Greedy Algorithms Questions Medium
The interval partitioning problem is a scheduling problem where we are given a set of intervals, each representing a task with a start time and an end time. The goal is to find the minimum number of resources (or rooms) required to schedule all the tasks, such that no two tasks overlap in time.
To solve this problem using a greedy algorithm, we can follow these steps:
1. Sort the intervals in ascending order based on their start times.
2. Initialize an empty list of resources (rooms).
3. Iterate through each interval in the sorted order.
4. For each interval, check if there is any resource (room) available whose end time is less than or equal to the start time of the current interval. If such a resource is found, assign the current interval to that resource.
5. If no such resource is found, create a new resource (room) and assign the current interval to it.
6. Repeat steps 4 and 5 for all intervals.
7. The number of resources (rooms) used will be the minimum number of resources required to schedule all the tasks.
The greedy strategy in this algorithm is to always assign the current interval to the first available resource (room) that can accommodate it. This ensures that no two overlapping tasks are assigned to the same resource, as we are always considering the intervals in sorted order.
The time complexity of this greedy algorithm is O(n log n), where n is the number of intervals. This is because we need to sort the intervals initially, which takes O(n log n) time, and then we iterate through each interval once, which takes O(n) time.