{"id":10079,"date":"2025-09-18T15:02:08","date_gmt":"2025-09-18T09:32:08","guid":{"rendered":"https:\/\/namastedev.com\/blog\/?p=10079"},"modified":"2025-09-19T20:29:02","modified_gmt":"2025-09-19T14:59:02","slug":"merge-intervals","status":"publish","type":"post","link":"https:\/\/namastedev.com\/blog\/merge-intervals\/","title":{"rendered":"Merge Intervals"},"content":{"rendered":"\n<!-- merge_7-->\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;   \/* 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  <h1 class=\"wp_blog_main-heading\"><\/h1>\n\n  <div class=\"wp_blog_explanation\">\n    <h2>Problem Statement:<\/h2>\n    <p>\n        Given an array of <code>intervals<\/code> where <code>intervals[i] = [starti, endi]<\/code>, merge all overlapping intervals, and return <i>an array of the non-overlapping intervals that cover all the intervals in the input<\/i>.\n    <\/p>\n\n    <h3>Example 1:<\/h2>\n    <p><strong>Input:<\/strong> intervals = [[1,3],[2,6],[8,10],[15,18]]\n<\/p>\n    <p><strong>Output:<\/strong> [[1,6],[8,10],[15,18]]<\/p>\n    <p><strong>Explanation:<\/strong>\n        Since intervals [1,3] and [2,6] overlap, merge them into [1,6].\n    <\/p>\n\n    <h3>Example 2:<\/h3>\n    <p><strong>Input: <\/strong>intervals = [[1,4],[4,5]]<\/p>\n    <p><strong>Output: <\/strong>[[1,5]]<\/p>\n    <p><strong>Explanation: <\/strong>\n       Intervals [1,4] and [4,5] are considered overlapping.\n    <\/p>\n\n    <h3>Example 3:<\/h3>\n    <p><strong>Input: <\/strong>intervals = [[4,7],[1,4]]<\/p>\n    <p><strong>Output: <\/strong>[[1,7]]<\/p>\n    <p><strong>Explanation: <\/strong>\n       Intervals [1,4] and [4,7] are considered overlapping.\n    <\/p>\n    <h3>Constraints<\/h3>\n    <ul>\n        <li><code>1 <= intervals.length <= 10<sup>4<\/sup><\/code><\/li>\n        <li><code>intervals[i].length == 2<\/code><\/li>\n        <li><code>0 <= start<sub>i<\/sub> <= end<sub>i<\/sub><= 10<sup>5<\/sup><\/code><\/li>\n    <\/ul>\n<h2>Approach:<\/h2>\n   <ul>\n    <li><strong>Sort intervals<\/strong> by their starting point.<\/li>\n    <li>Initialize <code>result with the first interval<\/code>.<\/li>\n    <li>Traverse <code>intervals<\/code> one by one:\n        <ul>\n            <li>If the <strong>current interval<\/strong> overlaps with the last interval in the result \u2192 merge them (update the end to the max end).<\/li>\n            <li>Otherwise \u2192 <code>add<\/code> it as a new interval.<\/li>\n        <\/ul>\n    <\/li>\n    <li>Return the merged list.<\/li>\n    <\/ul>\n\n    <h2>Time &#038; Space Complexity:<\/h2>\n    <p><strong>Time Complexity:<\/strong> <code>O(n log n)<\/code><\/p>\n    <p><strong>Space Complexity:<\/strong> <code>O(n)<\/code><\/p>\n\n<h2>Dry Run<\/h2> <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 = [[2,5],[1,3],[6,9]]<\/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);\">\nStep 0: Start\nFunction: merge(arr)\narr = [[2,5], [1,3], [6,9]]\nn = arr.length = 3\n(no ans yet)\nStep 1: Sort intervals by start \u2192 arr.sort((a,b) => a[0]-b[0])\nBefore sort: [[2,5], [1,3], [6,9]]\nAfter sort: [[1,3], [2,5], [6,9]]\nStep 2: Initialize answer array\nans = [arr[0]] = [[1,3]]\nStep 3: Loop through remaining intervals (for i = 1 \u2192 2)\nIteration (i = 1):\n- current = arr[1] = [2,5]\n- last in ans = ans[ans.length-1] = [1,3]\n- Check overlap: current[0] <= last[1] \u2192 2 <= 3 ? \u2192 true (overlap)\n- Merge: last[1] = max(last[1], current[1]) = max(3,5) = 5\n- ans becomes [[1,5]]\n- (do not push new interval)\nIteration (i = 2):\n- current = arr[2] = [6,9]\n- last in ans = [1,5]\n- Check overlap: 6 <= 5 ? \u2192 false (no overlap)\n- Push current into ans \u2192 ans = [[1,5], [6,9]]\nStep 4: End loop\nFinal ans = [[1,5], [6,9]]\nExplanation:\nSorting produced [[1,3],[2,5],[6,9]].\n[1,3] and [2,5] overlapped and merged into [1,5].\n[6,9] did not overlap, so it was appended unchanged.\n<\/pre> <p><strong>Output:<\/strong> <code>[[1,5],[6,9]]<\/code><\/p> <\/div>\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\">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 merge = function(arr) {\n    arr.sort((a, b) => (a[0] - b[0]));\n    let ans = [arr[0]];\n    for(let i = 1; i < arr.length; i++){\n        if(arr[i][0] <= ans[ans.length - 1][1]){\n            ans[ans.length-1][1] = Math.max(ans[ans.length-1][1], arr[i][1])\n        } else {\n            ans.push(arr[i]);\n        }\n    }\n    return ans;\n};\n<\/code><\/pre>\n    <\/div>\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"py\">\n      <pre><code class=\"language-python\">\nfrom typing import List\ndef merge(intervals: List[List[int]]) -> List[List[int]]:\n    if not intervals:\n        return []\n    intervals.sort(key=lambda x: x[0])\n    ans = [intervals[0]]\n    for i in range(1, len(intervals)):\n        if intervals[i][0] <= ans[-1][1]:\n            ans[-1][1] = max(ans[-1][1], intervals[i][1])\n        else:\n            ans.append(intervals[i])\n    return ans\n      <\/code><\/pre>\n    <\/div>\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"java\">\n      <pre><code class=\"language-java\">\nimport java.util.