My first instinct was the sliding window approach and I started explaining it before realizing negative numbers completely break that.
Start by clarifying the problem and edge cases, then propose a brute-force solution and optimize it using a hash map to track prefix sums. Explain how the hash map stores the frequency of each prefix sum and how to compute the count in O(n) time.
Pro tip: Mention that the hash map approach handles negative numbers seamlessly because it relies on prefix sums, not sliding window. Also, initialize the map with {0:1} to account for subarrays starting at index 0.
Ask about input constraints, expected output, and edge cases such as empty array or k=0. Confirm that subarrays must be contiguous and that negative numbers are allowed.
Mention that a naive solution checks all O(n^2) subarrays and sums them, which is inefficient. This shows you understand the baseline.
Explain that the sum of a subarray from i to j is prefixSum[j] - prefixSum[i-1]. So, for each j, we need to count how many i have prefixSum[i-1] = prefixSum[j] - k.
Iterate through the array, maintaining a running sum and a hash map that maps prefix sum to its frequency. For each element, add the frequency of (currentSum - k) to the count, then update the map with currentSum.
State that time complexity is O(n) and space is O(n). Discuss handling of negative numbers and initialization of the map with {0:1}.
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