Google Coding Question: Online Longest Subarray with Average

You are given a stream of integers and a fixed target average S. After each new integer arrives you must report the length of the longest contiguous subarray within the prefix seen so far whose average equals S (or 0 if none exists).

Core idea: convert the average condition into a zero-difference condition on a transformed prefix-sum. Let pref[i] be the sum of the first i values. A subarray (i, j] has average S iff pref[j] - pref[i] = S * (j - i). Rearranging gives pref[j] - Sj = pref[i] - Si. Maintain the earliest index you see for each value of the transformed key (pref - S*index) in a hashmap; at each step compute the current key and look up the earliest index to update the maximum length. This yields an online O(n) time, O(n) space solution.

Flow in an interview: you should (1) explain the mathematical transform, (2) propose the online hashmap design, (3) discuss numeric precision and edge cases (non-integer S, floating-point error) and (4) analyze complexity and memory trade-offs.

Skill signals: you must demonstrate algebraic manipulation of averages, use of prefix sums, hash table design for online tracking, and handling of floating-point precision (use scaling, rational representation, or an epsilon). Also explain why sliding-window/two-pointers fail when inputs can be negative.