Hashmap + Prefix Sum Subarray Round

Phone screen: classic hashmap + prefix-sum pattern over an integer array (subarray sum / count-of-subarrays variants). Standard implementation; round graded on clean handling of the empty-prefix case and clear complexity discussion. Requirements Input: an integer array (potentially with negative values), plus a target depending on the asked variant (subarray sum equal to k, count of subarrays summing to k, longest such subarray, etc.). Output: the requested boolean / count / index depending on variant. Standard contract follows LeetCode 560 / 525 / 974 family. Notes Maintain prefix = sum(nums[0..i]) while walking the array. The number of subarrays ending at i with sum k equals the number of past prefix sums equal to prefix − k. Use a hashmap prefix_count: Map<long, int> initialized with {0: 1} to handle subarrays that start at index 0. Negative values are allowed — this is the pattern's key edge over the sliding-window 'subarray with positive sum' template. Complexity O(n) time and O(n) space. Variants: longest subarray with sum k (store the earliest prefix index per sum, not the count); count of subarrays divisible by k (key by prefix % k, handle negative remainders). Common micro-bugs: forgetting the {0: 1} seed, off-by-one when storing 'earliest index', integer overflow for large prefixes. Preparation Drill LC 560, 525, 974 in one sit-down so the prefix-sum + hashmap idiom is automatic. Practice each variant's pivot (count vs longest vs divisible) — interviewers swap them mid-round. Be able to walk through the {0: 1} seed verbally; the interviewer in this round explicitly asked the candidate to explain that line.