The negative values thing is what kills people.
Use a hash map to store prefix sums and their frequencies. Iterate through the array, maintaining a running sum, and for each element check if (current_sum - k) exists in the map; if so, add its frequency to the count. Then update the map with the current sum. This handles negative numbers and runs in O(n) time.
Pro tip: Clarify that the array can contain negative numbers, which rules out sliding window; this shows you understand the problem constraints. Also, mention that the hash map approach is optimal and explain why it works with an example.
Confirm that the array can have negative numbers and that we need to count all contiguous subarrays, not just find one. Ask if the array can be empty or if k can be negative.
Mention that a brute force approach would check all O(n^2) subarrays, which is inefficient. Explain that negative numbers prevent using a sliding window technique.
Explain that a prefix sum is the sum of all elements from the start to the current index. Use a hash map to store the frequency of each prefix sum encountered so far.
Initialize a hash map with {0: 1} to handle subarrays starting at index 0. Iterate through the array, update the running sum, and for each element, add the frequency of (current_sum - k) to the count. Then increment the frequency of current_sum in the map.
State that the time complexity is O(n) and space complexity is O(n). Discuss edge cases like empty array, all zeros, and large negative numbers.
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