|You have a large square box and some smaller triangular boxes (all two-dimensional). The triangular boxes all lie inside the square box. Triangular boxes may lie inside other triangular boxes, but they must not overlap. You randomly throw an object (represented as a point) into the square box, and you want to know if it lands inside exactly inBox triangular boxes.
You are given a String boxes, each element of which is formatted as "X1.Y1 X2.Y2 X3.Y3" (quotes for clarity only), representing the three corners of a triangular box. The large square box has sides parallel to the axes, and has corners at (0, 0) and (100, 100). Return the probability (between 0 and 1) that a random point within the square is contained in exactly inBox triangular boxes.
|-||Your return value must have an absolute or relative error less than 1e-9.|
|-||boxes will contain between 0 and 50 elements, inclusive.|
|-||Each element of boxes will be formatted as "X1.Y1 X2.Y2 X3.Y3" (quotes for clarity only).|
|-||X1, Y1, X2, Y2, X3, Y3 will be integers with no leading zeros, each between 0 and 100, inclusive.|
|-||Triangles represented by different elements of boxes will have no common points.|
|-||inBox will be between 0 and 50, inclusive.|