Number of Triangles Containing The Point (0,0)

Question

First off, credits to Topcoder, as this problem was used in one of their SRMs (but they have no editorial for it..)

In this problem, I am given n points (where n is

Answer 1

Let there be a triangle with 3 points p1=(x_1,y_1),p2=(x_2,y_2) and p3=(x_3,y_3). Let p1,p2,p3 be the position vectors.If origin lies within, then cross product of any one position vector with other two will be different in sign ( one negative , one positive ). But if origin lies outside then there will be one point which has negative cross product with both the other points. So for each point i find points whose cross product is less than 0.Now if you select any two of these points and make a triangle along with point i , origin will be outside this triangle.Thats why you subtract from res ( selection of 2 from such points + point i ). This was by far the best solution many implemented as it did not have the problem of precision with double etc.