Prove that the divide-and-conquer algorithm for the closest-pair problem examines, for every point p in the vertical strip (see Figures 5.7a and 5.7b), no more than seven other points that can be closer to p than d min , the minimum distance between two points encountered by the algorithm up to that point.

x- m di dr dmin 8i) FIGURE 5.7 (a Idea of the divide-and-conquer algorithm for the closest-pair problem. x- m di dr dmin 8i) FIGURE 5.7 (a Idea of the divide-and-conquer algorithm for the closest-pair