Intervals mind map

Merge, insert, and schedule interval problems.

Core idea: Normalize endpoints and sort; every relationship becomes gap, touch, or overlap.

Mnemonic: Sort → compare endpoints → fold · Cost: O(n log n) sort · O(n) sweep

Fold: Merge & insert

Signal: Overlapping ranges should collapse into their union.

Move: Carry one active interval; extend it on overlap or emit it when a real gap begins.

Examples: Merge Intervals, Insert Interval, Summary Ranges

Signal: The goal is to keep the most non-overlapping work.

Move: Sort by earliest finish and accept the next interval that starts after the chosen end.

Examples: Erase Overlap, Meeting Selection, Minimum Arrows

Signal: You need maximum concurrency or state at every boundary.

Move: Encode start and end deltas, sort events with correct tie rules, then scan active count.

Examples: Meeting Rooms II, Skyline, Maximum Population

Signal: Ranges arrive online and must be queried, booked, or removed.

Move: Maintain searchable endpoints; state open/closed boundary semantics before updating.

Examples: My Calendar, Range Module, Employee Free Time