Consider a subset $A\subseteq \{0, 1, 2, \dots, n - 1\}$. We define $A + i = \{(a + i) \text{ mod } n \mid a \in A\}$. For example if $A = \{1, 3, 4\}$ and $n = 5$, $A + 2 = \{3, 0, 1\}$.
We want to find the smallest number of these shifted subsets that cover the entire set $\{0, 1, 2, \dots, n - 1\}$.
For the example of $A = \{1, 3, 4\}$ and $n = 5$, we can cover the entire set with $A$ and $A + 4$.
So far, I've tried converting it to a bipartite and set cover graph, but I found that set-cover is NP-compete. We also tried things with largest gaps between numbers, but none of those work either. Is there an efficient algorithm that, given $A,n$, computes the minimum number of shifted subsets that cover all of $\{0,\dots,n-1\}$?
