You are implementing a program to use as your calendar. We can add a new event if adding the event will not cause a triple booking.
A triple booking happens when three events have some non-empty intersection (i.e., some moment is common to all the three events.).
The event can be represented as a pair of integers startTime and endTime that represents a booking on the half-open interval [startTime, endTime), the range of real numbers x such that startTime <= x < endTime.
Implement the MyCalendarTwo class:
MyCalendarTwo() Initializes the calendar object.boolean book(int startTime, int endTime) Returns 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.
Example 1:
Input ["MyCalendarTwo", "book", "book", "book", "book", "book", "book"] [[], [10, 20], [50, 60], [10, 40], [5, 15], [5, 10], [25, 55]] Output [null, true, true, true, false, true, true] Explanation MyCalendarTwo myCalendarTwo = new MyCalendarTwo(); myCalendarTwo.book(10, 20); // return True, The event can be booked. myCalendarTwo.book(50, 60); // return True, The event can be booked. myCalendarTwo.book(10, 40); // return True, The event can be double booked. myCalendarTwo.book(5, 15); // return False, The event cannot be booked, because it would result in a triple booking. myCalendarTwo.book(5, 10); // return True, The event can be booked, as it does not use time 10 which is already double booked. myCalendarTwo.book(25, 55); // return True, The event 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.
Constraints:
0 <= start < end <= 1091000 calls will be made to book.In this approach, we maintain two separate lists: `single_booked` for bookings that have been added without conflicts, and `double_booked` for intervals where two events overlap. To add a new booking:
The C solution defines two lists to store the single_booked and double_booked intervals. The `book` function checks for triple bookings by testing overlaps with double_booked, then adds any necessary doubles before adding the event to the single_booked list.
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Time Complexity: O(N^2) because for each booking, we might need to check with all existing ones.
Space Complexity: O(N) to store all bookings.
In this approach, we use a segment tree to efficiently keep track of overlapping intervals. By maintaining a segment tree, we can:
This approach is optimal for datasets with large integer boundaries due to the logarithmic nature of segment trees for both update and query operations.
The C++ solution uses a `map` to simulate a segment tree on a line sweep basis. As intervals are booked or end, we increment or decrement from the timeline, respectively. The `book` method tracks active bookings to ensure it never surpasses two overlapping intervals.
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Time Complexity: O(N log N) due to map operations.
Space Complexity: O(N) for map storage.
| Approach | Complexity |
|---|---|
| Approach 1: Using Two Lists for Overlapping Intervals | Time Complexity: O(N^2) because for each booking, we might need to check with all existing ones. |
| Approach 2: Segment Tree for Interval Overlaps | Time Complexity: O(N log N) due to map operations. |
My Calendar II - Leetcode 731 - Python • NeetCodeIO • 11,150 views views
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