Find intersection of two line segments

## Problem Given two 2D line segments **AB** and **CD**, determine whether they intersect. Each segment is defined by its endpoints: - A(x1, y1), B(x2, y2) - C(x3, y3), D(x4, y4) ### Tasks 1. Return `true/false` indicating whether the two **closed** segments intersect. 2. (Optional follow-up) If they intersect at a **single point**, return that intersection point. If they overlap over an interval (collinear overlap), return an appropriate representation (e.g., "overlap" or the overlapping segment). ### Requirements / Edge cases to handle - Vertical segments (infinite slope) and horizontal segments. - Touching at endpoints counts as intersection. - Collinear segments that overlap partially or fully. - Large coordinates (avoid floating-point precision bugs if possible). ### Example - A(0,0), B(2,2) and C(0,2), D(2,0) → intersect at (1,1) - A(0,0), B(0,2) and C(1,0), D(1,2) → do not intersect (parallel vertical) - A(0,0), B(2,0) and C(1,0), D(3,0) → collinear overlap