Weighted Interval Scheduling

Problem Statement:

You are given a list of events. Each event is represented as a tuple (start, end, value), where:

• start is an integer representing the start time of the event.
• end is an integer representing the end time of the event (with the guarantee that start < end).
• value is a positive integer indicating the benefit of attending the event.

Two events are considered non-overlapping if they do not share any time period; that is, event A and B do not overlap if A's end is less than or equal to B's start, or vice versa.

Your task is to write a function that selects a subset of non-overlapping events so that the sum of their values is maximized.

Input:

• An array/list of events, where each event is provided as a tuple (start, end, value).

Output:

• An integer representing the maximum total value achievable by selecting a set of non-overlapping events.

Example:

For the input list:

[(1, 3, 5), (2, 5, 6), (4, 6, 5), (6, 7, 4)]

One optimal solution is to select the events [(1, 3, 5), (4, 6, 5), (6, 7, 4)], which yields a maximum total value of 14.

Constraints:

• The number of events can be as large as 10^5, so an efficient algorithm is required.
• Event times are integers.
• Edge cases such as an empty list of events should be handled gracefully.

Additional Requirements:

• Your code should be modular and well-documented.
• Consider optimal data structures to handle the input size and speed up the search for non-overlapping events.

Good luck!