Get Maximum Throughput (Fungible)

Problem Overview

• Group servers into clusters of three to maximize system_throughput, the sum of each cluster’s median host throughput.
• Input: int array host_throughput[n]; Output: long maximum system_throughput; each server can be used at most once, unused servers allowed.
• Constraints: 1 ≤ n ≤ 2e5, 1 ≤ host_throughput[i] ≤ 1e9; the cluster median is the 2nd largest of the three.
• Real-world context: optimizing database query times across host clusters.
• From Amazon interviews; a coding interview problem and interview question.