Problem Statement

Minimum Task Transfers Problem Description Three research-station engineers, Vera, Tomas, and Iris, share the workload whenever a batch of n numbered maintenance tasks comes in. Over many rotations they have settled on a fixed way of dividing the work: Vera always handles the opening tasks, covering everything from 1 up to i. Tomas takes the block right after her, covering tasks from i up to j. Iris finishes off the remaining tasks, covering everything from j up to n. Things run smoothly whenever the split follows this pattern — Vera first, Tomas in the middle, Iris last — with i <= j <= n. After one hectic shift, though, the tasks ended up scattered randomly among the three of them, no longer matching that arrangement. The team now wants to shuffle tasks back into their preferred layout: Vera's tasks up front, Tomas's in the middle, Iris's at the end. Each move lets exactly one engineer pass a single task to one of the others, and moves of this kind are costly, so th