Question

So here I am tonight with this question that came up into my mind :

What is your favourite way to access the items of a m x n matrix

there is the normal way where you use an index for the columns
and another index for the rows matrix[i][j]

and there’s another way where your matrix is a vector of length m*n
and you access the items using [i*n+j] as index number

tell me what method you prefeer most , are there any other methods
that would work for specific cases ?

Answer 1

There are only two reasons to go for the one-dimensional array to represent n-dimensions I can think of:

• Performance: The usual way to allocate n-dimensional arrays means that we get n dimensions that may not necessarily be allocated in one piece – which isn’t that great for spatial locality (and may also result in at least some additional memory accesses – in the worst case we need 1 additional read for each access). Now in C/C++ you can get around this (allocate memory in one piece, then afterwards specify the correct pointers; just be really careful not to forget this when you delete it) and other languages (C#) already can do this out of the box. Also note that in a language with a stop&copy GC the reasoning is unnecessary since all the objects will be allocated near each other anyhow. You avoid additional overhead for each single dimension though, so you use your memory and cache a bit better.

• For some algorithms it’s nicer to just use a one dimensional array which may make the code shorter and slightly faster – that’s probably the one thing that can be argued as subjective here.