Weighted Meeting Scheduler

Problem Description

You are given an array of meeting requests. Each meeting is represented as a tuple or object with three properties: start time, end time, and priority (a numerical value). Your task is to write a function that selects a subset of these meetings such that no two meetings overlap and the sum of the priorities of the selected meetings is maximized. In addition to computing the maximum total priority, your function should return the list of meetings that make up this optimum solution.

Requirements:

• Non-overlapping condition: Two meetings do not overlap if the end time of one meeting is less than or equal to the start time of the next meeting.
• The meetings are provided in an arbitrary order.
• The function should return both the maximum sum of priorities and the list of meetings used to achieve that sum. If there are multiple solutions, any one of them is acceptable.

Input Details:

• An array of meetings, where each meeting is represented as a tuple or an object, e.g., (start_time, end_time, priority). For example:

  [(1, 3, 5), (2, 5, 6), (4, 6, 5), (6, 8, 4)]
  

• You can assume that the start time and end time are integers and that start time < end time for any meeting.

Output Details:

• The maximum sum of priorities that can be achieved.
• A list of meetings that were selected to achieve this maximum sum.

Example:

Given the input:

meetings = [(1, 3, 5), (2, 5, 6), (4, 6, 5), (6, 8, 4)]

One possible valid output would be:

• Maximum Priority Sum: 14
• Selected Meetings: [(1, 3, 5), (4, 6, 5), (6, 8, 4)]

Additional Considerations:

• Efficiency: Your algorithm should be efficient enough to handle an array with up to a few thousand meeting requests.
• Language: You are free to choose any programming language for your implementation.

Design and implement your solution while ensuring clarity, correctness, and efficiency.