You are implementing a program to use as your calendar. We can add a new event if adding the event will not cause a double booking.

A double booking happens when two events have some non-empty intersection (i.e., some moment is common to both events.).

The event can be represented as a pair of integers start and end that represents a booking on the half-open interval [start, end), the range of real numbers x such that start <= x < end.

Implement the MyCalendar class:

• MyCalendar() Initializes the calendar object.
• boolean book(int start, int end) Returns true if the event can be added to the calendar successfully without causing a double booking. Otherwise, return false and do not add the event to the calendar.

Example 1:

Input ["MyCalendar", "book", "book", "book"] [[], [10, 20], [15, 25], [20, 30]] Output [null, true, false, true]

Explanation

MyCalendar myCalendar = new MyCalendar();
myCalendar.book(10, 20); // return True
myCalendar.book(15, 25); // return False, It can not be booked because time 15 is already booked by another event.
myCalendar.book(20, 30); // return True, The event can be booked, as the first event takes every time less than 20, but not including 20.

Constraints:

• 0 <= start < end <= 109
• At most 1000 calls will be made to book.

To implement the booking behaviour, we will use binary search to find a potential insertion index, then check whether the new booking can be actually scheduled into our calendar by checking whether the new booking overlaps with calendar[idx-1] and calendar[idx].

Implementation

class MyCalendar:
    def __init__(self):
        self.calendar = []

    def book(self, start: int, end: int) -> bool:
        left, right, idx = 0, len(self.calendar)-1, len(self.calendar)
        while left <= right:
          mid = (left + right) // 2
          if self.calendar[mid][0] > start:
              idx = mid
              right = mid - 1
          else:
              left = mid + 1
        # check if calendar[idx-1] or calendar[idx] overlaps with start and end
        if (idx > 0 and self.calendar[idx-1][1] > start) or (idx < len(self.calendar) and self.calendar[idx][0] < end):
            return False
        self.calendar.insert(idx, (start, end))
        return True