after about 6 months sway USACO, i decided to continue my USACO training page, and i have ben stuck in the problem "camelot" for a full day now!, here is the problem description : https://www.scribd.com/document/124295413/USACO-Training-Pages-Camelot my idea is calculating the minimum moves needed to gather at all the squares, but for the king that is hard, because we dont know when will the king get picked up.

can i have a small hint for this problem?