A prefix sum stores the cumulative total up to each index, so the sum of any subarray is the difference of two prefix values. It turns repeated range-sum queries from O(n) each into O(1) after O(n) preprocessing.
Prefix sums - Interview Concepts - ExtraBrain is part of ExtraBrain's local-first Mac workflow for live interviews, meetings, transcription, provider control, and responsible AI use.
A prefix sum stores the cumulative total up to each index, so the sum of any subarray is the difference of two prefix values. It turns repeated range-sum queries from O(n) each into O(1) after O(n) preprocessing.
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Build an array where each entry holds the sum of all earlier elements, then subtract endpoints for a range.
A 2D prefix sum answers submatrix-sum queries in constant time using inclusion and exclusion.
Prefix XOR, prefix counts, and difference arrays extend the same idea.
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When you answer many range-sum or range-count queries over static data, or need subarray sums quickly.
It is the inverse idea: record deltas at range endpoints, then take a prefix sum to apply many range updates efficiently.
