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

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

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

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Data Structures19 sections · 729 units49h total

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2D Range Sum - Build

Preprocessing step

Here's how to build the 2D prefix array:

function build2DPrefix(matrix)
    rows := number of rows in matrix
    cols := number of cols in matrix
    prefix := 2D array of size (rows + 1) x (cols + 1), all zeros

    for i from 1 to rows
        for j from 1 to cols
            prefix[i][j] := matrix[i-1][j-1]
                          + prefix[i-1][j]
                          + prefix[i][j-1]
                          - prefix[i-1][j-1]
    return prefix

Time: $O(nm)$ . Space: $O(nm)$ .