Compute conflicts and minimum meeting rooms

You are given a list of meeting room booking requests. Each request is a half-open time interval [start, end), meaning it uses the room starting at start and releases it at end (so a meeting ending at time t does not overlap one starting at time t).

A single meeting room can host at most one request at any time.

Tasks

1. Feasibility with one room: Determine whether all requests can be satisfied using only one meeting room (i.e., no time overlaps).
2. Minimum rooms needed: If one room is not enough, compute the minimum number of meeting rooms required so that all requests can be satisfied.

Input / Output

• Input: An array/list intervals of length n, where each element is [start, end) with start < end.
• Output:
  • A boolean canScheduleInOneRoom.
  • An integer minRooms (the minimum number of rooms needed).

Constraints (assume)

• 1 ≤ n ≤ 10^5
• start and end are integers (or comparable timestamps) within a reasonable range.

Example

• Input: [[0, 30], [5, 10], [15, 20]]
• Output: canScheduleInOneRoom = false, minRooms = 2

Part 1: Can All Meetings Fit in One Room?

You are given a list of meeting requests, where each request is a half-open interval [start, end). A meeting uses the room starting at time start and releases it at time end, so a meeting ending at time t does not conflict with one starting at time t.

Determine whether all meetings can be scheduled using only one meeting room.

Return True if no two meetings overlap in time; otherwise return False.

Constraints

• 0 <= n <= 10^5, where n is the number of intervals
• Each interval has exactly two integers: start and end
• For every interval, start < end
• Intervals are half-open: [start, end)

Examples

Example 1

Input: [[0, 30], [5, 10], [15, 20]]
Output: False

Explanation: The meeting [0, 30) overlaps with both [5, 10) and [15, 20), so one room is not enough.

Example 2

Input: [[1, 3], [3, 5], [5, 8]]
Output: True

Explanation: These meetings only touch at boundaries. Because the intervals are half-open, they do not overlap.

Hints

1. Try sorting the meetings by their start time first.
2. After sorting, it is enough to compare each meeting with the one that ends most recently before it.

Part 2: Minimum Number of Meeting Rooms

You are given a list of meeting requests, where each request is a half-open interval [start, end). A meeting ending at time t does not overlap with a meeting starting at time t.

Compute the minimum number of meeting rooms required so that all meetings can be scheduled.

Constraints

• 0 <= n <= 10^5, where n is the number of intervals
• Each interval has exactly two integers: start and end
• For every interval, start < end
• Intervals are half-open: [start, end)

Examples

Example 1

Input: [[0, 30], [5, 10], [15, 20]]
Output: 2

Explanation: At most two meetings overlap at once, so two rooms are required.

Example 2

Input: [[1, 3], [3, 5], [5, 8]]
Output: 1

Explanation: Each meeting starts exactly when the previous one ends, so one room can be reused.

Hints

1. If you process meetings in start-time order, you only need to know which scheduled meeting ends earliest.
2. A min-heap of end times is a good way to reuse rooms as soon as they become free.