{"id":9761,"date":"2025-08-29T15:06:18","date_gmt":"2025-08-29T09:36:18","guid":{"rendered":"https:\/\/namastedev.com\/blog\/?p=9761"},"modified":"2025-10-22T20:24:25","modified_gmt":"2025-10-22T14:54:25","slug":"binary-search_","status":"publish","type":"post","link":"https:\/\/namastedev.com\/blog\/binary-search_\/","title":{"rendered":"Binary Search"},"content":{"rendered":"\n<!-- Sum of all numbers in array using Recursion 1 -->\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<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\n<h1 class=\"wp_blog_main-heading\"><\/h1>\n\n<div class=\"wp_blog_explanation\">\n\n    <h2>Binary Search<\/h2>\n    <p><code>Binary Search is an efficient algorithm<\/code> used to <strong>find the position of a target value<\/strong> within a <code>sorted array<\/code>. Unlike <strong>linear search<\/strong>, it repeatedly divides the search interval in half, significantly <code>reducing the number<\/code> of comparisons.<\/p>   \n    <h2>Example 1:<\/h2>\n    <p><strong>Input:<\/strong> [1, 3, 5, 7, 9]<\/p>\n    <p><strong>Output:<\/strong> 7<\/p>\n\n    <!-- <h2>Example 2:<\/h2>\n    <p><strong>Input:<\/strong> arr = [6, 8, 0, 3]<\/p>\n    <p><strong>Output:<\/strong> -1<\/p>\n    <p><strong>Explanation: <\/strong>5 is not present in the array<\/p>\n -->\n\n    <h2>Approach:<\/h2>\n    <ul>\n        <li>Set <code>left = 0<\/code> <strong>right<\/strong> <code>= nums.length - 1<\/code>.<\/li>\n        <li>While <code>left <= right:<\/code><\/li>\n        <li>Calculate <code>middle = Math.floor((left + right) \/ 2)<\/code>.<\/li>\n        <li>If <code>nums[middle] === target,<\/code> return <code>middle<\/code>.<\/li>\n        <li>If <code>target < nums[middle]<\/code>, discard the right half: <code>right = middle - 1<\/code>.<\/li>\n        <li>Else discard the left half: <code>left = middle + 1<\/code>.<\/li>\n        <li>If the <code>target<\/code> is <strong>not found<\/strong><code> return -1<\/code>.<\/li>\n    <\/ul>\n\n    <h2>Time & Space Complexity:<\/h2>\n    <p><strong>Time Complexity: O(1) (Best Case)<\/strong>   when the target is found at the middle initially.<\/p>\n    <p><strong>Worst Case: O(log n)<\/strong> the array is halved every iteration.<\/p>\n    <p><strong>Space Complexity: O(1)<\/strong> <code>Constant Space<\/code>No additional data structures.<\/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>nums = [-1, 0, 3, 5, 9, 12], target = 9<\/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);\">\nInitial:\nleft = 0, right = 5\n\nIteration 1:\nmiddle = Math.floor((0 + 5) \/ 2) = 2\nnums[2] = 3\ntarget = 9\n   \u2192 target > nums[middle] \u2192 left = middle + 1 = 3\n\nState: left = 3, right = 5\n\nIteration 2:\nmiddle = Math.floor((3 + 5) \/ 2) = 4\nnums[4] = 9\ntarget = 9\n   \u2192 target === nums[middle] \u2192 return 4\n\nLoop ends (target found).\n  <\/pre> \n  \n  <p><strong>Output:<\/strong> <code>4<\/code> (Target found at index 4)<\/p> \n<\/div>\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\">\n            JavaScript\n        <\/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\">\n\n  var search = function(nums, target) {\n    let left = 0;\n    let right = nums.length - 1;\n  \n    while (right >= left) {\n      let middle = Math.floor((left + right) \/ 2);\n  \n      if (target === nums[middle]) {\n        return middle;\n      } else if (target < nums[middle]) {\n        right = middle - 1;\n      } else {\n        left = middle + 1;\n      }\n    }\n  \n    return -1;\n  };\n      \n    <\/code><\/pre>\n    <\/div>\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"py\">\n        <pre><code class=\"language-python\">\n class Solution(object):\n    def search(self, nums, target):\n      \"\"\"\n      :type nums: List[int]\n      :type target: int\n      :rtype: int\n      \"\"\"\n      left = 0\n      right = len(nums) - 1\n  \n      while left <= right:\n        middle = (left + right) \/\/ 2\n  \n        if nums[middle] == target:\n          return middle\n        elif target < nums[middle]:\n          