*;\npublic class Solution {\n    public int[][] merge(int[][] intervals) {\n        if (intervals == null || intervals.length == 0) return new int[0][];\n        Arrays.sort(intervals, (a, b) -> Integer.compare(a[0], b[0]));\n\n        List<int[]> ans = new ArrayList<>();\n        ans.add(new int[]{intervals[0][0], intervals[0][1]});\n\n        for (int i = 1; i < intervals.length; i++) {\n            int[] last = ans.get(ans.size() - 1);\n            if (intervals[i][0] <= last[1]) {\n                last[1] = Math.max(last[1], intervals[i][1]);\n            } else {\n                ans.add(new int[]{intervals[i][0], intervals[i][1]});\n            }\n        }\n\n        return ans.toArray(new int[ans.size()][]);\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;vector&gt; -->\n#include &lt;bits\/stdc++.h&gt;\nusing namespace std;\nvector<vector<int>> mergeIntervals(vector<vector<int>>& intervals) {\n    if (intervals.empty()) return {};\n    sort(intervals.begin(), intervals.end(), [](const vector<int>& a, const vector<int>& b){\n        return a[0] < b[0];\n    });\n    vector<vector<int>> ans;\n    ans.push_back(intervals[0]);\n    for (size_t i = 1; i < intervals.size(); ++i) {\n        if (intervals[i][0] <= ans.back()[1]) {\n            ans.back()[1] = max(ans.back()[1], intervals[i][1]);\n        } else {\n            ans.push_back(intervals[i]);\n        }\n    }\n    return ans;\n}\n<\/code><\/pre>\n    <\/div>\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"c\">\n      <pre><code class=\"language-c\">\n#include &lt;stdlib.h&gt;\n#include &lt;stdio.h&gt;\n\ntypedef struct {\n    int start;\n    int end;\n} Interval;\n\nint cmp(const void* a, const void* b) {\n    Interval *ia = (Interval*)a;\n    Interval *ib = (Interval*)b;\n    return ia->start - ib->start;\n}\nInterval* mergeIntervals(Interval* intervals, int intervalsSize, int* outSize) {\n    *outSize = 0;\n    if (intervalsSize == 0) return NULL;\n    Interval* arr = malloc(sizeof(Interval) * intervalsSize);\n    for (int i = 0; i < intervalsSize; ++i) arr[i] = intervals[i];\n\n    qsort(arr, intervalsSize, sizeof(Interval), cmp);\n    Interval* result = malloc(sizeof(Interval) * intervalsSize);\n    int ri = 0;\n    result[0] = arr[0];\n    ri = 1;\n    for (int i = 1; i < intervalsSize; ++i) {\n        if (arr[i].start <= result[ri-1].end) {\n            if (arr[i].end > result[ri-1].end)\n                result[ri-1].end = arr[i].end;\n        } else {\n            result[ri++] = arr[i];\n        }\n    }\n    free(arr);\n    *outSize = ri;\n    return result;\n} \n <\/code><\/pre>\n    <\/div>\n\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"cs\">\n      <pre><code class=\"language-csharp\">\nusing System;\nusing System.Collections.Generic;\npublic class Solution {\n    public IList<int[]> Merge(int[][] intervals) {\n        var res = new List<int[]>();\n        if (intervals == null || intervals.Length == 0) return res;\n\n        Array.Sort(intervals, (a, b) => a[0].CompareTo(b[0]));\n        res.Add(new int[] { intervals[0][0], intervals[0][1] });\n\n        for (int i = 1; i < intervals.Length; i++) {\n            int[] last = res[res.Count - 1];\n            if (intervals[i][0] <= last[1]) {\n                last[1] = Math.Max(last[1], intervals[i][1]);\n            } else {\n                res.Add(new int[] { intervals[i][0], intervals[i][1] });\n            }\n        }\n        return res;\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: Given an array of intervals where intervals[i] = [starti, endi], merge all overlapping intervals, and return an array of the non-overlapping intervals that cover all the intervals in the input. Example 1: Input: intervals = [[1,3],[2,6],[8,10],[15,18]] Output: [[1,6],[8,10],[15,18]] Explanation: Since intervals [1,3] and [2,6] overlap, merge them into [1,6]. Example 2: Input:<\/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-10079","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\/10079","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=10079"}],"version-history":[{"count":1,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/10079\/revisions"}],"predecessor-version":[{"id":10080,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/10079\/revisions\/10080"}],"wp:attachment":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/media?parent=10079"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/categories?post=10079"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/tags?post=10079"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}