computational-geometry
A line that is not parallel
Suppose that n points are given. Call the set of lines determined by them S. Can you find a line that is not parallel to any of the lines in S in better than quadratic time?
Solution
Sort all n points by increasing abscissa. It is clear that the largest slope occurs between two consecutive points. So pick the largest slope among the n-1 possibilities and use a yet larger slope.
The case of points vertically aligned is harmless: ignore these infinite slopes and stay with the largest among the finite ones.
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