{"id":8129,"date":"2025-07-22T10:24:27","date_gmt":"2025-07-22T04:54:27","guid":{"rendered":"https:\/\/namastedev.com\/blog\/?p=8129"},"modified":"2025-07-22T21:37:08","modified_gmt":"2025-07-22T16:07:08","slug":"best-practice-finding-middle-element","status":"publish","type":"post","link":"https:\/\/namastedev.com\/blog\/best-practice-finding-middle-element\/","title":{"rendered":"Best Practice &#8211; Finding Middle Element"},"content":{"rendered":"\n<!-- Prism.js CSS and JS -->\n<link href=\"https:\/\/cdn.jsdelivr.net\/npm\/prismjs@1.29.0\/themes\/prism-tomorrow.css\" rel=\"stylesheet\" \/>\n<script src=\"https:\/\/cdn.jsdelivr.net\/npm\/prismjs@1.29.0\/prism.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_code-tabs-container {\n    font-family: \"Segoe UI\", sans-serif !important;\n    max-width: 900px !important;\n    margin: 2rem auto !important;\n    border: 1px solid #ddd !important;\n    border-radius: 8px !important;\n    overflow: hidden !important;\n    background-color: white !important;\n  }\n\n  .wp_blog_code-tabs-header {\n    background: #f7f7f7 !important;\n    display: flex !important;\n    border-bottom: 1px solid #ddd !important;\n  }\n\n  .wp_blog_code-tab-button {\n    flex: 1 !important;\n    padding: 10px 15px !important;\n    border: none !important;\n    background: transparent !important;\n    cursor: pointer !important;\n    font-weight: bold !important;\n    transition: background 0.2s !important;\n    color: #242b33 !important;\n  }\n\n  .wp_blog_code-tab-button.active {\n    background: white !important;\n    border-bottom: 3px solid #0073aa !important;\n  }\n\n  .wp_blog_code-tab-content {\n    display: none !important;\n    padding: 20px !important;\n    background: #242b33 !important;\n  }\n\n  .wp_blog_code-tab-content > pre {\n    background: #242b33 !important;\n  }\n\n  .wp_blog_code-tab-content.active {\n    display: block !important;\n  }\n\n  .wp_blog_code-tab-content pre {\n    margin: 0 !important;\n    overflow-x: auto !important;\n  }\n\n  .wp_blog_explanation {\n    max-width: 900px !important;\n    margin: 2rem auto !important;\n    font-family: \"Segoe UI\", sans-serif !important;\n    line-height: 1.6 !important;\n    background: white !important;\n    color: black !important;\n    padding: 1rem !important;\n    border-radius: 8px !important;\n  }\n\n  .wp_blog_explanation h2 {\n    color: #0073aa !important;\n    font-size: 1.5rem !important;\n    margin-bottom: 0.5rem !important;\n  }\n\n  .wp_blog_explanation code {\n    background: #f1f1f1 !important;\n    padding: 2px 6px !important;\n    border-radius: 4px !important;\n    font-family: monospace !important;\n  }\n\n  .wp_blog_explanation h1,\n  .wp_blog_explanation h2,\n  .wp_blog_explanation h3,\n  .wp_blog_explanation h4,\n  .wp_blog_explanation h5,\n  .wp_blog_explanation h6,\n  .wp_blog_explanation p {\n    margin-top: 10px !important;\n    margin-bottom: 10px !important;\n  }\n<\/style>\n\n<div class=\"wp_blog_explanation\">\n  <p>This problem is about computing the floor of the square root of a number <code>x<\/code> using an optimized binary search approach. A best practice in binary search is to calculate the mid-point in a way that avoids integer overflow: <code>m = l + (r - l) \/ 2<\/code>.<\/p>\n\n  <h2>Steps<\/h2>\n  <ul>\n    <li>If <code>x<\/code> is less than 2, return <code>x<\/code>.<\/li>\n    <li>Set search boundaries: <code>l = 2<\/code>, <code>r = floor(x \/ 2)<\/code>.<\/li>\n    <li>Calculate mid-point safely: <code>m = l + floor((r - l) \/ 2)<\/code>.<\/li>\n    <li>Compare <code>m * m<\/code> with <code>x<\/code>.<\/li>\n    <li>If <code>m * m == x<\/code>, return <code>m<\/code>.<\/li>\n    <li>If <code>m * m &gt; x<\/code>, search left: <code>r = m - 1<\/code>.<\/li>\n    <li>If <code>m * m &lt; x<\/code>, search right: <code>l = m + 1<\/code>.<\/li>\n    <li>Return <code>r<\/code> at the end \u2014 it will be the floor of \u221ax.<\/li>\n  <\/ul>\n\n  <h2>Dry Run<\/h2>\n  <p><strong>Input:<\/strong> <code>x = 4<\/code><\/p>\n  <ol>\n    <li>l = 2, r = 2 \u2192 m = 2<\/li>\n    <li>2 * 2 = 4 \u2192 return 2<\/li>\n  <\/ol>\n  <p><strong>Output:<\/strong> <code>2<\/code><\/p>\n\n  <p><strong>Input:<\/strong> <code>x = 8<\/code><\/p>\n  <ol>\n    <li>l = 2, r = 4 \u2192 m = 3 \u2192 3*3 = 9 &gt; 8 \u2192 r = 2<\/li>\n    <li>l = 2, r = 2 \u2192 m = 2 \u2192 2*2 = 4 &lt; 8 \u2192 l = 3<\/li>\n    <li>Loop ends \u2192 return r = 2<\/li>\n  <\/ol>\n  <p><strong>Output:<\/strong> <code>2<\/code><\/p>\n\n  <h2>Time &#038; Space Complexity<\/h2>\n  <ul>\n    <li><strong>Time Complexity:<\/strong> O(log x)<\/li>\n    <li><strong>Space Complexity:<\/strong> O(1)<\/li>\n  <\/ul>\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=\"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=\"java\">Java<\/button>\n    <button class=\"wp_blog_code-tab-button\" data-lang=\"py\">Python<\/button>\n    <button class=\"wp_blog_code-tab-button\" data-lang=\"c#\">C#<\/button>\n  <\/div>\n\n  <div class=\"wp_blog_code-tab-content active\" data-lang=\"js\">\n    <pre><code class=\"language-javascript\">\nvar mySqrt = function(x) {\n    if (x < 2) return x;\n    let l = 2;\n    let r = Math.floor(x \/ 2);\n    while (l <= r) {\n        let m = l + Math.floor((r - l) \/ 2);\n        if (x === m * m) {\n            return m;\n        } else if (x < m * m) {\n            r = m - 1;\n        } else {\n            l = m + 1;\n        }\n    }\n    return r;\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;\nusing namespace std;\n\nint mySqrt(int x) {\n    if (x < 2) return x;\n    int l = 2, r = x \/ 2;\n    while (l <= r) {\n        int m = l + (r - l) \/ 2;\n        long long sq = 1LL * m * m;\n        if (sq == x) return m;\n        if (sq > x) r = m - 1;\n        else l = m + 1;\n    }\n    return r;\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;\n\nint mySqrt(int x) {\n    if (x < 2) return x;\n    int l = 2, r = x \/ 2;\n    while (l <= r) {\n        int m = l + (r - l) \/ 2;\n        long sq = (long)m * m;\n        if (sq == x) return m;\n        if (sq > x) r = m - 1;\n        else l = m + 1;\n    }\n    return r;\n}\n    <\/code><\/pre>\n  <\/div>\n\n  <div class=\"wp_blog_code-tab-content\" data-lang=\"java\">\n    <pre><code class=\"language-java\">\npublic class Solution {\n    public int mySqrt(int x) {\n        if (x < 2) return x;\n        int l = 2, r = x \/ 2;\n        while (l <= r) {\n            int m = l + (r - l) \/ 2;\n            long sq = (long)m * m;\n            if (sq == x) return m;\n            if (sq > x) r = m - 1;\n            else l = m + 1;\n        }\n        return r;\n    }\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 mySqrt(x: int) -> int:\n    if x < 2:\n        return x\n    l, r = 2, x \/\/ 2\n    while l <= r:\n        m = l + (r - l) \/\/ 2\n        if m * m == x:\n            return m\n        elif m * m > x:\n            r = m - 1\n        else:\n            l = m + 1\n    return r\n    <\/code><\/pre>\n  <\/div>\n\n  <div class=\"wp_blog_code-tab-content\" data-lang=\"c#\">\n    <pre><code class=\"language-csharp\">\npublic class Solution {\n    public int MySqrt(int x) {\n        if (x < 2) return x;\n        int l = 2, r = x \/ 2;\n        while (l <= r) {\n            int m = l + (r - l) \/ 2;\n            long sq = (long)m * m;\n            if (sq == x) return m;\n            if (sq > x) r = m - 1;\n            else l = m + 1;\n        }\n        return r;\n    }\n}\n    <\/code><\/pre>\n  <\/div>\n<\/div>\n\n\n\n<a href=\"https:\/\/leetcode.com\/problems\/sqrtx\/description\/\" target=\"blank\">Solve this problem.<\/a>\n<script>\n  document.addEventListener(\"DOMContentLoaded\", function () {\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        button.classList.add(\"active\");\n\n        contents.forEach((content) => {\n          content.classList.toggle(\"active\", content.getAttribute(\"data-lang\") === lang);\n        });\n      });\n    });\n  });\n<\/script>\n\n\n","protected":false},"excerpt":{"rendered":"<p>This problem is about computing the floor of the square root of a number x using an optimized binary search approach. A best practice in binary search is to calculate the mid-point in a way that avoids integer overflow: m = l + (r &#8211; l) \/ 2. Steps If x is less than 2,<\/p>\n","protected":false},"author":1,"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":[322,176,175,211,174,172,173],"tags":[],"class_list":["post-8129","post","type-post","status-publish","format-standard","category-algorithms-and-data-structures","category-csharp","category-cplusplus","category-data-structures","category-java","category-javascript","category-python"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/8129","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\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/comments?post=8129"}],"version-history":[{"count":1,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/8129\/revisions"}],"predecessor-version":[{"id":8130,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/8129\/revisions\/8130"}],"wp:attachment":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/media?parent=8129"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/categories?post=8129"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/tags?post=8129"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}