Merge overlapping weekly time intervals

Q: Merge overlapping weekly time intervals

This question evaluates the ability to parse weekday and 24-hour time strings, reason about interval overlap, and apply efficient merging and sorting techniques for time-based intervals.

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Question

You are given a list of time intervals representing meetings. Each interval is a pair of strings in the format:

"<Day> <H>:<MM>" (24-hour time)
<Day> is one of Mon, Tue, Wed, Thu, Fri, Sat, Sun
Examples: "Mon 9:00" , "Mon 13:00" , "Tue 09:30"

Example input:

[["Mon 9:00", "Mon 13:00"], ["Mon 11:00", "Mon 16:00"]]

Two intervals overlap if they occur on the same day and their time ranges intersect (endpoints may be treated as overlapping, i.e., [9:00, 13:00] overlaps [13:00, 14:00]).

Task:

Parse the strings into comparable time values.
Merge all overlapping intervals (per day) and return the merged list.

Output requirements:

Return intervals in the same string format.
Sort output by day-of-week (Mon→Sun), then by start time.

Clarify/assume:

All intervals start < end.
Intervals may span different days, but each individual interval’s start and end are on the same day.
Input size can be large enough that an efficient solution is expected (better than $O(n^2)$ ).

Merge overlapping weekly time intervals

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