Given N points on a circle, centered at the origin, design an
algorithm that determines whether there are two points that are
antipodal, i.e., the line connecting the two points goes through the
origin. Your algorithm should run in time proportional to N log N.

My logic is :
1) Sort the given points on the basis of their X-coordinates (NlogN)
2) Select first point and Binary Search for negative of its X-
coordinate (LogN)
3) If it returns true we are done else select sencond point and so
on....(NlogN in worst condition)

Am i Correct ??? Any more solutions ???

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