Here's a technique to do C — New Year and Curling in time with segment tree. Brute force n² is of course fast enough, but I think speeding it up was interesting.

Suppose we are about to place disk i at x_i. The relevant x range we should look for disks is [x_i - 2r, x_i + 2r] because things outside of this range are too far away to intersect with this disc. Say we find j such that j < i, x_j is in the needed range, and y_j is maximized. The intuition behind the approach is that is a good lower bound for y_i.