732. My Calendar III


Implement a MyCalendarThree class to store your events. A new event can always be added.

Your class will have one method, book(int start, int end). Formally, this represents a booking on the half open interval [start, end), the range of real numbers x such that start <= x < end.

A K-booking happens when K events have some non-empty intersection (ie., there is some time that is common to all K events.)

For each call to the method MyCalendar.book, return an integer K representing the largest integer such that there exists a K-booking in the calendar.

Your class will be called like this: MyCalendarThree cal = new MyCalendarThree(); MyCalendarThree.book(start, end)

Example 1:

MyCalendarThree();
MyCalendarThree.book(10, 20); // returns 1
MyCalendarThree.book(50, 60); // returns 1
MyCalendarThree.book(10, 40); // returns 2
MyCalendarThree.book(5, 15); // returns 3
MyCalendarThree.book(5, 10); // returns 3
MyCalendarThree.book(25, 55); // returns 3
Explanation: 
The first two events can be booked and are disjoint, so the maximum K-booking is a 1-booking.
The third event [10, 40) intersects the first event, and the maximum K-booking is a 2-booking.
The remaining events cause the maximum K-booking to be only a 3-booking.
Note that the last event locally causes a 2-booking, but the answer is still 3 because
eg. [10, 20), [10, 40), and [5, 15) are still triple booked.

Note:

  • The number of calls to MyCalendarThree.book per test case will be at most 400.
  • In calls to MyCalendarThree.book(start, end), start and end are integers in the range [0, 10^9].


    • Approach #1: Boundary Count [Accepted]

    Intuition and Algorithm

    When booking a new event [start, end), count delta[start]++ and delta[end]--. When processing the values of delta in sorted order of their keys, the largest such value is the answer.

    In Python, we sort the set each time instead, as there is no analog to TreeMap available.

    Complexity Analysis

    • Time Complexity: , where is the number of events booked. For each new event, we traverse delta in time. In Python, this is owing to the extra sort step.

    • Space Complexity: , the size of delta.

    Analysis written by: @awice. Solution in Approach #2 inspired by @cchao.

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