{"id":8035,"date":"2025-07-19T16:32:32","date_gmt":"2025-07-19T11:02:32","guid":{"rendered":"https:\/\/namastedev.com\/blog\/?p=8035"},"modified":"2025-07-19T16:39:13","modified_gmt":"2025-07-19T11:09:13","slug":"trapping-rain-water","status":"publish","type":"post","link":"https:\/\/namastedev.com\/blog\/trapping-rain-water\/","title":{"rendered":"Trapping Rain Water"},"content":{"rendered":"\n<!-- KMP -->\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 <code>n<\/code> non-negative integers representing an elevation map where the width of each bar is <code>1<\/code>, compute how much water it can trap after raining.\n        <\/p>\n\n                <h2>Examples:<\/h2>\n\n                <h5>Example 1:<\/h5>\n                <!-- visual -->\n                <img decoding=\"async\" src=\"https:\/\/namastedev.com\/blog\/wp-content\/uploads\/2025\/07\/Screenshot-2025-07-19-at-4.30.24\u202fPM.png\" alt=\"rain\" \/>\n                <p><strong>Input:<\/strong> height = [0,1,0,2,1,0,1,3,2,1,2,1]<\/p>\n                <p><strong>Output:<\/strong> 6<\/p>\n                <p>\n                  <code>Explanation:<\/code>\n                  The above elevation map (black section) is represented by array [0,1,0,2,1,0,1,3,2,1,2,1]. In this case, 6 units of rain water (blue section) are being trapped.\n                <\/p>\n\n                <h5>Example 2:<\/h5>\n                <p><strong>Input:<\/strong> height = [4,2,0,3,2,5]<\/p>\n                <p><strong>Output:<\/strong>9<\/p>\n\n                    <h2>Constraints:<\/h2>\n                    <ul>\n                      <li><code> n == height.length <\/code><\/li>\n                      <li><code>1 <= n <= 2 * 10<sup>4<\/sup><\/code><\/li>\n                      <li><code>0 <= height[i] <= 10<sup>5<\/sup><\/code><\/li>\n                    <\/ul>\n\n                <h2>Approach<\/h2>\n                <ul>\n                    <li><strong>Create two arrays<\/strong>\n                    <ul>\n                        <li><code>maxL[i]<\/code>: Max height to the left of index <code>i<\/code> (including i).<\/li>\n                        <li><code>maxR[i]<\/code>: Max height to the right of index <code>i<\/code> (including i).<\/li>\n                    <\/ul>\n                    <\/li>\n\n                    <li><strong>Pre-fill<\/strong> <code>maxL<\/code> and <code>maxR<\/code>:\n                    <ul>\n                        <li>Traverse from left to right for <code>maxL<\/code>.<\/li>\n                        <li>Traverse from right to left for <code>maxR<\/code>.<\/li>\n                    <\/ul>\n                    <\/li>\n                    <li><strong>Calculate water trapped<\/strong> at each index i as:\n                    <ul>\n                        <li><code>min(maxL[i], maxR[i]) - height[i]<\/code><\/li>\n                    <\/ul>\n                    <\/li>\n                    <li><strong>Sum it up <\/strong>to get the final answer.