You have two $n$-point sets $P$ and $Q$ of two-dimensional points: $$ P = \{p_1,\dots,p_n\}, \text{ where } p_i = \{a_i, b_i\} \\ Q = \{q_1,\dots,q_n\}, \text{ where } q_i = \{c_i, d_i\} $$
You must determine whether there is a line $L$ so that $P$ and $Q$ are on opposite sides. This line essentially must separate both of the sets. The algorithm must run in $O(n)$, and is aimed to be deterministic (yes or no).
Could anyone provide help regarding this problem?
