Question

how to find all the neighbors in a n-dimensional array in python?
thank you in advance

all the neighboors of a coordinate*

Answer 1

We can do that recursively easily.

We can use the concept of Cartesian Product here to do that .

Try to understand and visualize the n-dimensional array , we are currently on some cordinate * we want all the co-ordinates in range (-1 to 1) calculating from current co-ordinate

So for example in 2-D matrix if we are on co-ordinate (x,y) we can say the neighbors are (x-1,y) , (x-1,y-1) ,(x-1,y+1) , (x,y-1) ,(x,y+1) , (x+1,y+1) ,(x+1,y) , (x+1,y-1)

As it is for 2-D matrix we can easily get the neighbors all we have done is consider all cases where the difference between the co-ordinates is in between range -1 to 1 . ( Just the reference co-ordinate is to be ignored )

Now what cartesian product do is : It gives the set of all ordered pairs ( Giving all possibilities under given circumstances)

SOLUTION :

Here what we will do is perform Cartesian Product of set {-1 , 0 , 1 } with the each i-th dimension and we will do this for all N-dimensions so that no possible neighbor is left behind.

(Just keep in mind to remove the entry with all n-zeroes as it will point to the reference co-ordinate ( who's neighbors we are finding)

We can write a recursive algorithm to do the above task :

algo
 func(n : dimension
                    index : n-tuple)
    answer := empty list
    for ind in cpower({-1, 0, 1}, n) do
        if not (ind is all zeros then)
            temp := [index[i] + ind[i] #for i in 1..n]
            answer := append(answer, temp)
        end
    loop
    return answer

Here is the recursive algorithm to do that.

I tried my best to explain the question but as this is quite tough problem so if you need any more help or clarification in answer you can comment and I will help you out in best possible way .