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Minimum Station Tracks for a Train Schedule

BNSF Railway● MediumFULLTIMEONSITE INTERVIEW

Problem statement

A station has a schedule of trains. Each trains[i] = [arrival, departure] gives the minute a train arrives and the minute it leaves. While a train is in the station it needs a track of its own.

A train holds its track from arrival up to, but not including, departure.
A track freed at minute t can take a train that arrives at minute t.
Any train can use any track.

Return the smallest number of tracks that lets every train on the schedule stop at the station.

Function

minTracks(trains: int[][]) → int

Examples

Example 1

trains = [[540,600],[555,620],[610,700],[615,640]]return = 3

From minute 555 to 600 the first two trains are both in the station, and from 615 to 620 the trains [555,620], [610,700] and [615,640] are all there at once. Three tracks are needed.

Example 2

trains = [[100,200],[200,300],[300,400]]return = 1

Each train arrives exactly when the previous one leaves. A track that is freed at minute 200 can take the train arriving at minute 200, so one track is enough.

Example 3

trains = [[0,50],[10,20],[30,40],[45,60]]return = 2

The long train [0,50] holds one track. The other three trains never overlap each other: [10,20] leaves before [30,40] arrives, which leaves before [45,60] arrives. They can share a second track, so the answer is 2.

Constraints

1 <= trains.length <= 2000
trains[i].length == 2
0 <= arrival < departure <= 10^6