OA: Largest Group Sharing a Digit

Second problem in the 90-min Google SWE Early Career / NG OA. Given a list of two-digit numbers, return the size of the largest subset where every chosen number shares at least one common digit. Requirements Input: an integer array (length ≤ 100), each value is a two-digit number (10–99). A group is valid only if there exists at least one digit d ∈ {0..9} that appears in every number in the group. Return: the maximum group size. Examples Input: [52, 25, 55, 11, 34] Group: [52, 25, 55] all contain digit 5 → size 3 Output: 3 Input: [11, 21, 31, 41, 16, 17, 18, 34, 57] Group: [11, 21, 31, 41, 16, 17, 18] all contain digit 1 → size 7 Output: 7 Notes Each number has at most two distinct digits, so there are only 10 candidate digits to enumerate. A number with repeated digits (e.g. 55) still has one distinct digit; that's fine. The OA gives 2 sample test cases and no hidden tests — add your own (digit 0 in tens place is impossible for two-digit numbers, but still verify singletons and full-array cases). Standard pattern: for each number, union it with a virtual node for each of its digits (0-9). Largest component size via DSU rank/size tracking, O(N * d) where d is digits per number. The 10 digit-nodes act as connector hubs so you avoid O(N^2) pairwise checks. Preparation For each digit d in 0–9, count how many input numbers contain d; return the maximum count. Practice writing it cleanly in 5 minutes — this is the easier of the two OA problems, so save time for the coin board.