right = middle - 1\n        else:\n          left = middle + 1\n  \n      return -1  # Target not found\n    <\/code><\/pre>\n    <\/div>\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"java\">\n        <pre><code class=\"language-java\">\n public class Solution {\n    public static int search(int[] nums, int target) {\n      int left = 0, right = nums.length - 1;\n  \n      while (left <= right) {\n        int middle = left + (right - left) \/ 2;\n  \n        if (nums[middle] == target) {\n          return middle;\n        } else if (target < nums[middle]) {\n          right = middle - 1;\n        } else {\n          left = middle + 1;\n        }\n      }\n  \n      return -1;\n    }\n  }\n<\/code><\/pre>\n    <\/div>\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"cpp\">\n        <pre><code class=\"language-cpp\">\n<!-- #include &lt;iostream&gt; -->\n\nclass Solution {\n  public:\n    int search(vector<int>& nums, int target) {\n      int left = 0;\n      int right = nums.size() - 1;\n  \n      while (left <= right) {\n        int middle = left + (right - left) \/ 2;\n  \n        if (nums[middle] == target) {\n          return middle;\n        } else if (target < nums[middle]) {\n          right = middle - 1;\n        } else {\n          left = middle + 1;\n        }\n      }\n  \n      return -1;\n    }\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 int search(int* nums, int numsSize, int target) {\n    int left = 0;\n    int right = numsSize - 1;\n  \n    while (left <= right) {\n      int middle = left + (right - left) \/ 2;\n  \n      if (nums[middle] == target) {\n        return middle;\n      } else if (target < nums[middle]) {\n        right = middle - 1;\n      } else {\n        left = middle + 1;\n      }\n    }\n  \n    return -1; \/\/ Target not found\n  }\n<\/code><\/pre>\n    <\/div>\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"cs\">\n        <pre><code class=\"language-csharp\">\nusing System;\npublic class Program\n{\n    public static int Search(int[] nums, int target)\n    {\n        int left = 0;\n        int right = nums.Length - 1;\n        while (right >= left)\n        {\n            int middle = (left + right) \/ 2;\n            if (target == nums[middle])\n            {\n                return middle;\n            }\n            else if (target < nums[middle])\n            {\n                right = middle - 1;\n            }\n            else\n            {\n                left = middle + 1;\n            }\n        }\n        return -1;\n    }\n    public static void Main()\n    {\n        int[] nums = { 1, 3, 5, 7, 9 };\n        int target = 7;\n        int result = Search(nums, target);\n        Console.WriteLine(\"Element found at index: \" + result);\n    }\n}\n\n  <\/code><\/pre>\n    <\/div>\n<\/div>\n<\/div>\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","protected":false},"excerpt":{"rendered":"<p>\ud83c\udf19 Binary Search Binary Search is an efficient algorithm used to find the position of a target value within a sorted array. Unlike linear search, it repeatedly divides the search interval in half, significantly reducing the number of comparisons. Example 1: Input: [1, 3, 5, 7, 9] Output: 7 Approach: Set left = 0 right<\/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":[176,175,211,811,810,174,172,173],"tags":[],"class_list":["post-9761","post","type-post","status-publish","format-standard","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\/9761","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=9761"}],"version-history":[{"count":4,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/9761\/revisions"}],"predecessor-version":[{"id":10543,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/9761\/revisions\/10543"}],"wp:attachment":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/media?parent=9761"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/categories?post=9761"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/tags?post=9761"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}