A bitonic sequence first increases, then decreases. Find the longest bitonic subsequence. For [1, 11, 2, 10, 4, 5, 2, 1], the answer is 6 because the longest bitonic subsequence has 6 elements, for example [1, 2, 10, 4, 2, 1] (increases to 10, then decreases).
The key: every element could be the peak. You need to know the LIS ending at each position AND the LDS (longest decreasing subsequence) starting at each position. Read the problem statement carefully, noting the constraints. Try to identify the recursive structure before looking at the solution.