Start by clarifying the problem constraints (e.g., array size, element ranges, whether negative numbers are allowed) and then present a brute-force O(n^2) approach. Follow with an optimized O(n) solution using a hash map to store prefix sums and their frequencies, explaining how it avoids redundant computations. Walk through a concrete example to illustrate the logic and discuss edge cases.
Pro tip: Mention that the hash map approach works even with negative numbers, unlike sliding window, and emphasize that you're optimizing for time complexity while using O(n) extra space. This shows you understand trade-offs and can adapt to constraints.
Ask about input constraints (array size, element range, negative numbers) and confirm that subarrays must be contiguous. This ensures you don't make incorrect assumptions.
Briefly explain the O(n^2) solution: iterate over all possible subarrays and check if their sum equals k. This establishes a baseline and shows you can think of a simple solution.
Explain that we can use a hash map to store the frequency of prefix sums. For each element, compute the running sum and check if (running sum - k) exists in the map; if so, add its frequency to the count.
Choose a small array (e.g., [1,2,3], k=3) and step through the algorithm, showing how the hash map is updated and how the count is incremented.
State that time complexity is O(n) and space is O(n). Discuss edge cases: empty array, k=0, negative numbers, and large arrays.
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