Problem Description
You are given an integer eventTime denoting the duration of an event, where the event occurs from time t = 0 to time t = eventTime. You are also given two integer arrays startTime and endTime, each of length n. These represent the start and end time of n non-overlapping meetings, where the ith meeting occurs during the time [startTime[i], endTime[i]]. You can reschedule at most k meetings by moving their start time while maintaining the same duration, to maximize the longest continuous period of free time during the event. The relative order of all the meetings should stay the same and they should remain non-overlapping. Return the maximum amount of free time possible after rearranging the meetings. Note that the meetings cannot be rescheduled to a time outside the event.
Key Insights
- Meetings are non-overlapping, allowing for easier management of free time.
- Rescheduling is limited to k meetings, meaning we must prioritize which meetings to move for maximum impact on free time.
- The order of meetings must remain the same, which influences how we can shift their start times.
- The problem can be approached using a greedy algorithm or dynamic programming to optimize the selection of meetings to reschedule.
Space and Time Complexity
Time Complexity: O(n)
Space Complexity: O(1)
Solution
To solve the problem, we can use a greedy approach combined with a two-pointer technique. We will iterate through the meetings while keeping track of the maximum free time. For each meeting, we compute the free time available before it. If we have the ability to reschedule meetings (up to k), we will consider shifting the earliest meetings to create larger blocks of free time. We will maintain a running count of how many meetings we have rescheduled and update our maximum free time accordingly.