linear simulation of multidimensional array

Question

I know how to simulate a 2d array in a linear array using [x + y * width] as a linear index.

I can extend this to 3d arrays: [x + y * width + z * width * height].

Is there a general formula for N-dimensional array?

I'm looking for a language-agnostic answer.

Answer 1

Sure. Just extending your example gives x + y*width + z*width*height + w*width*height*depth + ...

In other words, dim1 + dim2*size1 + dim3*size1*size2 + dim4*size1*size2*size3 + ...

Answer 2

Eh, if you want some code... :-) C is language-agnostic enough, ya?

Assume input: location[dimensions]

Assume a table exists maxBound[dimensions] that contains the maximum boundaries of each dimension of the table.

int index = 0;
int multiplier = 1;
for (int i = 0;i < dimensions;i++)
{
  index += location[i] * multiplier;
  multiplier *= maxBound[i];
}

Your index will end up in the index field.

Test:
location = [3,4,5]
maxBound = [10,20,30]
loop initial: index = 0, multiplier = 1.
loop i=0: index = 3, multiplier = 10.
loop i=1: index = 43, multiplier = 200.
loop i=2: index = 1043, multipler = 6000.

I think this makes sense, but this is just coming out of the top of my head.