Find available reservation time slots

Problem

You are building an API to show which time slots are available for booking at a restaurant.

You are given:

• The restaurant’s opening hours (per day), and
• A list of existing reservations (per day), each with a start and end time.

Opening hours and reservations are provided in a nested dictionary structure.

Input

Assume times are in the same timezone and represented as minutes-from-midnight or as HH:MM strings that can be converted to minutes.

• hours[day] = [open_time, close_time]
• reservations[day] = [[start1, end1], [start2, end2], ...]

Example shape:

hours = {
  "Mon": ["11:00", "22:00"],
  "Tue": ["11:00", "22:00"],
}

reservations = {
  "Mon": [["12:00", "12:30"], ["18:00", "19:15"]],
  "Tue": [],
}

Task

Write a function that returns, for each day, the list of available time intervals within opening hours that are not blocked by existing reservations.

Clarify/handle these cases:

• Reservations may be unsorted.
• Reservations may touch endpoints (e.g., one ends at 13:00 and another starts at 13:00).
• If reservations overlap, they should be merged before computing availability.

Output

Return a nested dictionary:

• available[day] = [[free_start1, free_end1], [free_start2, free_end2], ...]

(Optionally, if a booking duration D minutes is provided, return only free intervals of length >= D, or return discrete start times valid for a D-minute reservation—state your choice.)