Four Rules, One Map

A town planner has plotted houses as [x, y] points in hundreds of metres. There are two neighbourhoods, and sometimes a thin row of houses along a road joins them.

The linkage rule decides what "distance between two groups" means, and the four rules can split the same map very differently.

Task: write sizes_by_linkage(points, n_groups).

• For each rule in this order: "ward", "complete", "average", "single", fit AgglomerativeClustering(n_clusters=n_groups, linkage=rule) on the points as given. Don't scale them.
• Count the points in each cluster and sort the counts from largest to smallest.
• Return a dict mapping each rule's name to its sorted counts.