Aggregate Event Times

Function Name: mergeTimeIntervals

Description

Write a function that takes a list of time intervals for various events, where each interval is represented as a pair of strings (start, end) in 24-hour 'HH:MM' format. The function should return a list of merged intervals if any two intervals overlap.

The input list can be unsorted and there might be multiple intervals overlapping. The merged intervals should be outputted in sorted order, without any overlapping.

Assume that time intervals are closed, meaning '10:00' - '12:00' and '12:00' - '13:00' do overlap at '12:00'.

Requirements

• The function should take a single parameter: a list of time interval tuples, where each interval is represented by a pair of strings.
• The returned list should consist of merged intervals represented as tuples, sorted by their start times.
• If an interval is contained entirely within another, it should only appear as part of the merged interval.
• The function should handle edge cases, such as the start time being the same as the end time of the previous interval.
• Assume that all given times are valid and within the same day.

Examples

Given a list of intervals: [('09:00', '11:30'), ('11:20', '13:00'), ('14:00', '15:00'), ('10:30', '12:00')]The function should return: [('09:00', '13:00'), ('14:00', '15:00')]