Count Workdays without Any Meeting

### Problem An employee is available on every day from day `1` through day `days`. Each row `meetings[i] = [start_i, end_i]` schedules a meeting on every day in that inclusive range. Meetings may overlap. Return the number of available days on which no meeting is scheduled. ```cpp class Solution { public: int countDays(int days, vector<vector<int>>& meetings); }; ``` ### Examples **Example 1:** ```text Input: days = 12, meetings = [[8,10],[2,5],[4,7]] Output: 3 Explanation: Days 2 through 10 have meetings. The free days are 1, 11, and 12. ``` **Example 2:** ```text Input: days = 8, meetings = [[1,8],[3,3],[1,2]] Output: 0 Explanation: The meeting from day 1 through day 8 covers every available day. ``` ### Constraints - `1 <= days <= 10^9`. - `1 <= meetings.length <= 10^5`. - Each `meetings[i]` contains exactly two integers. - `1 <= meetings[i][0] <= meetings[i][1] <= days`. ### Clarifying Questions - Are both meeting endpoints occupied? Yes, both are included. - Are meetings sorted or disjoint? Neither property is guaranteed. - Does an overlapping day count more than once? No. A day either has a meeting or is free. - Can free days occur before the first meeting or after the last one? Yes. ### What a Strong Answer Covers - Counts every free day exactly once, including days at either end of the calendar. - Handles overlapping, contained, and adjacent meeting ranges correctly. - Supports the full day bound without allocating one entry per calendar day. ```hint Compare covered ranges Consider the union of the inclusive meeting ranges. Account separately for any free days outside the first and last covered ranges. ```