language agnostic - 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 + ...