The subarray sum part I knew, prefix sums with a hashmap, seen it before.
Use a hash map to store prefix sums and their frequencies, allowing you to find subarrays summing to k in O(n) time. For each element, compute the running sum and check if (running sum - k) exists in the map, adding its frequency to the count. Then, update the map with the current running sum.
Pro tip: Explicitly discuss how negative numbers and zeros affect the prefix sum approach, and mention that using a hash map with prefix sums handles them naturally. Also, bring up integer overflow and suggest using 64-bit integers for the prefix sum to avoid overflow.
Confirm that the array can contain negative numbers and zeros, and discuss the expected input size to determine if O(n) is necessary. Ask about integer overflow concerns if the sum can exceed 32-bit range.
Describe how to maintain a running sum and a hash map that counts occurrences of each prefix sum. For each element, check if (current sum - k) exists in the map to count valid subarrays ending at the current index.
Choose a small array with negatives and zeros, and step through the algorithm to demonstrate correctness, showing how the map is updated and how counts are accumulated.
State that the algorithm runs in O(n) time and uses O(n) space in the worst case due to the hash map. Contrast with the O(n²) brute-force approach.
Discuss handling of negative numbers, zeros, and large sums. Mention using a 64-bit integer for the running sum to prevent overflow, and note that the hash map keys should also be 64-bit if necessary.
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