What is the most efficient algorithm to find a line that goes through most points?

Programmer Question

The problem:

N points are given on a 2-dimensional plane. What is the maximum number of points on the same straight line?

The problem has O(N²) solution: go through each point and find the number of points which have the same dx / dy with relation to the current point. Store dx / dy relations in a hash map for efficiency.

Is there a better solution to this problem than O(N²)?

Find the answer here