{"id":10085,"date":"2025-09-19T20:24:24","date_gmt":"2025-09-19T14:54:24","guid":{"rendered":"https:\/\/namastedev.com\/blog\/?p=10085"},"modified":"2025-09-19T20:31:52","modified_gmt":"2025-09-19T15:01:52","slug":"non-overlapping-intervals","status":"publish","type":"post","link":"https:\/\/namastedev.com\/blog\/non-overlapping-intervals\/","title":{"rendered":"Non Overlapping 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 intervals<code>intervals<\/code> where <code>intervals[i] = [start<sub>i<\/sub>, end<sub>i<\/sub>]<\/code>, return the <i>minimum number of intervals you need to remove to make the rest of the intervals non-overlapping<\/i>.\n    <\/p>\n\n    <p>\n        <strong>Note<\/strong> that intervals which only touch at a point are <strong>non-overlapping<\/strong>. For example, <code>[1, 2]<\/code> and <code>[2, 3]<\/code> are non-overlapping.\n    <\/p>\n    <h3>Example 1:<\/h2>\n    <p><strong>Input:<\/strong> intervals = [[1,2],[2,3],[3,4],[1,3]]\n<\/p>\n    <p><strong>Output:<\/strong> 1<\/p>\n    <p><strong>Explanation:<\/strong>\n        [1,3] can be removed and the rest of the intervals are non-overlapping.\n    <\/p>\n\n    <h3>Example 2:<\/h3>\n    <p><strong>Input: <\/strong>intervals = [[1,2],[1,2],[1,2]]<\/p>\n    <p><strong>Output: <\/strong>2<\/p>\n    <p><strong>Explanation: <\/strong>You need to remove two [1,2] to make the rest of the intervals non-overlapping.<\/p>\n\n    <h3>Example 3:<\/h3>\n    <p><strong>Input: <\/strong>intervals = [[1,2],[2,3]]<\/p>\n    <p><strong>Output: <\/strong>0<\/p>\n    <p><strong>Explanation: <\/strong>\n       You don&#8217;t need to remove any of the intervals since they&#8217;re already non-overlapping.\n    <\/p>\n\n    <h3>Constraints<\/h3>\n    <ul>\n        <li><code>1 <= intervals.length <= 10<sup>5<\/sup><\/code><\/li>\n        <li><code>intervals[i].length == 2<\/code><\/li>\n        <li><code>-5 * 10<code>4<\/code> <= start<sub>i<\/sub> < end<sub>i<\/sub> <= 10<sup>4<\/sup><\/code><\/li>\n    <\/ul>\n<h2>Approach:<\/h2>\n   <ul>\n        <li><strong>Sort intervals by end time<\/strong> \u2192 This ensures we always keep the interval that finishes earliest.<\/li>\n        <li>Track the end of the last chosen interval <code>(k)<\/code> \u2192 Start with <code>-Infinity<\/code>.<\/li>\n        <li><strong>Iterate over intervals:<\/strong>\n            <ul>\n                <li>If the current interval starts before <code>k<\/code>, it overlaps \u2192 increment <code>removeCount<\/code> (we &#8220;remove&#8221; this one).<\/li>\n                <li>Else, update <code>k<\/code> to the current interval\u2019s end (keep it).<\/li>\n            <\/ul>\n        <\/li>\n        <li>Return the total <code>removeCount<\/code>.<\/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(1)<\/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);\"> <p><strong>Input:<\/strong> <code>arr = [[1,2],[2,3],[3,4],[1,3]]<\/code><\/p> <pre style=\"white-space: pre-wrap; background: var(--code-bg); padding: 1rem; border-radius: 8px; overflow-x: auto; color: var(--code-text);\"> Step 0: Start Function: eraseOverlapIntervals(arr) arr = [[1,2],[2,3],[3,4],[1,3]] removeCount = 0 k = -Infinity ------------------------------------------------------------ Step 1: Sort intervals by end (arr.sort((a,b) => a[1] - b[1])) Compare ends: 2,3,4,3 \u2192 sorted order (one valid result): arr = [[1,2], [2,3], [1,3], [3,4]] \/\/ intervals ordered by their end values ------------------------------------------------------------ Step 2: Iterate through sorted intervals Iteration (i = 0, interval = [1,2]): Check if arr[0][0] < k \u2192 1 < -Infinity ? false else -> k = arr[0][1] = 2 removeCount = 0 Current k = 2 Iteration (i = 1, interval = [2,3]): Check if arr[1][0] < k \u2192 2 < 2 ? false (strict <) else -> k = arr[1][1] = 3 removeCount = 0 Current k = 3 Iteration (i = 2, interval = [1,3]): Check if arr[2][0] < k \u2192 1 < 3 ? true -> ++removeCount => removeCount = 1 (k remains 3) Iteration (i = 3, interval = [3,4]): Check if arr[3][0] < k \u2192 3 < 3 ? false else -> k = arr[3][1] = 4 removeCount = 1 Current k = 4 ------------------------------------------------------------ Step 3: End Final removeCount = 1 <\/pre> <p><strong>Output:<\/strong> <code>1<\/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 eraseOverlapIntervals = function(arr) {\n    arr.sort((a, b) => (a[1] - b[1]));\n    let removeCount = 0;\n    let k = -Infinity;\n    for(let i=0; i < arr.length; i++){\n        