One rotation moves center by at most 2r (a 180° half-turn around the pin). So each step shifts the center up to the circle's full diameter.

Compute Euclidean distance d between (x,y) and (x',y'). Minimum steps = ceil(d / (2r)).

Use integer arithmetic to avoid floating error: compare d² with (2r)². Special-case d = 0 (already there, answer 0).