{"id":9913,"date":"2025-09-03T12:58:39","date_gmt":"2025-09-03T07:28:39","guid":{"rendered":"https:\/\/namastedev.com\/blog\/?p=9913"},"modified":"2025-09-20T22:30:11","modified_gmt":"2025-09-20T17:00:11","slug":"square-root-of-x_","status":"publish","type":"post","link":"https:\/\/namastedev.com\/blog\/square-root-of-x_\/","title":{"rendered":"Square Root of X"},"content":{"rendered":"\n<!-- SUM of two numbers -->\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: #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\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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The goal is to use binary search to compute the answer efficiently.\n    <\/p>\n\n    <h2>Approach:<\/h2>\n    <ul>\n      <li>If <code>x<\/code> is <code>0<\/code> or <code>1<\/code>, return <code>x<\/code>.<\/li>\n      <li>Set the binary search range: <code>l = 2, r = floor(x \/ 2)<\/code>.<\/li>\n      <li>Use <strong>binary search<\/strong> to find the greatest number <code>m<\/code> such that <code>m * m \u2264 x<\/code>.<\/li>\n      <li>If <code>m * m === x<\/code>, return <code>m<\/code>.<\/li>\n      <li>If <code>m * m > x<\/code>, search left side.<\/li>\n      <li>If <code>m * m < x<\/code>, search right side.<\/li>\n      <li><code>Return<\/code> <code>r<\/code> as the <strong>floor square root<\/strong>.<\/li>\n    <\/ul>\n\n    <h2>Time & Space Complexity:<\/h2>\n    <p><strong>Time Complexity:<\/strong> O(logx)<\/p>\n    <p><strong>Space Complexity:<\/strong> O(1)<\/p>\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>x = 8<\/code><\/p>\n      <pre style=\"white-space: pre-wrap; background: #fff5ea; padding: 1rem; border-radius: 8px; overflow-x: auto;\">\nInitial:\nif (x < 2) \u2192 false (since 8 \u2265 2)\nl = 2, r = Math.floor(8 \/ 2) = 4\n\nLoop 1:\nm = Math.floor((2 + 4) \/ 2) = 3\nm * m = 9\n8 < 9 \u2192 r = m - 1 = 2\n\nLoop 2:\nm = Math.floor((2 + 2) \/ 2) = 2\nm * m = 4\n8 > 4 \u2192 l = m + 1 = 3\n\nExit condition:\nl = 3, r = 2 \u2192 l > r \u2192 loop ends\n\nReturn r = 2\n      <\/pre>\n      <!-- <p><strong>Output:<\/strong> <code>Result: 2<\/code><\/p> -->\n    <\/div>\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 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 = Math.floor((l + r) \/ 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=\"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) \/\/ 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=\"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=\"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=\"cs\">\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<\/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 problem is about finding the floor value of the square root of a non-negative integer x. You cannot use built-in square root functions. The goal is to use binary search to compute the answer efficiently. Approach: If x is 0 or 1, return x. Set the binary search range: l =<\/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":[210,322,176,175,211,811,810,173],"tags":[],"class_list":["post-9913","post","type-post","status-publish","format-standard","category-algorithms","category-algorithms-and-data-structures","category-csharp","category-cplusplus","category-data-structures","category-data-structures-and-algorithms","category-dsa","category-python"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/9913","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=9913"}],"version-history":[{"count":4,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/9913\/revisions"}],"predecessor-version":[{"id":10090,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/9913\/revisions\/10090"}],"wp:attachment":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/media?parent=9913"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/categories?post=9913"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/tags?post=9913"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}