Gift delivery scheduler with limited agents

You are planning gift deliveries to employees in an office. The workday runs from hour 9 to hour 17.

You get:

• intervals, a list of [start, end] pairs with integer hours. Employee i is in the office from start_i until end_i.
• n, the number of delivery agents.

Rules:

• A delivery takes exactly one hour and must start on a whole hour.
• A delivery to employee i that starts at hour h is allowed only if start_i <= h and h + 1 <= end_i.
• Each agent makes at most one delivery per hour, so at most n deliveries can happen in the same hour.
• Each employee gets at most one gift.

Implement schedule_deliveries(intervals, n). Return the largest number of employees who can get their gift, and a schedule that achieves it: for each employee, the start hour of their delivery, or None if they are not served.

Constraints: 0 <= len(intervals) <= 10^5, 9 <= start <= end <= 17, 0 <= n <= 10^5. Aim for better than trying all assignments.

Example 1

intervals = [[9, 11], [9, 10], [9, 10]], n = 1
-> 2

Only one agent works. One of the two employees who leave at 10 gets the 9:00 slot, and the employee who stays until 11 gets the 10:00 slot. The other early leaver misses out.

Example 2

intervals = [[9, 12], [10, 11], [9, 10]], n = 1
-> 3   schedule: [11, 10, 9]

Serve whoever leaves first: [9, 10] at 9:00, [10, 11] at 10:00, and [9, 12] at 11:00.

Reconstructed from the reported question; details may differ from what interviewers ask.