{"id":10193,"date":"2025-09-30T15:05:30","date_gmt":"2025-09-30T09:35:30","guid":{"rendered":"https:\/\/namastedev.com\/blog\/?p=10193"},"modified":"2025-09-30T15:48:42","modified_gmt":"2025-09-30T10:18:42","slug":"maximum-product-subarray-approach-one","status":"publish","type":"post","link":"https:\/\/namastedev.com\/blog\/maximum-product-subarray-approach-one\/","title":{"rendered":"Maximum Product Subarray Approach 1"},"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>Start with the first element as:<\/strong>\n    <ul>\n      <li> <code>maxProdSoFar<\/code> \u2192 maximum product ending at current index.<\/li>\n      <li><code>minProdSoFar<\/code> \u2192 <strong>minimum product ending at current index<\/strong> (important because multiplying with a negative can flip it).<\/li>\n      <li><code>totalMax<\/code> \u2192 overall maximum product.<\/li>\n    <\/ul>\n    <\/li>\n\n    <li><strong>Iterate through the array:<\/strong>\n    <ul>\n        <li>For each element <strong>arr[i]<\/strong> (from index 1 to end):\n        <ul>\n            <li>Store the <code>previous maxProdSoFar<\/code> in a temporary variable (maxProdSoFarCopy).<\/li>\n            <li>Update <strong>maxProdSoFar<\/strong> as the maximum among:\n            <ul>\n                <li>Current element alone <code>(arr[i])<\/code><\/li>\n                <li>Product of current element with previous <strong>max<\/strong> product <code>(maxProdSoFar * arr[i])<\/code><\/li>\n                <li>Product of current element with previous <strong>min<\/strong> product <code> (minProdSoFar * arr[i])<\/code><\/li>\n                <li>Update <code>minProdSoFar<\/code> as the minimum among the <strong>same three values.<\/strong><\/li>\n                <li>Update <strong>totalMax as the maximum<\/strong> between current <code>totalMax<\/code> and <code>maxProdSoFar<\/code>.<\/li>\n            <\/ul>\n            \n            <\/li>\n        <\/ul>\n        <\/li>\n    <\/ul>\n    <\/li>\n\n    <li>After <strong>traversing the whole array<\/strong>, totalMax holds the <code>maximum product of any 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);\">\nStep 0: Start Function maxProduct([2, 3, -2, 4])\nInitialize:\nmaxProdSoFar = minProdSoFar = totalMax = arr[0] = 2\n\nIteration i = 1, arr[1] = 3\n- maxProdSoFarCopy = maxProdSoFar = 2\n- maxProdSoFar = Math.max( arr[1], maxProdSoFar * arr[1], minProdSoFar * arr[1] )\n               = Math.max( 3, 2 * 3 = 6, 2 * 3 = 6 ) = 6\n- minProdSoFar = Math.min( arr[1], maxProdSoFarCopy * arr[1], minProdSoFar * arr[1] )\n               = Math.min( 3, 2 * 3 = 6, 2 * 3 = 6 ) = 3\n- totalMax = Math.max(totalMax, maxProdSoFar) = Math.max(2, 6) = 6\n\nState after i=1:\nmaxProdSoFar = 6, minProdSoFar = 3, totalMax = 6\n\nIteration i = 2, arr[2] = -2\n- maxProdSoFarCopy = maxProdSoFar = 6\n- maxProdSoFar = Math.max( -2, 6 * (-2) = -12, 3 * (-2) = -6 ) = -2\n- minProdSoFar = Math.min( -2, 6 * (-2) = -12, 3 * (-2) = -6 ) = -12\n- totalMax = Math.max(6, -2) = 6\n\nState after i=2:\nmaxProdSoFar = -2, minProdSoFar = -12, totalMax = 6\n\nIteration i = 3, arr[3] = 4\n- maxProdSoFarCopy = maxProdSoFar = -2\n- maxProdSoFar = Math.max( 4, -2 * 4 = -8, -12 * 4 = -48 ) = 4\n- minProdSoFar = Math.min( 4, -2 * 4 = -8, -12 * 4 = -48 ) = -48\n- totalMax = Math.max(6, 4) = 6\n\nState after i=3:\nmaxProdSoFar = 4, minProdSoFar = -48, totalMax = 6\n\nStep 3: End\nReturn totalMax = 6\n  <\/pre> \n\n  <p><strong>Output:<\/strong> <code>6<\/code> (Maximum product subarray is [2,3] \u2192 6)<\/p>\n<\/div>\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  if (!arr || arr.length === 0) return 0; \/\/ defensive\n  let maxProdSoFar = arr[0];\n  let minProdSoFar = arr[0];\n  let totalMax = arr[0];\n\n  for (let i = 1; i < arr.length; i++) {\n    const current = arr[i];\n    const prevMax = maxProdSoFar;\n\n    maxProdSoFar = Math.max(current, prevMax * current, minProdSoFar * current);\n    minProdSoFar = Math.min(current, prevMax * current, minProdSoFar * current);\n\n    totalMax = Math.max(totalMax, maxProdSoFar);\n  }\n\n  return totalMax;\n};\n\n<\/code><\/pre>\n    <\/div>\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"py\">\n      <pre><code class=\"language-python\">\ndef max_product(arr):\n    if not arr:\n        return 0  # defensive\n    max_prod_so_far = arr[0]\n    min_prod_so_far = arr[0]\n    total_max = arr[0]\n\n    for i in range(1, len(arr)):\n        current = arr[i]\n        prev_max = max_prod_so_far\n\n        max_prod_so_far = max(current, prev_max * current, min_prod_so_far * current)\n        min_prod_so_far = min(current, prev_max * current, min_prod_so_far * current)\n\n        total_max = max(total_max, max_prod_so_far)\n\n    return total_max\n      <\/code><\/pre>\n    <\/div>\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"java\">\n      <pre><code class=\"language-java\">\npublic class Solution {\n    public static int maxProduct(int[] arr) {\n        if (arr == null || arr.length == 0) return 0; \/\/ defensive\n\n        int maxProdSoFar = arr[0];\n        int minProdSoFar = arr[0];\n        int totalMax = arr[0];\n\n        for (int i = 1; i < arr.length; i++) {\n            int current = arr[i];\n            int prevMax = maxProdSoFar;\n\n            maxProdSoFar = Math.max(current, Math.max(prevMax * current, minProdSoFar * current));\n            minProdSoFar = Math.min(current, Math.min(prevMax * current, minProdSoFar * current));\n\n            totalMax = Math.max(totalMax, maxProdSoFar);\n        }\n\n        return totalMax;\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;vector&gt;     \n#include &lt;algorithm&gt;    \n\nint maxProduct(const std::vector<int>& arr) {\n    if (arr.empty()) return 0; \/\/ defensive\n\n    int maxProdSoFar = arr[0];\n    int minProdSoFar = arr[0];\n    int totalMax = arr[0];\n\n    for (size_t i = 1; i < arr.size(); ++i) {\n        int current = arr[i];\n        int prevMax = maxProdSoFar;\n\n        maxProdSoFar = std::max(current, std::max(prevMax * current, minProdSoFar * current));\n        minProdSoFar = std::min(current, std::min(prevMax * current, minProdSoFar * current));\n\n        totalMax = std::max(totalMax, maxProdSoFar);\n    }\n\n    return totalMax;\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;limits.h&gt;\n\nint maxProduct(int arr[], int n) {\n    if (n <= 0) return 0; \/\/ defensive\n\n    int maxProdSoFar = arr[0];\n    int minProdSoFar = arr[0];\n    int totalMax = arr[0];\n\n    for (int i = 1; i < n; ++i) {\n        int current = arr[i];\n        int prevMax = maxProdSoFar;\n\n        int candidate1 = current;\n        int candidate2 = prevMax * current;\n        int candidate3 = minProdSoFar * current;\n\n        \/\/ compute max of three\n        int newMax = candidate1;\n        if (candidate2 > newMax) newMax = candidate2;\n        if (candidate3 > newMax) newMax = candidate3;\n\n        \/\/ compute min of three\n        int newMin = candidate1;\n        if (candidate2 < newMin) newMin = candidate2;\n        if (candidate3 < newMin) newMin = candidate3;\n\n        maxProdSoFar = newMax;\n        minProdSoFar = newMin;\n\n        if (maxProdSoFar > totalMax) totalMax = maxProdSoFar;\n    }\n    return totalMax;\n}\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\npublic class Solution {\n    public static int MaxProduct(int[] arr) {\n        if (arr == null || arr.Length == 0) return 0; \/\/ defensive\n\n        int maxProdSoFar = arr[0];\n        int minProdSoFar = arr[0];\n        int totalMax = arr[0];\n\n        for (int i = 1; i < arr.Length; i++) {\n            int current = arr[i];\n            int prevMax = maxProdSoFar;\n\n            maxProdSoFar = Math.Max(current, Math.Max(prevMax * current, minProdSoFar * current));\n            minProdSoFar = Math.Min(current, Math.Min(prevMax * current, minProdSoFar * current));\n\n            totalMax = Math.Max(totalMax, maxProdSoFar);\n        }\n\n        return totalMax;\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":[210,322,260,176,175,211,811,174,172,173],"tags":[],"class_list":["post-10193","post","type-post","status-publish","format-standard","category-algorithms","category-algorithms-and-data-structures","category-c-c-plus-plus","category-csharp","category-cplusplus","category-data-structures","category-data-structures-and-algorithms","category-java","category-javascript","category-python"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/10193","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=10193"}],"version-history":[{"count":1,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/10193\/revisions"}],"predecessor-version":[{"id":10194,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/10193\/revisions\/10194"}],"wp:attachment":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/media?parent=10193"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/categories?post=10193"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/tags?post=10193"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}