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Asked: 2026-06-01T03:04:08+00:00

Please look at this picture: Is it possible to find per-column sum for all

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Please look at this picture:

enter image description here

Is it possible to find per-column sum for all columns faster than in O(n^2)?

Firstly I thought it’s possible to make it n * log(n), if we regroup summation like this (to sum 2 rows at time, then remaining 2 rows, and then remaining 2 rows…):

enter image description here

But then I counted the number of pluses and it came out to be equal in both cases – 7 = 7 from both pictures.

So is it possible to compose such a sum in n * log(n) time, or I have fooled myself (I know there are FHT or FFT like transforms, so that might be the case)?

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1 Answer

  1. Editorial Team

    No, our input size is O(n^2), so our algorithm can not be faster than that (because we are using all the input values).

    This is assuming that n is the amount of rows, that the matrix is square (giving n^2) and there is no special relation between the elements.

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