Prof. Pang does research on the minimum covering circle problem. He does not like random algorithms so he decides to find an efficient deterministic one. He starts with the classical idea of binary search. In each iteration of the binary search, the following problem needs to be solved: Given the radius rrr of a circle and a convex hull CCC, let SSS be defined as SSS === {p{p{p ∣|∣ thethethe circlecirclecircle withwithwith centercentercenter ppp andandand radiusradiusradius rrr coverscoverscovers CCC }}}. Find the area ofSSS.
Prof. Pang does research on the minimum covering circle problem. He does not like random algorithms so he decides to find an efficient deterministic one. He starts with the classical idea of binary search. In each iteration of the binary search, the following problem needs to be solved: Given the radius rrr of a circle and a convex hull CCC, let SSS be defined as SSS === {p{p{p ∣|∣ thethethe circlecirclecircle withwithwith centercentercenter ppp andandand radiusradiusradius rrr coverscoverscovers CCC }}}. Find the area of SSS.
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