Implement a calendar with non-overlapping bookings

Problem

Design a calendar booking system that stores half-open time intervals [start, end) (inclusive of start, exclusive of end).

Implement a class with a method:

• book(start, end) -> boolean

The method should:

• Return true and add the event if it does not overlap with any existing event.
• Return false and do not add the event if it overlaps with an existing event.

Two events [s1, e1) and [s2, e2) overlap iff max(s1, s2) < min(e1, e2).

Example

Operations:

• book(10, 20) → true
• book(15, 25) → false (overlaps with [10,20) )
• book(20, 30) → true (touching at 20 is allowed)

Constraints (typical)

• Up to 10^3 to 10^5 bookings
• 0 <= start < end <= 10^9