C++ Data Structure to Find Neighbouring Values in Multidimensional Array

Question

I have a project where I read in an array that has 1 or more dimensions, and for this project I need to be able to determine a given element's neighbours quickly. I do not know the dimensionality ahead of time, and I likewise do not know the size of the dimensions ahead of time. What would be the best C++ data structure to store this data in? A colleague recommended a vector of vectors of vectors of . . ., but that seems incredibly unwieldy.

Answer 1

If you know the address of which element you need the neighbors for, could you just do pointer arithmetic to find out the neighbors. For example, if p is the location of the element, then p-- is the left neighbor and p++ is the right neighbor.

Answer 2

Think your multidimensional array as a 1D array. Let the dimension of the array is d1 * d2 * ....* dn

Then allocate memory for a 1D array, say A of size d1 * d2 * ....* dn . For example,

int *A = new int[d1 * d2 * ....* dn];

If you need to store data in the [i1][i2]...[in] th index, then store in the following index:

A[i1 * (d2*d3*d4.. *dn) + i2 * (d3*d4*....dn) + ..... + in] 

Neighboring elements will be:

A[(i1 + 1) * (d2*d3*d4.. *dn) + i2 * (d3*d4*....dn) + ..... + in] 
A[(i1 - 1) * (d2*d3*d4.. *dn) + i2 * (d3*d4*....dn) + ..... + in] 

A[i1 * (d2*d3*d4.. *dn) + (i2 + 1) * (d3*d4*....dn) + ..... + in] 
A[i1 * (d2*d3*d4.. *dn) + (i2 - 1) * (d3*d4*....dn) + ..... + in] 

.............................
A[i1 * (d2*d3*d4.. *dn) + i2 * (d3*d4*....dn) + ..... + (in + 1)] 
A[i1 * (d2*d3*d4.. *dn) + i2 * (d3*d4*....dn) + ..... + (in - 1)]