How to quickly calculate range queries on arrays using prefix sum and sparse tables.

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The Polymathic Engineer

Range queries allow efficient retrieval of information from array intervals. Prefix sum arrays enable constant-time sum queries after O(n) preprocessing, extending to 2D matrices for rectangular subarrays. Sparse tables handle minimum/maximum queries in O(1) time with O(n log n) preprocessing. These techniques significantly outperform naive approaches that recalculate results for each query, making them essential for handling multiple queries on static datasets.

Range Queries