Question

N points are given as input.

Let’s say (x1,y1), (x2,y2)... (xn,yn).

Is there a non-combinatorial solution to find the maximum number of collinear points? Can they be arranged in a fancy data structure that would help this computation?

Answer 1

For each point i, find the slope to every other point j and
look for duplicates. Duplicates can be found by sorting the slopes and
comparing adjacent values. Point i is collinear with the points in
each set of duplicates. Keep track of the maximal set as you go.

For each i, you have n-1 slopes to calculate and sort and compare.
Therefore, using a (n log n) sorting, the complexity of the algorithm is
O(n^2 log n).