 # LeetCode My Calendar I Solution

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

``````1MyCalendar myCalendar = new MyCalendar();
2myCalendar.book(10, 20); // return True
3myCalendar.book(15, 25); // return False, It can not be booked because time 15 is already booked by another event.
4myCalendar.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`.

## Solution

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

``````1class MyCalendar:
2    def __init__(self):
3        self.calendar = []
4
5    def book(self, start: int, end: int) -> bool:
6        left, right, idx = 0, len(self.calendar)-1, len(self.calendar)
7        while left <= right:
8          mid = (left + right) // 2
9          if self.calendar[mid] > start:
10              idx = mid
11              right = mid - 1
12          else:
13              left = mid + 1
14        # check if calendar[idx-1] or calendar[idx] overlaps with start and end
15        if (idx > 0 and self.calendar[idx-1] > start) or (idx < len(self.calendar) and self.calendar[idx] < end):
16            return False
17        self.calendar.insert(idx, (start, end))
18        return True ``````