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Keep prefix sums of both arrays.
Can the difference between the prefix sums at an index help us?
What happens if the difference between the two prefix sums at an index a is x, and x again at a different index b?
This means that the sum of nums1 from index a + 1 to index b is equal to the sum of nums2 from index a + 1 to index b.
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If two indices have the same prefix sum difference between the arrays, it means the incremental sums between those indices are equal. This mathematical property allows us to convert a range comparison problem into a prefix difference lookup.
While the exact problem may not always appear, its underlying concepts are common in interviews. Prefix sums, difference arrays, and hash map optimizations frequently appear in coding interviews at companies like Google, Amazon, and Meta.
A hash map is the most effective data structure for this problem. It stores the earliest index where each prefix difference appears, allowing quick lookups when the same difference occurs again during traversal.
The optimal approach uses prefix sums combined with a hash map. By tracking the difference between prefix sums of the two arrays, repeated differences indicate equal range sums. The hash map stores the first occurrence of each difference to maximize the distance between indices.