DSA & Implementation · core

Intervals

Merge, overlap, sweep line.

dsaintervals

Mental model

Interval problems almost always start by sorting — usually by start time, sometimes by end. After sorting, a single pass with a couple of running variables (last end, current count) handles merge, overlap, scheduling, and room allocation.

How to study Intervals

Begin by restating the mental model in your own words, then connect it to a concrete system you have built or operated. Name the mechanism, the constraint it addresses, and the trade-off it introduces. Use Interval scheduling (Wikipedia) to check details, but close the source before writing your explanation. Retrieval is the learning step; rereading is only preparation.

Next, compare Intervals with the neighboring concepts in its roadmap. Ask what changes in correctness, latency, resource use, operability, and failure recovery. Complete Merge overlapping intervals and preserve the command, input, output, and one failed attempt as evidence. Finish by explaining the idea without jargon to someone who has not studied the track.

Proof of understanding

Explain the mechanism from first principles and identify the state it reads or changes.
Give one situation where the concept is the right choice and one where it is not.
Predict a realistic failure mode before running the drill, then compare the prediction with evidence.
Connect the result to a roadmap or build artifact instead of treating the concept as isolated trivia.