My first instinct was the brute force nested loop and I actually started coding it before catching myself.
Start by clarifying the problem constraints (e.g., array size, element types, whether negative numbers are allowed) and then propose an efficient solution using a hash map to store prefix sums. Explain that this approach reduces the time complexity from O(n^2) to O(n) by leveraging the relationship between prefix sums and the target sum.
Pro tip: Mention edge cases like empty array, all zeros, and negative numbers, and discuss how the prefix sum approach handles them. Also, briefly compare with the brute-force method to highlight the efficiency gain.
Ask about constraints: array size, element range, whether negative numbers are allowed, and if the subarrays must be non-empty. Confirm the expected return type (integer count).
Mention that a naive solution would check all subarrays, leading to O(n^2) time complexity, which is inefficient for large inputs.
Explain that by keeping a running sum and using a hash map to store the frequency of each prefix sum, we can find the number of subarrays ending at each index that sum to k in O(1) average time.
Initialize a hash map with {0:1} to handle subarrays starting from index 0. Iterate through the array, update the running sum, and for each element, add the count of (running sum - k) from the map to the result, then update the map with the current running sum.
State that time complexity is O(n) and space complexity is O(n) in the worst case. Discuss edge cases like empty array, k=0, and negative numbers, and confirm the algorithm handles them correctly.
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