Efficient Techniques for 2D Point Counting
Given $n$ points $(x_i, y_i)$ and $m$ rectangles, determine the number of points inside each rectangle. Solution Approach The problem requires counting points satisfying $l_j \le x_i \le r_j$ and $d_j \le y_i \le u_j$. By applying inclusion-exclusion, the count for a rectangle can be expressed as: $...