = -24 * 2 = -48\nfinalMax = max(6, -48, -48) = 6\n\nLoop ends\nReturn finalMax = 6\n  <\/pre> \n\n  <p><strong>Output:<\/strong> <code>6<\/code><\/p>\n<\/div>\n\n\n        <!-- <h2>Visualisation:<\/h2>\n        <img decoding=\"async\" src=\"https:\/\/namastedev.com\/blog\/wp-content\/uploads\/2025\/09\/Screenshot-2025-09-30-at-3.00.03\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\">\nvar maxProduct = function(arr) {\n    let n = arr.length; \n    let ltrProd = 1, rtlProd = 1;\n    let finalMax = -Infinity;\n\n    for (let i = 0; i < n; i++) {\n        ltrProd = ltrProd * arr[i];\n        rtlProd = rtlProd * arr[n - i - 1];\n\n        finalMax = Math.max(finalMax, ltrProd, rtlProd);\n\n        if (ltrProd === 0) ltrProd = 1;\n        if (rtlProd === 0) rtlProd = 1;\n    }\n\n    return finalMax;\n};\n<\/code><\/pre>\n    <\/div>\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"py\">\n      <pre><code class=\"language-python\">\ndef maxProduct(arr):\n    n = len(arr)\n    ltrProd = 1\n    rtlProd = 1\n    finalMax = float('-inf')\n    for i in range(n):\n        ltrProd *= arr[i]\n        rtlProd *= arr[n - i - 1]\n        finalMax = max(finalMax, ltrProd, rtlProd)\n        if ltrProd == 0:\n            ltrProd = 1\n        if rtlProd == 0:\n            rtlProd = 1\n    return finalMax\n\nif __name__ == \"__main__\":\n    arr = [2, -3, 4, 0, -2, -1]\n    print(\"Max product:\", maxProduct(arr))\n\n      <\/code><\/pre>\n    <\/div>\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"java\">\n      <pre><code class=\"language-java\">\npublic class MaxProduct {\n    public static long maxProduct(int[] arr) {\n        int n = arr.length;\n        long ltrProd = 1, rtlProd = 1;\n        long finalMax = Long.MIN_VALUE;\n        for (int i = 0; i < n; i++) {\n            ltrProd *= arr[i];\n            rtlProd *= arr[n - i - 1];\n            finalMax = Math.max(finalMax, Math.max(ltrProd, rtlProd));\n            if (ltrProd == 0) ltrProd = 1;\n            if (rtlProd == 0) rtlProd = 1;\n        }\n        return finalMax;\n    }\n\n    public static void main(String[] args) {\n        int[] arr = {2, -3, 4, 0, -2, -1};\n        System.out.println(\"Max product: \" + maxProduct(arr));\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;bits\/stdc++.h&gt;     \nusing namespace std;\n\nlong long maxProduct(const vector<int>& arr) {\n    int n = arr.size();\n    long long ltrProd = 1, rtlProd = 1;\n    long long finalMax = LLONG_MIN;\n    for (int i = 0; i < n; ++i) {\n        ltrProd *= arr[i];\n        rtlProd *= arr[n - i - 1];\n        finalMax = max(finalMax, max(ltrProd, rtlProd));\n        if (ltrProd == 0) ltrProd = 1;\n        if (rtlProd == 0) rtlProd = 1;\n    }\n    return finalMax;\n}\n\nint main() {\n    vector<int> arr = {2, -3, 4, 0, -2, -1};\n    cout << \"Max product: \" << maxProduct(arr) << endl;\n    return 0;\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;\n#include &lt;limits.h&gt;\n\nlong long maxProduct(int *arr, int n) {\n    long long ltrProd = 1, rtlProd = 1;\n    long long finalMax = LLONG_MIN;\n    for (int i = 0; i < n; ++i) {\n        ltrProd *= arr[i];\n        rtlProd *= arr[n - i - 1];\n        if (ltrProd > finalMax) finalMax = ltrProd;\n        if (rtlProd > finalMax) finalMax = rtlProd;\n        if (ltrProd == 0) ltrProd = 1;\n        if (rtlProd == 0) rtlProd = 1;\n    }\n    return finalMax;\n}\n\nint main() {\n    int arr[] = {2, -3, 4, 0, -2, -1};\n    int n = sizeof(arr)\/sizeof(arr[0]);\n    printf(\"Max product: %lld\\n\", maxProduct(arr, n));\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    static long MaxProduct(int[] arr) {\n        int n = arr.Length;\n        long ltrProd = 1, rtlProd = 1;\n        long finalMax = long.MinValue;\n        for (int i = 0; i < n; i++) {\n            ltrProd *= arr[i];\n            rtlProd *= arr[n - i - 1];\n            finalMax = Math.Max(finalMax, Math.Max(ltrProd, rtlProd));\n            if (ltrProd == 0) ltrProd = 1;\n            if (rtlProd == 0) rtlProd = 1;\n        }\n        return finalMax;\n    }\n\n    static void Main() {\n        int[] arr = {2, -3, 4, 0, -2, -1};\n        Console.WriteLine(\"Max product: \" + MaxProduct(arr));\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 Problem Statement: Given an integer array nums, find a subarray that has the largest product, and return the product. The test cases are generated so that the answer will fit in a 32-bit integer. Example 1: Input: nums = [2,3,-2,4] Output: 6 Explanation: [2,3] has the largest product 6. Example 2: Input: nums =<\/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],"tags":[],"class_list":{"0":"post-10195","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"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/10195","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=10195"}],"version-history":[{"count":1,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/10195\/revisions"}],"predecessor-version":[{"id":10196,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/10195\/revisions\/10196"}],"wp:attachment":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/media?parent=10195"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/categories?post=10195"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/tags?post=10195"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}