Why it matters

2D BIT handles grid problems efficiently.

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The architecture

BIT[x][y]: 2D array with BIT structure per row + column.

Update: iterate both dimensions.

2D BITBIT[x][y]2D structureUpdatelog² operationsQuerylog² rect sumRectangle sum via inclusion-exclusion of prefix sums
2D BIT operations.
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How it works end to end

Rectangle sum: sum(x1..x2, y1..y2) via inclusion-exclusion.

Applications: image processing, 2D range queries.