732. My Calendar III (Hard)


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.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
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.



  • 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].



class MyCalendarThree {

    // Also, you can use Map<Integer, List<Integer>> to keep all the specific books in this range
    // assume the problem requires which ranges contain most books and return them if found.
    Map<Integer, Integer> delta = new TreeMap();

    public int book(int start, int end) {
        // You don't have to know which book begins from 'start', the number of books will
        // be sufficient.

        delta.put(start, delta.getOrDefault(start, 0) + 1);

        // The only thing you should know is how many books ends here, no the specific books.
        delta.put(end, delta.getOrDefault(end, 0) - 1);

        int max = 0;
        int active = 0;

        // For TreeMap, keys are sorted.
        for (int d : delta.values()) {
            active += d;

            if (active > max) {
                max = active;

        return max;

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