732 - My Calendar III\.

Hard

A k\-booking happens when k events have some non-empty intersection (i.e., there is some time that is common to all k events.)

You are given some events [start, end), after each given event, return an integer k representing the maximum k\-booking between all the previous events.

Implement the MyCalendarThree class:

• MyCalendarThree() Initializes the object.

• int book(int start, int end) Returns an integer k representing the largest integer such that there exists a k\-booking in the calendar.

Example 1:

Input

"MyCalendarThree", "book", "book", "book", "book", "book", "book"

[ [], 10, 20, 50, 60, 10, 40, 5, 15, 5, 10, 25, 55]

Output: null, 1, 1, 2, 3, 3, 3

Explanation:

MyCalendarThree myCalendarThree = new MyCalendarThree();
myCalendarThree.book(10, 20); // return 1, The first event can be booked and is disjoint, so the maximum k-booking is a 1-booking.
myCalendarThree.book(50, 60); // return 1, The second event can be booked and is disjoint, so the maximum k-booking is a 1-booking.
myCalendarThree.book(10, 40); // return 2, The third event [10, 40) intersects the first event, and the maximum k-booking is a 2-booking.
myCalendarThree.book(5, 15); // return 3, The remaining events cause the maximum K-booking to be only a 3-booking.
myCalendarThree.book(5, 10); // return 3
myCalendarThree.book(25, 55); // return 3

Constraints:

• <code>0 <= start < end <= 10⁹</code>

• At most 400 calls will be made to book.