Determining neighbours of cell two dimensional list

Question

I have a list of lists, something like

[[1, 2, 3,],[4, 5, 6,],[7, 8, 9]].

Represented graphically as:

1 2 3
4 5 6
7 8 9

I'm looking for an elegant approach to check the value of neighbours of a cell, horizontally, vertically and diagonally. For instance, the neighbours of [0][2] are [0][1], [1][1] and [1][2] or the numbers 2, 5, 6.

Now I realise, I could just do a bruteforce attack checking every value a la:

[i-1][j]
[i][j-1]
[i-1][j-1]
[i+1][j]
[i][j+1]
[i+1][j+1]
[i+1][j-1]
[i-1][j+1]

But thats easy, and I figured I can learn more by seeing some more elegant approaches.

Answer 1

# Size of "board"
X = 10
Y = 10

neighbors = lambda x, y : [(x2, y2) for x2 in range(x-1, x+2)
                               for y2 in range(y-1, y+2)
                               if (-1 < x <= X and
                                   -1 < y <= Y and
                                   (x != x2 or y != y2) and
                                   (0 <= x2 <= X) and
                                   (0 <= y2 <= Y))]

>>> print(neighbors(5, 5))
[(4, 4), (4, 5), (4, 6), (5, 4), (5, 6), (6, 4), (6, 5), (6, 6)]

I don't know if this is considered clean, but this one-liner gives you all neighbors by iterating over them and discarding any edge cases.

Answer 2

Assuming you have a square matrix:

from itertools import product

size = 3

def neighbours(cell):
    for c in product(*(range(n-1, n+2) for n in cell)):
        if c != cell and all(0 <= n < size for n in c):
            yield c

Using itertools.product and thanks to Python's yield expression and star operator, the function is pretty dry but still readable enough.

Given a matrix size of 3, you can then (if needed) collect the neighbours in a list:

>>> list(neighbours((2,2)))
[(1, 1), (1, 2), (2, 1)]

What the function does can be visualized as follows:

Answer 3

mb...

from itertools import product, starmap

x, y = (8, 13)
cells = starmap(lambda a,b: (x+a, y+b), product((0,-1,+1), (0,-1,+1)))

// [(8, 12), (8, 14), (7, 13), (7, 12), (7, 14), (9, 13), (9, 12), (9, 14)]
print(list(cells)[1:])