Happy Number Service

Implement a service that decides whether a positive integer is a happy number, then scale it to billions of requests. Requirements Implement a service that takes a positive integer and decides whether it is happy: Replace the number with the sum of the squares of its digits. Repeat the process. The number is happy if it eventually reaches 1; otherwise it loops endlessly in a cycle that never reaches 1. Return whether the input is happy. Notes Standard cycle detection applies: non-happy numbers fall into a fixed cycle, so either a set of seen values or Floyd's slow/fast pointers terminates the loop. Any starting integer collapses into a small range within one or two iterations, because the sum of squares of the digits of a large number is far smaller than the number itself. Scaling follow-up "Now scale this to billions of requests." The intended answer is precomputation: every integer drops below a few thousand after one or two digit-square steps, so precompute and cache the happy / not-happy verdict for the small range the inputs collapse into (the interviewer pointed at numbers below ~1,000). At request time, fold the input down into the cached range with one or two steps and return the memoized answer, turning each query into near-constant work. Preparation Implement both the set-based and Floyd cycle-detection versions. Precompute the verdict for every integer below 1,000 and write the fold-down lookup that reduces an arbitrary input into that table.