{"id":10131,"date":"2025-09-26T14:45:34","date_gmt":"2025-09-26T09:15:34","guid":{"rendered":"https:\/\/namastedev.com\/blog\/?p=10131"},"modified":"2025-09-26T14:51:01","modified_gmt":"2025-09-26T09:21:01","slug":"house-robber-ii","status":"publish","type":"post","link":"https:\/\/namastedev.com\/blog\/house-robber-ii\/","title":{"rendered":"House Robber II"},"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;   \/* light bg instead of dark blue *\/\n  color: #E58C32;        \/* brand orange *\/\n  padding: 3px 6px;\n  border-radius: 4px;\n  font-family: 'Courier New', monospace;\n  font-weight: 600;      \/* optional, makes it pop *\/\n}\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\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\n.wp_blog_code-tab-button:hover {\n  background: var(--secondary);\n}\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\n.wp_blog_code-tab-content.active {\n  display: block;\n}\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\n\/* Dark mode variables *\/\n.wp_blog_theme.dark-mode {\n  --light-bg: #121212;\n  --text-dark: #f5f5f5;\n  --shadow: 0 4px 12px rgba(255, 255, 255, 0.08);\n  --code-bg: #1e1e1e;\n  --code-text: #c5f0ff;\n}\n\n.wp_blog_theme.dark-mode .wp_blog_explanation {\n  background: #1e1e1e;\n}\n\n\/* Dark mode code highlight *\/\n.wp_blog_theme.dark-mode .wp_blog_explanation code {\n  background: #333;\n  color: #ffd27f;\n}\n\n.wp_blog_theme {\n  position: relative; \/* 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      You are a professional robber planning to rob houses along a street. Each house has a certain amount of money stashed. All houses at this place are <strong>arranged in a circle<\/strong>. That means the first house is the neighbor of the last one. Meanwhile, adjacent houses have a security system connected, and <strong>it will automatically contact the police if two adjacent houses were broken into on the same night<\/strong>.  \n    <\/p>\n    \n    <p>\n      Given an integer array <code>nums<\/code> representing the amount of money of each house, return <i>the maximum amount of money you can rob tonight <strong>without alerting the police<\/strong><\/i>.\n    <\/p>\n\n\n    <h3>Example 1:<\/h2>\n    <p><strong>Input:<\/strong> nums = [2,3,2]<\/p>\n    <p><strong>Output:<\/strong> 3<\/p>\n    <p><strong>Explanation:<\/strong>  \n      You cannot rob house 1 (money = 2) and then rob house 3 (money = 2), because they are adjacent houses.\n    <\/p>\n\n    <h3>Example 2:<\/h2>\n    <p><strong>Input:<\/strong> nums = [1,2,3,1]<\/p>\n    <p><strong>Output:<\/strong> 4<\/p>\n    <p><strong>Explanation:<\/strong> Rob house 1 (money = 1) and then rob house 3 (money = 3). Total amount you can rob = 1 + 3 = 4.\n\n    <p>Example 3:<\/p>\n    <p><strong>Input:<\/strong> nums = [1,2,3]<\/p>\n    <p><strong>Output:<\/strong> 3<\/p>\n\n    <h3>Constraints<\/h3>\n    <ul>\n       <li><code>1 <= nums.length <= 100<\/code><\/li>\n       <li><code>0 <= nums[i] <= 1000<\/code><\/li>\n    <\/ul>\n    \n<h2>Approach:<\/h2>\n<ul>\n  <li>Since houses are in a <strong>circle<\/strong>, you can\u2019t rob both the <strong>first and last<\/strong> house.<\/li>\n  <li>So, split the problem into <strong>two linear cases:<\/strong>\n\n    <ul>\n      <li><strong>Case 1<\/strong> \u2192 Rob houses from <code>0 to n-2<\/code> (exclude last).<\/li>\n      <li><strong>Case 2<\/strong> \u2192 Rob houses from <code>1 to n-1<\/code> (exclude first).<\/li>\n    <\/ul>\n  <\/li>\n\n  <li>For each case, use <strong>DP with space optimization<\/strong> (p1, p2) to decide for every house:\n    <code>curr=max(val[i]+p2,p1)<\/code>\n    <ul>\n      <li>Rob current house \u2192 <code>val[i] + p2<\/code><\/li>\n      <li>Skip current house \u2192 <code>p1<\/code><\/li>\n    <\/ul>\n  <\/li>\n\n  <li><code>Final = max of both cases.<\/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>val = [2, 3, 2]<\/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: rob([2, 3, 2])\nn = 3\nSince n != 1 \u2192 continue\n\nWe call:\n- robHelper(0, n-2) \u2192 robHelper(0, 1)\n- robHelper(1, n-1) \u2192 robHelper(1, 2)\n\nCall robHelper(0, 1):\np1 = 0, p2 = 0\n\nIteration (i = 0):\n- curr = Math.max(val[0] + p2, p1)\n       = Math.max(2 + 0, 0) = 2\n- temp = p1 = 0\n- p1 = curr = 2\n- p2 = temp = 0\n- curr++ \u2192 3\nState \u2192 p1 = 2, p2 = 0\n\nIteration (i = 1):\n- curr = Math.max(val[1] + p2, p1)\n       = Math.max(3 + 0, 2) = 3\n- temp = p1 = 2\n- p1 = curr = 3\n- p2 = temp = 2\n- curr++ \u2192 4\nState \u2192 p1 = 3, p2 = 2\n\nLoop ends\nReturn p1 = 3\n\n---------------------------------------\nCall robHelper(1, 2):\np1 = 0, p2 = 0\n\nIteration (i = 1):\n- curr = Math.max(val[1] + p2, p1)\n       = Math.max(3 + 0, 0) = 3\n- temp = p1 = 0\n- p1 = curr = 3\n- p2 = temp = 0\n- curr++ \u2192 4\nState \u2192 p1 = 3, p2 = 0\n\nIteration (i = 2):\n- curr = Math.max(val[2] + p2, p1)\n       = Math.max(2 + 0, 3) = 3\n- temp = p1 = 3\n- p1 = curr = 3\n- p2 = temp = 3\n- curr++ \u2192 4\nState \u2192 p1 = 3, p2 = 3\n\nLoop ends\nReturn p1 = 3\n\n---------------------------------------\n\nFinal Step:\nReturn Math.max(robHelper(0,1), robHelper(1,2))\n= Math.max(3, 3) = 3\n  <\/pre> \n  \n  <p><strong>Output:<\/strong> <code>3<\/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-2025-09-26-at-2.44.14\u202fPM.png\" alt=\"\" \/>\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 rob = function(val) {\n    let n = val.length;\n    if (n == 1) return val[0];\n    var robHelper = function(start, end) {\n        let p2 = 0, p1 = 0;\n        for (let i = start; i <= end; i++) {\n            let curr = Math.max(val[i] + p2, p1);\n            let temp = p1;\n            p1 = curr;\n            p2 = temp;\n            curr++;\n        }\n        return p1;\n    };\n    return Math.max(robHelper(0, n - 2), robHelper(1, n - 1));\n};\n<\/code><\/pre>\n    <\/div>\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"py\">\n      <pre><code class=\"language-python\">\nfrom typing import List\n\ndef rob(val: List[int]) -> int:\n    n = len(val)\n    if n == 0:\n        return 0\n    if n == 1:\n        return val[0]\n\n    def rob_helper(start: int, end: int) -> int:\n        p1 = 0\n        p2 = 0\n        for i in range(start, end + 1):\n            curr = max(val[i] + p2, p1)\n            temp = p1\n            p1 = curr\n            p2 = temp\n        return p1\n\n    return max(rob_helper(0, n - 2), rob_helper(1, n - 1))\n      <\/code><\/pre>\n    <\/div>\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"java\">\n      <pre><code class=\"language-java\">\nclass Solution {\n    public int rob(int[] val) {\n        int n = val.length;\n        if (n == 0) return 0;\n        if (n == 1) return val[0];\n\n        java.util.function.IntBinaryOperator robHelper = (start, end) -> {\n            int p1 = 0, p2 = 0;\n            for (int i = start; i <= end; i++) {\n                int curr = Math.max(val[i] + p2, p1);\n                int temp = p1;\n                p1 = curr;\n                p2 = temp;\n            }\n            return p1;\n        };\n        return Math.max(robHelper.applyAsInt(0, n - 2), robHelper.applyAsInt(1, n - 1));\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;\nusing namespace std;\nclass Solution {\npublic:\n    int rob(const vector<int>& val) {\n        int n = (int)val.size();\n        if (n == 0) return 0;\n        if (n == 1) return val[0];\n        auto robHelper = [&](int start, int end) {\n            int p1 = 0, p2 = 0;\n            for (int i = start; i <= end; ++i) {\n                int curr = max(val[i] + p2, p1);\n                int temp = p1;\n                p1 = curr;\n                p2 = temp;\n            }\n            return p1;\n        };\n        return max(robHelper(0, n - 2), robHelper(1, n - 1));\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) { return a > b ? a : b; }\n\nint robHelper(const int *val, int start, int end) {\n    int p1 = 0, p2 = 0;\n    for (int i = start; i <= end; ++i) {\n        int curr = max(val[i] + p2, p1);\n        int temp = p1;\n        p1 = curr;\n        p2 = temp;\n    }\n    return p1;\n}\nint rob(const int *val, int n) {\n    if (n == 0) return 0;\n    if (n == 1) return val[0];\n    int a = robHelper(val, 0, n - 2);\n    int b = robHelper(val, 1, n - 1);\n    return max(a, b);\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;\npublic class Solution {\n    public int Rob(int[] val) {\n        int n = val.Length;\n        if (n == 0) return 0;\n        if (n == 1) return val[0];\n\n        int RobHelper(int start, int end) {\n            int p1 = 0, p2 = 0;\n            for (int i = start; i <= end; i++) {\n                int curr = Math.Max(val[i] + p2, p1);\n                int temp = p1;\n                p1 = curr;\n                p2 = temp;\n            }\n            return p1;\n        }\n\n        return Math.Max(RobHelper(0, n - 2), RobHelper(1, n - 1));\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: You are a professional robber planning to rob houses along a street. Each house has a certain amount of money stashed. All houses at this place are arranged in a circle. That means the first house is the neighbor of the last one. Meanwhile, adjacent houses have a security system connected, and<\/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":[210,322,176,175,211,811,810,174,172,173],"tags":[],"class_list":{"0":"post-10131","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-algorithms","7":"category-algorithms-and-data-structures","8":"category-csharp","9":"category-cplusplus","10":"category-data-structures","11":"category-data-structures-and-algorithms","12":"category-dsa","13":"category-java","14":"category-javascript","15":"category-python"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/10131","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=10131"}],"version-history":[{"count":1,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/10131\/revisions"}],"predecessor-version":[{"id":10132,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/10131\/revisions\/10132"}],"wp:attachment":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/media?parent=10131"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/categories?post=10131"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/tags?post=10131"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}