Given that this is a terrible ring, we consider two points.
Easy to think of a set of knowledge, the intersection of two adjacent set is the empty set, and set the minimum size requirements.
Then we can try to look at half of all medals \ (the n-\) .
feasibility:
For each set \ (S_i \) , where that is feasible to satisfy my
\ [provided Min_i = \ min S_i \ cap S_1 (S_i \ cap S_ {i-1} = \ empty) \\ Min_i = n-Size (S_ {i-1} \ cup S_1 ) \\ i.e. Size (S_ {i-1} \ cup S_1) is as small as possible \\ Minn_ {i-1} as large as possible (referred to as Maxx_ {i-1}) \
] something similar results using mathematical induction:
\ [Maxx_i = \ min \ {A_i, A_1. 1-I-Minn_ {} \} \\ \ # up number may be selected from the selected number may be selected from = min may be selected from the maximum number \\ Minn_i = \ max \ {{ 0, A_i- (n- (A_ {i-1} + A_1-Maxx_ {i-1})}) \} \]