Efficient Tasks / Three-Server Difficulty Split

Partition task difficulties across three servers, then each server chooses one task to minimize `|d1-d2| + |d2-d3|`; maximize that minimized value over all valid partitions. Multiple 2026 OA candidates describe this as the harder coding problem. Requirements Input: integer array difficulty, where difficulty[i] is the difficulty of one software module. Partition all modules across exactly three servers. Every module must be assigned once, and each server must receive at least one module. For a fixed partition, one module is selected from each server to compute |d1 - d2| + |d2 - d3|. The selected modules are chosen to minimize this expression. Return the maximum possible value of that minimized expression across all valid partitions. Examples difficulty = [5, 1, 2, 5, 3, 5] return 6 Notes A quant-track version describes the same core formula as selecting three numbers from an array; the Engineering OA version frames it as deployment across three servers. Clarify whether duplicate difficulty values are distinct modules. The deployment wording implies they are distinct items even if values match. The high-level invariant is to make the closest possible triple across the three groups as far apart as possible; sorting the difficulties is the natural first step. Preparation Work several sorted-array examples by hand before coding; the objective is maximin, so intuitive greedy splits can fail silently. State the brute-force partition search first, then explain the sorted / boundary-based optimization you choose.