{"id":9773,"date":"2025-08-29T16:07:22","date_gmt":"2025-08-29T10:37:22","guid":{"rendered":"https:\/\/namastedev.com\/blog\/?p=9773"},"modified":"2025-10-22T20:29:41","modified_gmt":"2025-10-22T14:59:41","slug":"merge-sort","status":"publish","type":"post","link":"https:\/\/namastedev.com\/blog\/merge-sort\/","title":{"rendered":"Merge Sort"},"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\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\n<h1 class=\"wp_blog_main-heading\"><\/h1>\n\n<div class=\"wp_blog_explanation\">\n\n    <h2>Merge Sort<\/h2>\n    <ul>\n        <li><strong>Merge Sort<\/strong> is a popular <code>divide-and-conquer<\/code> sorting algorithm that divides the input <strong>array into two halves<\/strong>, recursively sorts them, and then merges the sorted halves into one <code>sorted result<\/code>.<\/li>\n        <li>It is an <strong>example<\/strong> of a <code>stable sort<\/code> that guarantees <code>O(n log n)<\/code> performance in all <code>cases<\/code> \u2014 best, worst, and average.<\/li>\n    <\/ul>\n    <!-- <h2>Example 1:<\/h2>\n    <p><strong>Input:<\/strong> [4, 5, 1, 3, 9]<\/p>\n    <p><strong>Output:<\/strong> [1, 3, 4, 5, 9]<\/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><strong>Divide: <\/strong>Split the array into <code>two<\/code> halves.<\/li>\n        <li><strong>Conquer: <\/strong>Recursively <code>sort<\/code> each half using <strong>merge sort<\/strong>.<\/li>\n        <li><strong>Combine: <\/strong> <code>Merge the two sorted<\/code> halves into one sorted array.<\/li>\n    <\/ul>\n\n    <h2>Key Concept: <code>Merge Step<\/code><\/h2>\n    <ul>\n        <li>The key step is <strong>merging two sorted arrays<\/strong> efficiently into one <code>sorted array<\/code>.<\/li>\n        <li>This is done using a <code>two-pointer approach<\/code>, comparing elements from <code>both<\/code> <strong>arrays and adding the smaller one into a new result array<\/strong>.<\/li>\n    <\/ul>\n\n    <h2>Time &#038; Space Complexity:<\/h2>\n    <p><strong>Time Complexity: O(n log n) <\/strong> Divide takes log n steps and merging takes linear time.<\/p>\n    <p><strong>Space Complexity: O(n)<\/strong> Additional space is needed to store the merged arrays.<\/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 = [4, 5, 1, 3, 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);\"> \nStep 1: sortArray([4, 5, 1, 3, 9])\nmid = 2\nleft = sortArray([4, 5])\nright = sortArray([1, 3, 9])\n\n---\nStep 2: sortArray([4, 5])\nmid = 1\nleft = sortArray([4]) \u2192 [4]  (base case)\nright = sortArray([5]) \u2192 [5] (base case)\nmerge([4], [5]) \u2192 [4, 5]\n\n---\nStep 3: sortArray([1, 3, 9])\nmid = 1\nleft = sortArray([1]) \u2192 [1]  (base case)\nright = sortArray([3, 9])\n\nStep 4: sortArray([3, 9])\nmid = 1\nleft = sortArray([3]) \u2192 [3]  (base case)\nright = sortArray([9]) \u2192 [9] (base case)\nmerge([3], [9]) \u2192 [3, 9]\n\nmerge([1], [3, 9]) \u2192 [1, 3, 9]\n\n---\nStep 5: merge([4, 5], [1, 3, 9])\nCompare 4 and 1 \u2192 take 1 \u2192 [1]\nCompare 4 and 3 \u2192 take 3 \u2192 [1, 3]\nCompare 4 and 9 \u2192 take 4 \u2192 [1, 3, 4]\nCompare 5 and 9 \u2192 take 5 \u2192 [1, 3, 4, 5]\nRemaining \u2192 [9] \u2192 [1, 3, 4, 5, 9]\n\n<strong>Final Sorted Array:<\/strong> [1, 3, 4, 5, 9]\n  <\/pre> \n\n  <p><strong>Output:<\/strong> <code>[1, 3, 4, 5, 9]<\/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\">\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\">\nvar sortArray = function(nums) {\n    if (nums.length <= 1) return nums;\n    let mid = Math.floor(nums.length \/ 2);\n    let left = sortArray(nums.slice(0, mid));\n    let right = sortArray(nums.slice(mid));\n    return merge(left, right);\n};\n\nfunction merge(left, right) {\n    let res = [], i = 0, j = 0;\n    while (i < left.length &#038;&#038; j < right.length) {\n        if (left[i] < right[j]) {\n            res.push(left[i++]);\n        } else {\n            res.push(right[j++]);\n        }\n    }\n    return [...res, ...left.slice(i), ...right.slice(j)];\n}   \n    <\/code><\/pre>\n    <\/div>\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"py\">\n        <pre><code class=\"language-python\">\nclass Solution(object):\n    def sortArray(self, nums):\n        if len(nums) <= 1:\n            return nums\n        mid = len(nums) \/\/ 2\n        left = self.sortArray(nums[:mid])\n        right = self.sortArray(nums[mid:])\n        return self.merge(left, right)\n\n    def merge(self, left, right):\n        res = []\n        i = j = 0\n        while i < len(left) and j < len(right):\n            if left[i] < right[j]:\n                res.append(left[i])\n                i += 1\n            else:\n                res.append(right[j])\n                j += 1\n        res.extend(left[i:])\n        res.extend(right[j:])\n        return res  \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[] sortArray(int[] nums) {\n        if (nums.length <= 1) return nums;\n        int mid = nums.length \/ 2;\n        int[] left = sortArray(Arrays.copyOfRange(nums, 0, mid));\n        int[] right = sortArray(Arrays.copyOfRange(nums, mid, nums.length));\n        return merge(left, right);\n    }\n\n    private int[] merge(int[] left, int[] right) {\n        int[] res = new int[left.length + right.length];\n        int i = 0, j = 0, k = 0;\n        while (i < left.length &#038;&#038; j < right.length)\n            res[k++] = (left[i] < right[j]) ? left[i++] : right[j++];\n        while (i < left.length) res[k++] = left[i++];\n        while (j < right.length) res[k++] = right[j++];\n        return res;\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;vector&gt;\n <!