731. My Calendar II

Implement a MyCalendarTwo class to store your events. A new event can be added if adding the event will not cause a triple booking.
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 triple booking happens when three events have some non-empty intersection (ie., there is some time that is common to all 3 events.)
For each call to the method MyCalendar.book, return true if the event can be added to the calendar successfully without causing a triple booking. Otherwise, return false and do not add the event to the calendar.
Your class will be called like this: MyCalendar cal = new MyCalendar(); MyCalendar.book(start, end)
Example 1:

MyCalendar();
MyCalendar.book(10, 20); // returns true
MyCalendar.book(50, 60); // returns true
MyCalendar.book(10, 40); // returns true
MyCalendar.book(5, 15); // returns false
MyCalendar.book(5, 10); // returns true
MyCalendar.book(25, 55); // returns true
Explanation: 
The first two events can be booked.  The third event can be double booked.
The fourth event (5, 15) can't be booked, because it would result in a triple booking.
The fifth event (5, 10) can be booked, as it does not use time 10 which is already double booked.
The sixth event (25, 55) can be booked, as the time in [25, 40) will be double booked with the third event;
the time [40, 50) will be single booked, and the time [50, 55) will be double booked with the second event.







https://www.youtube.com/watch?v=rRMdxFA-8G4


class MyCalendarTwo {
    private List<int[]> booked;
    private List<int[]> overlaps;

    public MyCalendarTwo() {
        booked = new ArrayList<>();
        overlaps = new ArrayList<>();
        
    }
    
    public boolean book(int start, int end) {
        for(int[] overlap : overlaps){
            if(Math.max(start, overlap[0]) < Math.min(end, overlap[1])) return false;
        }
        
        for(int[] range : booked){
            int s = Math.max(range[0], start);
            int e = Math.min(range[1], end);
            if(s < e) overlaps.add(new int[]{s, e});
        }
        booked.add(new int[]{start, end});
        return true;
        
    }
}




// data structure: one list for storing all the valid ranges
// another list is for storing all the twice lapping ranges 

// so if the new range comes in and overlap with anyone in the twice lapping list, 
// then we know the new range is tripple lapping with the existing ranges 
// so return false 

// comes a new range 
// check if the new range overlap with anyone from the overlap list 
// if yes, return false
// if no, so it's not overlapping with any twice lapping ranges, so 
// check if this new range overlaps with anyone from the valid ranges, 
// if yes, then we add the twice overlap into the overlap list 
// if no, do nothing. 
// and finally add the new range into the valid range list and return true