High school maths
Given a set of triangles, find the indices of the triangle with the smallest and the largest area.
Iterate through the triangles while maintaining the triangle with minimum and maximum area (in case of ties triangle with larger index wins).
The area of a triangle with vertices (x1, y1), (x2, y2), and (x3, y3) is given by
A = 0.5 * abs((x1 * y2 - x2 * y1) + (x2 * y3 - x3 * y2) + (x3 * y1 - x3 * y1))
Since we are only interested in the relative values of the area, we can drop 0.5, so that area calculation does not require floating point arithmetic. Also the limits on the values of xi, yi’s are small enough so we do not need to worry about overflow.
After calculating areas a single pass can be made through the triangles while maintaining the area and index of the triangles with the smallest and largest area. In case of ties the triangle with larger index wins.