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$ curl repovive.com/roadmaps/data-structures/arrays-prefix-sums/2d-range-sum-query

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$ curl repovive.com/roadmaps/data-structures/arrays-prefix-sums/2d-range-sum-query

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2D Range Sum - Query - Arrays & Prefix Sums | Data Structures | Repovive

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Data Structures19 sections · 729 units49h total

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2D Range Sum - Query

Four-term formula

Querying uses the inclusion-exclusion formula:

function sumRegion(row1, col1, row2, col2)
    return prefix[row2+1][col2+1]
         - prefix[row1][col2+1]
         - prefix[row2+1][col1]
         + prefix[row1][col1]

Time: $O(1)$ . Four array accesses, three arithmetic operations.

Trace this on a small example. Draw the four rectangles. The formula will make sense.