Sort the intervals. Everything else is easy.

An interval is a pair of numbers that mark a range, like a meeting from 9 to 10. Interview rounds test whether you can spot the range pattern and pick the right sort key. Most answers collapse to sort-by-start.

Interval problems show up constantly because they model real things: meetings, time slots, ranges, bookings. Nearly every interval problem starts with the same move -- sort by start time.

The Core Insight

Sort by start time. Process left to right. Every interval problem is a variation of this.

PYTHON

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intervals.sort(key=lambda x: x[0])

Once sorted, consecutive intervals can only relate in three ways:

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1. No overlap -- current starts after previous ends
2. Overlap -- current starts before previous ends
3. Containment -- one is entirely within the other

The Key Problems

Merge Intervals

LC 56 · The most-asked interval problem. Sort by start, merge overlapping.

PYTHON

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def merge(intervals): intervals.sort() merged = [intervals[0]] for start, end in intervals[1:]: if start <= merged[-1][1]: merged[-1][1] = max(merged[-1][1], end) else: merged.append([start, end]) return merged

After sorting, you only compare each interval with the last merged one. That's what makes it O(n) after the sort.

Meeting Rooms II

LC 253 · Minimum number of meeting rooms needed. This is where a min-heap enters.

PYTHON

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import heapq def minMeetingRooms(intervals): intervals.sort() heap = [] for start, end in intervals: if heap and heap[0] <= start: heapq.heappop(heap) heapq.heappush(heap, end) return len(heap)

The heap tracks the earliest-ending meeting. If the next meeting starts after that end time, reuse the room.

Insert Interval

LC 57 · Insert a new interval into a sorted, non-overlapping list. Three phases: add intervals before, merge overlapping, add intervals after. Don't binary search -- a single linear scan is cleaner and what interviewers expect.

Non-overlapping Intervals

LC 435 · Minimum intervals to remove so the rest don't overlap. Sort by end time (not start), then greedily keep non-conflicting intervals. Sorting by end is counterintuitive but correct -- it maximizes the count by preferring shorter intervals.

When Interviewers Ask This

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The sort-by-end variant trips people up. If they ask about maximizing non-overlapping intervals or activity selection, always sort by end time.

Common Mistakes

• Not sorting first. If the interviewer gives you pre-sorted intervals, that's a deliberate hint. Don't re-sort.
• Sort by start when you should sort by end. Non-overlapping Intervals and Activity Selection need end-time sort. Merge Intervals and Meeting Rooms use start-time sort. Know the difference.
• Not drawing the intervals. Sketch a timeline on the whiteboard. Three overlapping intervals drawn on a number line reveals edge cases that staring at code won't.
• Using < instead of <= for overlap checks. [1,2] and [2,3] -- do they overlap? Depends on the problem. Clarify with the interviewer.

Practice Problems

1. Merge Intervals (LC 56) -- the foundation
2. Meeting Rooms (LC 252) -- simple overlap check
3. Meeting Rooms II (LC 253) -- min-heap for room counting
4. Insert Interval (LC 57) -- three-phase linear scan
5. Non-overlapping Intervals (LC 435) -- greedy with end-time sort
6. Minimum Number of Arrows (LC 452) -- non-overlapping intervals in disguise

Sources

• NeetCode Intervals Roadmap -- curated problem order with video walkthroughs
• LeetCode Intervals Tag -- problems sorted by company frequency
• Tech Interview Handbook: Intervals -- study plan and time allocation advice