# 732. My Calendar III (Hard)

https://leetcode.com/problems/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]`.

## Solutions

``````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;
}
}
``````