Point Reachability Below a Strict Distance Threshold

You are given unordered points in the plane, an integer radius r, and the indices start and end.

Two different point indices i and j are directly connected exactly when their distance is strictly less than r. Connections work in both directions, and a route may use intermediate points.

For this exercise, assume points are immutable two-dimensional integer coordinates, distance is Euclidean, and both endpoints are indices into this collection. Equal coordinates at different indices remain different vertices.

Equivalently, the direct connection test is (points[i][0] - points[j][0])^2 + (points[i][1] - points[j][1])^2 < r^2. A distance equal to r is excluded.

Return true if a route from start to end exists, and false otherwise. For this exercise, assume a point reaches itself through a path of length zero, even when r == 0.

For this exercise, assume one reachability query over one immutable point set. Return only this Boolean; distance caching is a discussion follow-up, with no additional returned values or required spatial partitioning.

What the interview report shared

The report supplies a distance function, uses the strict rule distance < r, and describes graph construction with BFS or DFS. A large-data follow-up discusses caching or precomputing distances to avoid repeated calculations.