3169. Count Days Without Meetings
Description
You are given a positive integer days
representing the total number of days an employee is available for work (starting from day 1). You are also given a 2D array meetings
of size n
where, meetings[i] = [start_i, end_i]
represents the starting and ending days of meeting i
(inclusive).
Return the count of days when the employee is available for work but no meetings are scheduled.
Note: The meetings may overlap.
Example 1:
Input: days = 10, meetings = [[5,7],[1,3],[9,10]]
Output: 2
Explanation:
There is no meeting scheduled on the 4th and 8th days.
Example 2:
Input: days = 5, meetings = [[2,4],[1,3]]
Output: 1
Explanation:
There is no meeting scheduled on the 5th day.
Example 3:
Input: days = 6, meetings = [[1,6]]
Output: 0
Explanation:
Meetings are scheduled for all working days.
Constraints:
1 <= days <= 109
1 <= meetings.length <= 105
meetings[i].length == 2
1 <= meetings[i][0] <= meetings[i][1] <= days
Solutions
Solution 1: Sorting
We can sort all the meetings by their start time, and use a variable last
to record the latest end time of the previous meetings.
Then we traverse all the meetings. For each meeting $(st, ed)$, if last < st
, it means that the time period from last
to st
is a time period when employees can work and no meetings are scheduled. We add this time period to the answer. Then we update last = max(last, ed)
.
Finally, if last < days
, it means that there is a time period after the end of the last meeting when employees can work and no meetings are scheduled. We add this time period to the answer.
The time complexity is $O(n \times \log n)$, and the space complexity is $O(\log n)$. Where $n$ is the number of meetings.
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