> For the complete documentation index, see [llms.txt](https://chunhthanhde.gitbook.io/leetcode-top-interview/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://chunhthanhde.gitbook.io/leetcode-top-interview/topic-6-intervals.md).

# Topic 6 Intervals

## 🛠 Overview

**Intervals** problems on LeetCode involve working with ranges of values, typically represented as pairs of numbers `[start, end]`. These problems often require operations like merging, inserting, or determining overlaps between intervals. Understanding these problems is crucial for mastering algorithmic concepts in sorting, greedy algorithms, and binary search.

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## 🎯 Common Operations on Intervals

* **Merging Overlapping Intervals**
* **Inserting Intervals**
* **Checking Overlap**
* **Counting Non-Overlapping Intervals**

## 🧠 Tips and Tricks

1. **Sorting is Key:**
   * Many interval problems require sorting by the start (or end) of intervals. Sorting simplifies comparisons and merging.
2. **Greedy Algorithms Work Well:**
   * Problems involving overlapping intervals often use a greedy approach, focusing on choosing the "best" interval at each step.
3. **Edge Cases to Watch For:**
   * Empty interval lists.
   * Single intervals.
   * Completely overlapping intervals, e.g., `[1, 10]` and `[2, 5]`.
   * Non-overlapping intervals, e.g., `[1, 2]` and `[3, 4]`.
4. **Understand the Mathematical Overlap Condition:**
   * Two intervals overlap if `max(start1, start2) <= min(end1, end2)`.

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## 🔥 Popular LeetCode Problems on Intervals

1. [**Summary RangesRanges**](/leetcode-top-interview/topic-6-intervals/048-summary-ranges.md)
2. [**Merge Intervals**](/leetcode-top-interview/topic-6-intervals/049-merge-intervals.md)
3. [**Insert Interval**](/leetcode-top-interview/topic-6-intervals/050-insert-interval.md)
4. [**Minimum Number of Arrows to Burst Balloons**](/leetcode-top-interview/topic-6-intervals/051-minimum-number-of-arrows-to-burst-balloons.md)

Happy Coding