I jumped straight to the brute force O(n²) approach and the interviewer let me run with it for a bit before nudging me toward something better.
Use a hash map to store prefix sums and their frequencies, allowing O(n) time by checking for each prefix sum if (prefix sum - k) exists. This handles negative numbers and zeros efficiently. Explain the intuition and walk through a small example.
Pro tip: Mention that the hash map approach is optimal for arbitrary integers, and clarify why sliding window fails with negatives. Also, discuss edge cases like empty array and large k.
Confirm that subarrays are contiguous and non-empty, and that the array can contain negative numbers and zeros. Ask about constraints if not provided.
Acknowledge that checking all subarrays takes O(n^2) time, which is inefficient for large inputs. This shows you consider trade-offs.
Explain that the sum of a subarray from i to j is prefix[j] - prefix[i-1]. So we need to count pairs where prefix[j] - prefix[i] = k.
Iterate through the array, maintaining a running sum and a hash map of prefix sum frequencies. For each sum, add the frequency of (sum - k) to the count, then update the map.
State that time and space are O(n). Discuss edge cases: empty array, k=0, all negatives, and large values causing overflow (use long if needed).
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.