The naive approach is obvious and wrong for the time constraint.
Use a hash map to store the earliest index where each prefix sum occurs, then iterate through the array computing the running sum. For each index, check if (current sum - target) exists in the map; if so, update the maximum length. This yields O(n) time and O(n) space.
Pro tip: Clarify upfront that the array can contain negative numbers, which rules out sliding window and necessitates the prefix sum approach. Also, mention that you store the earliest index to maximize subarray length.
Ask about array size, possible values (negative, zero), and whether the subarray must be non-empty. Confirm that O(n) time is required and O(n) space is acceptable.
Define prefix sum at index i as the sum of elements from 0 to i. The sum of subarray (i, j] is prefix[j] - prefix[i], so we need prefix[j] - prefix[i] = target.
Use a hash map to store the first occurrence of each prefix sum. Initialize with {0: -1} to handle subarrays starting at index 0. Iterate through the array, updating the running sum and checking if (sum - target) is in the map.
If (sum - target) exists, compute the subarray length as current index minus the stored index, and update the maximum. If the current sum is not in the map, add it with the current index to preserve the earliest occurrence.
State that time complexity is O(n) and space is O(n). Walk through a small example, including a case with negative numbers and a case with no valid subarray, to verify correctness.
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