# Recurrence of splitting a matrix array? [on hold]

If we have a matrix of nxn, what is the recurrence of splitting it into 4 equal parts of size (n/2)*(n/2)?

I thought it would be 4T(n/4) since we are splitting it into a 1/4 of the original size, but I saw from my book there is a similar problem (matrix multiplication) where the recurrence they got from splitting two matrices into 8 (n/2)*(n/2) matrices was 8T(n/2).

Would it be kT(n/2) or kT(n/4)?

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## put on hold as unclear what you're asking by gnat, Doc Brown, BobDalgleish, Bart van Ingen Schenau, Jörg W MittagSep 14 at 7:10

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## 1 Answer

What is n?

• If n is the number of elements in the matrix, then after splitting it into four pieces every piece will contain n/4 elements.
• If n is the number of rows/columns in the matrix so that overall size is n×n, then after splitting the matrix into four pieces each piece will have n/2 rows/columns.

The correct approach depends purely on your definition for n in the problem you are investigating. It seems that since you have a n×n matrix and not n elements, you should model this as kT(n/2).

• In this case, n is the number of rows and column. I appreciate the response. – mymemesarespiciest Sep 11 at 21:35
• Going off that, if I had T(n) = kT(n/2) + f(n), would f(n) have to follow the same definition as the recurrence? For example, if I iterated through every row, would that be n because I went through each row or n^2 because I had to go through every element? Just trying to get this completely straight in my head. I was thinking it is n^2, but I'm not sure. – mymemesarespiciest Sep 11 at 21:37
• @mymemesarespiciest well, are you iterating through every row or every element? I have no idea what you're actually doing. But your analysis seems correct so far. – amon Sep 11 at 21:44
• For the problem I am working on, I am iterating through every row, but every element in the row. In other words, the entire nxn matrix. – mymemesarespiciest Sep 11 at 21:45