{"id":10050,"date":"2025-09-09T15:22:57","date_gmt":"2025-09-09T09:52:57","guid":{"rendered":"https:\/\/namastedev.com\/blog\/?p=10050"},"modified":"2025-09-09T15:51:22","modified_gmt":"2025-09-09T10:21:22","slug":"single-element-in-a-sorted-array_","status":"publish","type":"post","link":"https:\/\/namastedev.com\/blog\/single-element-in-a-sorted-array_\/","title":{"rendered":"Single Element in a Sorted Array"},"content":{"rendered":"\n\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   \n    <p>\n        This <strong>algorithm<\/strong> finds the <strong>single non-duplicate element<\/strong> in a sorted array where every other <strong>element appears exactly twice<\/strong>.\n    <\/p>\n\n    <h2>Approach:<\/h2>\n    <ul>\n        <li>Use binary search between <strong>left (l) and right (r)<\/strong>.<\/li>\n        <li>At each <code>mid<\/code> (m):<\/li>\n        <li>If <code>arr[m] === arr[m - 1]<\/code>, count elements on the left.<\/li>\n        <li>If that count is odd \u2192 single lies <code>left \u2192 r = m - 2<\/code>.<\/li>\n        <li>If count is even \u2192 single lies <code>right \u2192 l = m + 1<\/code>.<\/li>\n        <li>Same logic applies if <code>arr[m] === arr[m + 1]<\/code>.<\/li>\n        <li>If neither left nor right match \u2192 <code>return arr[m]<\/code>.<\/li>\n    <\/ul>\n\n    <h2>Time &#038; Space Complexity:<\/h2>\n    <p><strong>Time Complexity:<\/strong> O(logn)<\/p>\n    <p><strong>Space Complexity:<\/strong> O(1)<\/p>\n\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 = [1, 1, 2, 2, 3, 4, 4, 5, 5]<\/code><\/p>\n  <pre style=\"white-space: pre-wrap; background: var(--code-bg); padding: 1rem; border-radius: 8px; overflow-x: auto; color: var(--code-text);\">\n\nInitial:\nl = 0, r = 8\n\n--- While Loop Execution ---\n\nLoop 1:\nm = 0 + Math.floor((8 - 0) \/ 2) = 4\narr[m] = arr[4] = 3\narr[m-1] = arr[3] = 2\narr[m+1] = arr[5] = 4\n\nCheck 1: arr[m] === arr[m - 1] \u2192 3 === 2 \u2192 false\nCheck 2: arr[m] === arr[m + 1] \u2192 3 === 4 \u2192 false\n\nSince neither neighbor equals arr[m], we hit the else branch:\nreturn arr[m] \u2192 return 3\n\n--- Final Result ---\nFunction returns 3 (the single non-duplicate element)\n  <\/pre>\n  <p><strong>Output:<\/strong> <code>Result: 3<\/code><\/p>\n<\/div>\n\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    <div class=\"wp_blog_code-tab-content active\" data-lang=\"js\">\n      <pre><code class=\"language-javascript\">\nvar singleNonDuplicate = function(arr) {\n    let l = 0;\n    let r = arr.length - 1;\n    while (l < r) {\n        let m = l + Math.floor((r - l) \/ 2);\n        if (arr[m] === arr[m - 1]) {\n            let leftCount = m - l;\n            if (leftCount % 2 === 1) {\n                r = m - 2;\n            } else {\n                l = m + 1;\n            }\n        } else if (arr[m] === arr[m + 1]) {\n            let leftCount = m - l;\n            if (leftCount % 2 === 1) {\n                r = m - 1;\n            } else {\n                l = m + 2;\n            }\n        } else {\n            return arr[m];\n        }\n    }\n    return arr[l];\n};\n      <\/code><\/pre>\n    <\/div>\n\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"py\">\n      <pre><code class=\"language-python\">\ndef singleNonDuplicate(arr):\n    l, r = 0, len(arr) - 1\n    while l < r:\n        m = l + (r - l) \/\/ 2\n        if arr[m] == arr[m - 1]:\n            leftCount = m - l\n            if leftCount % 2 == 1:\n                r = m - 2\n            else:\n                l = m + 1\n        elif arr[m] == arr[m + 1]:\n            leftCount = m - l\n            if leftCount % 2 == 1:\n                r = m - 1\n            else:\n                l = m + 2\n        else:\n            return arr[m]\n    return arr[l]\n      <\/code><\/pre>\n    <\/div>\n\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"java\">\n      <pre><code