-- #include <iostream> -->\n using namespace std;\n  class Solution {\n  public:\n      vector<int> sortArray(vector<int>& nums) {\n          if (nums.size() <= 1) return nums;\n          int mid = nums.size() \/ 2;\n          vector<int> left(nums.begin(), nums.begin() + mid);\n          vector<int> right(nums.begin() + mid, nums.end());\n          return merge(sortArray(left), sortArray(right));\n      }\n  \n      vector<int> merge(const vector<int>& left, const vector<int>& right) {\n          vector<int> res;\n          int i = 0, j = 0;\n          while (i < (int)left.size() &#038;&#038; j < (int)right.size()) {\n              if (left[i] < right[j]) res.push_back(left[i++]);\n              else res.push_back(right[j++]);\n          }\n          while (i < (int)left.size()) res.push_back(left[i++]);\n          while (j < (int)right.size()) res.push_back(right[j++]);\n          return res;\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;stdlib.h&gt;\n\n  void merge(int* arr, int l, int m, int r) {\n      int i, j, k;\n      int n1 = m - l + 1;\n      int n2 = r - m;\n      int* L = (int*)malloc(n1 * sizeof(int));\n      int* R = (int*)malloc(n2 * sizeof(int));\n      for (i = 0; i < n1; i++)\n          L[i] = arr[l + i];\n      for (j = 0; j < n2; j++)\n          R[j] = arr[m + 1 + j];\n      i = 0; j = 0; k = l;\n      while (i < n1 &#038;&#038; j < n2) {\n          if (L[i] <= R[j]) {\n              arr[k++] = L[i++];\n          } else {\n              arr[k++] = R[j++];\n          }\n      }\n      while (i < n1) {\n          arr[k++] = L[i++];\n      }\n      while (j < n2) {\n          arr[k++] = R[j++];\n      }\n      free(L);\n      free(R);\n  }\n  void mergeSort(int* arr, int l, int r) {\n      if (l < r) {\n          int m = l + (r - l) \/ 2;\n          mergeSort(arr, l, m);\n          mergeSort(arr, m + 1, r);\n          merge(arr, l, m, r);\n      }\n  }\n  \n  \/**\n   * Note: The returned array must be malloced, assume caller calls free().\n   *\/\n  int* sortArray(int* nums, int numsSize, int* returnSize) {\n      int* result = (int*)malloc(numsSize * sizeof(int));\n      for (int i = 0; i < numsSize; i++) {\n          result[i] = nums[i];\n      }\n      mergeSort(result, 0, numsSize - 1);\n      *returnSize = numsSize;\n      return result;\n  }\n<\/code><\/pre>\n    <\/div>\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"cs\">\n        <pre><code class=\"language-csharp\">\npublic class Solution {\n    public int[] SortArray(int[] nums) {\n        if (nums.Length <= 1) return nums;\n        int mid = nums.Length \/ 2;\n        int[] left = SortArray(nums[..mid]);\n        int[] right = SortArray(nums[mid..]);\n        return Merge(left, right);\n    }\n    private int[] Merge(int[] left, int[] right) {\n        int[] res = new int[left.Length + right.Length];\n        int i = 0, j = 0, k = 0;\n        while (i < left.Length &#038;&#038; j < right.Length)\n            res[k++] = (left[i] < right[j]) ? left[i++] : right[j++];\n        while (i < left.Length) res[k++] = left[i++];\n        while (j < right.Length) res[k++] = right[j++];\n        return res;\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 Merge Sort Merge Sort is a popular divide-and-conquer sorting algorithm that divides the input array into two halves, recursively sorts them, and then merges the sorted halves into one sorted result. It is an example of a stable sort that guarantees O(n log n) performance in all cases \u2014 best, worst, and average. Approach:<\/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":[210,322,260,176,175,211,811,174,172,173],"tags":[],"class_list":["post-9773","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-java","category-javascript","category-python"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/9773","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=9773"}],"version-history":[{"count":3,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/9773\/revisions"}],"predecessor-version":[{"id":10547,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/9773\/revisions\/10547"}],"wp:attachment":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/media?parent=9773"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/categories?post=9773"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/tags?post=9773"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}