if(arr[i][0] < k){\n            ++removeCount;\n        } else {\n            k = arr[i][1];\n        }\n    }\n    return removeCount;\n};\n<\/code><\/pre>\n    <\/div>\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"py\">\n      <pre><code class=\"language-python\">\ndef eraseOverlapIntervals(arr):\n    if not arr:\n        return 0\n    arr.sort(key=lambda x: x[1])\n    removeCount = 0\n    k = float('-inf')\n    for start, end in arr:\n        if start < k:\n            removeCount += 1\n        else:\n            k = end\n    return removeCount\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.Arrays;\npublic class Solution {\n    public int eraseOverlapIntervals(int[][] intervals) {\n        if (intervals == null || intervals.length == 0) return 0;\n        Arrays.sort(intervals, (a, b) -> Integer.compare(a[1], b[1]));\n        int removeCount = 0;\n        int k = Integer.MIN_VALUE;\n        for (int[] iv : intervals) {\n            if (iv[0] < k) {\n                ++removeCount;\n            } else {\n                k = iv[1];\n            }\n        }\n        return removeCount;\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;vector&gt;\n#include &lt;algorithm&gt;\n#include &lt;limits&gt;\nint eraseOverlapIntervals(std::vector<std::vector<int>>& intervals) {\n    if (intervals.empty()) return 0;\n    std::sort(intervals.begin(), intervals.end(),\n              [](const std::vector<int>& a, const std::vector<int>& b){\n                  return a[1] < b[1];\n              });\n    int removeCount = 0;\n    int k = std::numeric_limits<int>::min(); \/\/ acts like -Infinity for ints\n    for (const auto &iv : intervals) {\n        if (iv[0] < k) {\n            ++removeCount;\n        } else {\n            k = iv[1];\n        }\n    }\n    return removeCount;\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;limits.h&gt;\n\ntypedef struct {\n    int start;\n    int end;\n} Interval;\nint cmp_end(const void *a, const void *b) {\n    Interval *ia = (Interval*)a;\n    Interval *ib = (Interval*)b;\n    if (ia->end < ib->end) return -1;\n    if (ia->end > ib->end) return 1;\n    return 0;\n}\nint eraseOverlapIntervals(Interval *arr, int n) {\n    if (n == 0) return 0;\n    qsort(arr, n, sizeof(Interval), cmp_end);\n    int removeCount = 0;\n    int k = INT_MIN;\n    for (int i = 0; i < n; ++i) {\n        if (arr[i].start < k) {\n            ++removeCount;\n        } else {\n            k = arr[i].end;\n        }\n    }\n    return removeCount;\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;\npublic class Solution {\n    public int EraseOverlapIntervals(int[][] intervals) {\n        if (intervals == null || intervals.Length == 0) return 0;\n        Array.Sort(intervals, (a, b) => a[1].CompareTo(b[1]));\n        int removeCount = 0;\n        int k = Int32.MinValue;\n        foreach (var iv in intervals) {\n            if (iv[0] < k) {\n                ++removeCount;\n            } else {\n                k = iv[1];\n            }\n        }\n        return removeCount;\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 intervalsintervals where intervals[i] = [starti, endi], return the minimum number of intervals you need to remove to make the rest of the intervals non-overlapping. Note that intervals which only touch at a point are non-overlapping. For example, [1, 2] and [2, 3] are non-overlapping. Example 1: Input: intervals<\/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":{"0":"post-10085","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-algorithms","7":"category-algorithms-and-data-structures","8":"category-c-c-plus-plus","9":"category-csharp","10":"category-cplusplus","11":"category-data-structures","12":"category-data-structures-and-algorithms","13":"category-dsa","14":"category-java","15":"category-javascript","16":"category-python"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/10085","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=10085"}],"version-history":[{"count":1,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/10085\/revisions"}],"predecessor-version":[{"id":10086,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/10085\/revisions\/10086"}],"wp:attachment":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/media?parent=10085"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/categories?post=10085"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/tags?post=10085"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}