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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:
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.
1#include <stdbool.h>
2#include <stdio.h>
3#include <stdlib.h>
4
5typedef struct {
6 int start
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.
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.
Time Complexity: O(N log N) due to map operations.
Space Complexity: O(N) for map storage.
1
The Python solution employs `SortedDict` from `sortedcontainers` to manage bookings efficiently. With each booking event, the timeline is checked for overlap counts that could imply triple booking, altering the dictionary accordingly.