<\/li>\n                <\/ul>\n\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\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>arr = [0,1,0,2,1,0,1,3,2,1,2,1]<\/code><\/p> \n  <pre style=\"white-space: pre-wrap; background: #fff5ea; padding: 1rem; border-radius: 8px; overflow-x: auto;\"> \n\n\/\/ Step 1: Build maxL array (maximum height to the left including current)\n\nInitialize: maxL[0] = arr[0] = 0\n\ni = 1 \u2192 maxL[1] = max(maxL[0], arr[1]) = max(0, 1) = 1  \ni = 2 \u2192 maxL[2] = max(1, 0) = 1  \ni = 3 \u2192 maxL[3] = max(1, 2) = 2  \ni = 4 \u2192 maxL[4] = max(2, 1) = 2  \ni = 5 \u2192 maxL[5] = max(2, 0) = 2  \ni = 6 \u2192 maxL[6] = max(2, 1) = 2  \ni = 7 \u2192 maxL[7] = max(2, 3) = 3  \ni = 8 \u2192 maxL[8] = max(3, 2) = 3  \ni = 9 \u2192 maxL[9] = max(3, 1) = 3  \ni = 10 \u2192 maxL[10] = max(3, 2) = 3  \ni = 11 \u2192 maxL[11] = max(3, 1) = 3\n\nFinal maxL = [0,1,1,2,2,2,2,3,3,3,3,3]\n\n\/\/ Step 2: Build maxR array (maximum height to the right including current)\n\nInitialize: maxR[11] = arr[11] = 1\n\ni = 10 \u2192 maxR[10] = max(arr[10], maxR[11]) = max(2, 1) = 2  \ni = 9 \u2192 maxR[9] = max(1, 2) = 2  \ni = 8 \u2192 maxR[8] = max(2, 2) = 2  \ni = 7 \u2192 maxR[7] = max(3, 2) = 3  \ni = 6 \u2192 maxR[6] = max(1, 3) = 3  \ni = 5 \u2192 maxR[5] = max(0, 3) = 3  \ni = 4 \u2192 maxR[4] = max(1, 3) = 3  \ni = 3 \u2192 maxR[3] = max(2, 3) = 3  \ni = 2 \u2192 maxR[2] = max(0, 3) = 3  \ni = 1 \u2192 maxR[1] = max(1, 3) = 3  \ni = 0 \u2192 maxR[0] = max(0, 3) = 3\n\nFinal maxR = [3,3,3,3,3,3,3,3,2,2,2,1]\n\n\/\/ Step 3: Calculate water trapped at each index\n\nInitialize: ans = 0\n\ni = 0 \u2192 min(0, 3) - 0 = 0 \u2192 ans = 0  \ni = 1 \u2192 min(1, 3) - 1 = 0 \u2192 ans = 0  \ni = 2 \u2192 min(1, 3) - 0 = 1 \u2192 ans = 1  \ni = 3 \u2192 min(2, 3) - 2 = 0 \u2192 ans = 1  \ni = 4 \u2192 min(2, 3) - 1 = 1 \u2192 ans = 2  \ni = 5 \u2192 min(2, 3) - 0 = 2 \u2192 ans = 4  \ni = 6 \u2192 min(2, 3) - 1 = 1 \u2192 ans = 5  \ni = 7 \u2192 min(3, 3) - 3 = 0 \u2192 ans = 5  \ni = 8 \u2192 min(3, 2) - 2 = 0 \u2192 ans = 5  \ni = 9 \u2192 min(3, 2) - 1 = 1 \u2192 ans = 6  \ni = 10 \u2192 min(3, 2) - 2 = 0 \u2192 ans = 6  \ni = 11 \u2192 min(3, 1) - 1 = 0 \u2192 ans = 6\n\nFinal trapped water = 6\n<\/pre> \n  <p><strong>Output:<\/strong> <code>Result: 6<\/code><\/p> \n<\/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-4.30.31\u202fPM.png\" alt=\"Rain\" \/>\n    <\/div>\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 trap = function(arr) {\n    let n = arr.length;\n    let maxL = [];\n    maxL[0] = arr[0];\n    for (let i = 1; i < n; i++) {\n        maxL[i] = Math.max(maxL[i - 1], arr[i]);\n    }\n    let maxR = [];\n    maxR[n - 1] = arr[n - 1];\n    for (let i = n - 2; i >= 0; i--) {\n        maxR[i] = Math.max(arr[i], maxR[i + 1]);\n    }\n    let ans = 0;\n    for (let i = 0; i < n; i++) {\n        let waterTrapped = Math.min(maxL[i], maxR[i]) - arr[i];\n        ans += Math.max(waterTrapped, 0);  \/\/ Avoid negative values\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\">\ndef trap(arr):\n    n = len(arr)\n    maxL = [0] * n\n    maxL[0] = arr[0]\n    for i in range(1, n):\n        maxL[i] = max(maxL[i-1], arr[i])\n\n    maxR = [0] * n\n    maxR[n-1] = arr[n-1]\n    for i in range(n-2, -1, -1):\n        maxR[i] = max(arr[i], maxR[i+1])\n\n    ans = 0\n    for i in range(n):\n        waterTrapped = min(maxL[i], maxR[i]) - arr[i]\n        ans += max(waterTrapped, 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 int trap(int[] arr) {\n        int n = arr.length;\n        int[] maxL = new int[n];\n        maxL[0] = arr[0];\n        for (int i = 1; i < n; i++) {\n            maxL[i] = Math.max(maxL[i - 1], arr[i]);\n        }\n        int[] maxR = new int[n];\n        maxR[n - 1] = arr[n - 1];\n        for (int i = n - 2; i >= 0; i--) {\n            maxR[i] = Math.max(arr[i], maxR[i + 1]);\n        }\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            int waterTrapped = Math.min(maxL[i], maxR[i]) - arr[i];\n            ans += Math.max(waterTrapped, 0);\n        }\n        return 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    int trap(vector<int>& arr) {\n        int n = arr.size();\n        vector<int> maxL(n);\n        maxL[0] = arr[0];\n\n        for (int i = 1; i < n; i++) {\n            maxL[i] = max(maxL[i - 1], arr[i]);\n        }\n        vector<int> maxR(n);\n        maxR[n - 1] = arr[n - 1];\n        for (int i = n - 2; i >= 0; i--) {\n            maxR[i] = max(arr[i], maxR[i + 1]);\n        }\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            int waterTrapped = min(maxL[i], maxR[i]) - arr[i];\n            ans += max(waterTrapped, 0);\n        }\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\">\nint trap(int* arr, int n){\n    int maxL[n];\n    maxL[0] = arr[0];\n    for(int i=1; i<n; i++){\n        maxL[i] = (maxL[i-1] > arr[i]) ? maxL[i-1] : arr[i];\n    }\n    int maxR[n];\n    maxR[n-1] = arr[n-1];\n    for(int i=n-2; i>=0; i--){\n        maxR[i] = (arr[i] > maxR[i+1]) ? arr[i] : maxR[i+1];\n    }\n    int ans = 0;\n    for(int i=0; i<n; i++){\n        int minLR = (maxL[i] < maxR[i]) ? maxL[i] : maxR[i];\n        int waterTrapped = minLR - arr[i];\n        ans += (waterTrapped > 0) ? waterTrapped : 0;\n    }\n    return ans;\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 int Trap(int[] arr) {\n        int n = arr.Length;\n        int[] maxL = new int[n];\n        maxL[0] = arr[0];\n\n        for (int i = 1; i < n; i++) {\n            maxL[i] = Math.Max(maxL[i - 1], arr[i]);\n        }\n        int[] maxR = new int[n];\n        maxR[n - 1] = arr[n - 1];\n\n        for (int i = n - 2; i >= 0; i--) {\n            maxR[i] = Math.Max(arr[i], maxR[i + 1]);\n        }\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            int waterTrapped = Math.Min(maxL[i], maxR[i]) - arr[i];\n            ans += Math.Max(waterTrapped, 0);\n        }\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 n non-negative integers representing an elevation map where the width of each bar is 1, compute how much water it can trap after raining. Examples: Example 1: Input: height = [0,1,0,2,1,0,1,3,2,1,2,1] Output: 6 Explanation: The above elevation map (black section) is represented by array [0,1,0,2,1,0,1,3,2,1,2,1]. In this case, 6 units of rain<\/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":[260,176,175,211,811,174,172,173],"tags":[],"class_list":{"0":"post-8035","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-c-c-plus-plus","7":"category-csharp","8":"category-cplusplus","9":"category-data-structures","10":"category-data-structures-and-algorithms","11":"category-java","12":"category-javascript","13":"category-python"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/8035","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=8035"}],"version-history":[{"count":2,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/8035\/revisions"}],"predecessor-version":[{"id":8037,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/8035\/revisions\/8037"}],"wp:attachment":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/media?parent=8035"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/categories?post=8035"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/tags?post=8035"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}