class=\"language-java\">\npublic int singleNonDuplicate(int[] arr) {\n    int l = 0, r = arr.length - 1;\n    while (l < r) {\n        int m = l + (r - l) \/ 2;\n        if (m > 0 && arr[m] == arr[m - 1]) {\n            int leftCount = m - l;\n            if (leftCount % 2 == 1)\n                r = m - 2;\n            else\n                l = m + 1;\n        } else if (m < arr.length - 1 &#038;&#038; arr[m] == arr[m + 1]) {\n            int leftCount = m - l;\n            if (leftCount % 2 == 1)\n                r = m - 1;\n            else\n                l = m + 2;\n        } else {\n            return arr[m];\n        }\n    }\n    return arr[l];\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; -->\nint singleNonDuplicate(vector& arr) {\n    int l = 0, r = arr.size() - 1;\n    while (l < r) {\n        int m = l + (r - l) \/ 2;\n        if (arr[m] == arr[m - 1]) {\n            int leftCount = m - l;\n            if (leftCount % 2 == 1)\n                r = m - 2;\n            else\n                l = m + 1;\n        } else if (arr[m] == arr[m + 1]) {\n            int leftCount = m - l;\n            if (leftCount % 2 == 1)\n                r = m - 1;\n            else\n                l = m + 2;\n        } else {\n            return arr[m];\n        }\n    }\n    return arr[l];\n}\n<\/code><\/pre>\n    <\/div>\n\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"c\">\n      <pre><code class=\"language-c\">\n<!-- #include &lt;stdio.h&gt; -->\nint singleNonDuplicate(int* arr, int arrSize) {\n    int l = 0, r = arrSize - 1;\n    while (l < r) {\n        int m = l + (r - l) \/ 2;\n        if (arr[m] == arr[m - 1]) {\n            int leftCount = m - l;\n            if (leftCount % 2 == 1)\n                r = m - 2;\n            else\n                l = m + 1;\n        } else if (arr[m] == arr[m + 1]) {\n            int leftCount = m - l;\n            if (leftCount % 2 == 1)\n                r = m - 1;\n            else\n                l = m + 2;\n        } else {\n            return arr[m];\n        }\n    }\n    return arr[l];\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\">\npublic int SingleNonDuplicate(int[] arr) {\n    int l = 0, r = arr.Length - 1;\n    while (l < r) {\n        int m = l + (r - l) \/ 2;\n        if (arr[m] == arr[m - 1]) {\n            int leftCount = m - l;\n            if (leftCount % 2 == 1)\n                r = m - 2;\n            else\n                l = m + 1;\n        } else if (arr[m] == arr[m + 1]) {\n            int leftCount = m - l;\n            if (leftCount % 2 == 1)\n                r = m - 1;\n            else\n                l = m + 2;\n        } else {\n            return arr[m];\n        }\n    }\n    return arr[l];\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: This algorithm finds the single non-duplicate element in a sorted array where every other element appears exactly twice. Approach: Use binary search between left (l) and right (r). At each mid (m): If arr[m] === arr[m &#8211; 1], count elements on the left. If that count is odd \u2192 single lies left<\/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":["post-10050","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-dsa","category-java","category-javascript","category-python"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/10050","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=10050"}],"version-history":[{"count":1,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/10050\/revisions"}],"predecessor-version":[{"id":10051,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/10050\/revisions\/10051"}],"wp:attachment":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/media?parent=10050"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/categories?post=10050"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/tags?post=10050"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}