Group points by distance threshold

You are given **N points** in 2D space, `points[i] = (xi, yi)`, and a distance threshold `k > 0`. Define an undirected graph where there is an edge between two points `i` and `j` if their **Euclidean distance** is **strictly less than `k`**. A **group** is a connected component of this graph (i.e., grouping is **transitive**: if A is within `k` of B and B is within `k` of C, then A, B, C are in the same group even if A and C are not directly within `k`). ### Task Return the grouping of points (e.g., the number of groups and/or the list of point indices in each group). ### Follow-up If `N` is very large and points are very **sparse** (most pairs are far apart), how would you **reduce the number of distance computations** compared to checking all `O(N^2)` pairs? ### Assumptions / constraints (you may state your own) - `1 <= N <= 2e5` - Coordinates are integers in a large range (e.g., `[-1e9, 1e9]`). - Distance is Euclidean: `dist((x1,y1),(x2,y2)) = sqrt((x1-x2)^2 + (y1-y2)^2)`.