Find largest digit-sum bucket size

You are given two integers low and high (inclusive). Define s(x) as the sum of the decimal digits of x. For every integer x in [low, high], place x into bucket s(x). Return the size of the largest bucket (i.e., the maximum count of numbers that share the same digit sum). If multiple buckets tie, return that common size. Describe your algorithm and analyze its time and space complexity. Follow-ups: ( 1) Can you avoid iterating over every x when high − low is very large? ( 2) How would your approach change if numbers were represented in an arbitrary base b (2 ≤ b ≤ 36)?