Approach #1: Brute Force [Accepted]
Intuition
Maintain a list of bookings and a list of double bookings. When booking a new event [start, end)
, if it conflicts with a double booking, it will have a triple booking and be invalid. Otherwise, parts that overlap the calendar will be a double booking.
Algorithm
Evidently, two events [s1, e1)
and [s2, e2)
do not conflict if and only if one of them starts after the other one ends: either e1 <= s2
OR e2 <= s1
. By De Morgan's laws, this means the events conflict when s1 < e2
AND s2 < e1
.
If our event conflicts with a double booking, it's invalid. Otherwise, we add conflicts with the calendar to our double bookings, and add the event to our calendar.
Complexity Analysis

Time Complexity: , where is the number of events booked. For each new event, we process every previous event to decide whether the new event can be booked. This leads to complexity.

Space Complexity: , the size of the
calendar
.
Approach #2: 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 running sum active
is the number of events open at that time. If the sum is 3 or more, that time is (at least) triple booked.
A Python implementation was not included for this approach because there is no analog to TreeMap available.
class MyCalendarTwo { TreeMap<Integer, Integer> delta; public MyCalendarTwo() { delta = new TreeMap(); } public boolean book(int start, int end) { delta.put(start, delta.getOrDefault(start, 0) + 1); delta.put(end, delta.getOrDefault(end, 0)  1); int active = 0; for (int d: delta.values()) { active += d; if (active >= 3) { delta.put(start, delta.get(start)  1); delta.put(end, delta.get(end) + 1); if (delta.get(start) == 0) delta.remove(start); return false; } } return true; } }
Complexity Analysis

Time Complexity: , where is the number of events booked. For each new event, we traverse
delta
in time. 
Space Complexity: , the size of
delta
.
Analysis written by: @awice. Solution in Approach #2 inspired by @cchao.