Finding neighbours in a two-dimensional array

Question

Is there an easy way of finding the neighbours (that is, the eight elements around an element) of an element in a two-dimensional array? Short of just subtracting and adding

Answer 1

I think Ben is correct in his approach, though I might reorder it, to possibly improve locality.

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

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

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

One trick to avoid bounds checking issues, is to make the array dimensions 2 larger than needed. So, a little matrix like this

3 1 4
1 5 9
2 6 5

is actually implemented as

0 0 0 0 0
0 3 1 4 0
0 1 5 9 0
0 2 6 5 0
0 0 0 0 0 

then while summing, I can subscript from 1 to 3 in both dimensions, and the array references above are guaranteed to be valid, and have no effect on the final sum. I am assuming c, and zero based subscripts for the example

Answer 2

here is some code for C#:

public Cell[,] MeetNeigbours(Cell[,] Grid)
    {
        for (int X = 0; X < Grid.GetLength(0); X++)
        {
            for (int Y = 0; Y < Grid.GetLength(1); Y++)
            {
                int NeighbourCount = 0;
                for (int i = -1; i < 2; i++)
                {
                    for (int j = -1; j < 2; j++)
                    {
                        if (CellExists(Grid, (X + i)), (Y + j) && (i != 0 && j != 0))
                        {
                            Grid[X, Y].Neighbours[NeighbourCount] = Grid[(X + i), (Y + j)];
                        }
                        if(!(i == 0 && j == 0))
                        {
                            NeighbourCount++;
                        }
                    }
                }
            }
        }
        return Grid;
    }

    public bool CellExists(Cell[,] Grid, int X, int Y)
    {
        bool returnValue = false;
        if (X >= 0 && Y >= 0)
        {
            if (X < Grid.GetLength(0) && Y < Grid.GetLength(1))
            {
                returnValue = true;
            }
        }

        return returnValue;
    }

with the "Cell" class looking like this:

public class Cell
{
    public Cell()
    {
        Neighbours = new Cell[8];
    }

    /// <summary>
    /// 0 3 5
    /// 1 X 6
    /// 2 4 7
    /// </summary>
    public Cell[] Neighbours;
}