The famous pancake theorem states that for every finite set $X$ in the plane, there exist two orthogonal lines that divide $X$ into four equal parts. We propose an algorithm whose running time is linear in the number of points in $X$ and prove that this complexity is optimal. We also consider generalizations of the pancake theorem and show that orthogonal hyperplanes can be found in polynomial time.

翻译：著名的薄饼定理指出，对于平面上的任意有限点集$X$，总存在两条正交直线将$X$划分为四个等量部分。本文提出一种运行时间与$X$中点数呈线性关系的算法，并证明该复杂度是最优的。同时我们探讨了薄饼定理的推广形式，证明正交超平面可在多项式时间内求解。