My Calendar III Python Solution with Tests

lcpy gen -n 732   # by problem number
lcpy gen -s my_calendar_iii   # by problem name

Input
["MyCalendarThree", "book", "book", "book", "book", "book", "book"]
[[], [10, 20], [50, 60], [10, 40], [5, 15], [5, 10], [25, 55]]
Output
[null, 1, 1, 2, 3, 3, 3]

Explanation
MyCalendarThree myCalendarThree = new MyCalendarThree();
myCalendarThree.book(10, 20); // return 1
myCalendarThree.book(50, 60); // return 1
myCalendarThree.book(10, 40); // return 2
myCalendarThree.book(5, 15);  // return 3
myCalendarThree.book(5, 10);  // return 3
myCalendarThree.book(25, 55); // return 3

class MyCalendarThree:
    # Boundary delta map: a booking adds +1 at start and -1 at end, so a sweep
    # over the sorted boundaries gives the number of events alive at each point;
    # the answer is a running maximum and only ever grows.
    # Time: O(n log n) per book (n = bookings so far)
    # Space: O(n)
    def __init__(self) -> None:
        self._delta: dict[int, int] = {}
        self._max_k = 0

    def book(self, start_time: int, end_time: int) -> int:
        self._delta[start_time] = self._delta.get(start_time, 0) + 1
        self._delta[end_time] = self._delta.get(end_time, 0) - 1
        active = 0
        for time in sorted(self._delta):
            active += self._delta[time]
            if active > self._max_k:
                self._max_k = active
        return self._max_k