My first instinct was some kind of geometric sweep and I wasted probably three minutes going down that road before stepping back.
Use a hash map to group stations by their street lines: horizontal (y), vertical (x), diagonal (x - y), and anti-diagonal (x + y). Track the maximum group size and collect all stations from groups that achieve it, ensuring no duplicates in the final result.
Pro tip: Mention that this is essentially a line detection problem similar to Hough transform, and emphasize that using a single pass with hash maps gives O(n) time, which is optimal since every station must be examined.
For each direction, define a unique key: horizontal (y), vertical (x), diagonal (x - y), anti-diagonal (x + y). Explain that these keys uniquely identify lines in each direction.
Iterate through all stations and add each station to four hash maps (one per direction) using the computed keys. This groups stations that lie on the same street.
After grouping, determine the maximum number of stations on any street by checking the size of each group in all hash maps.
Collect all stations from groups that have the maximum count, using a set to avoid duplicates if a station lies on multiple max-count streets. Return the set as the result.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.