I don't know if I'm wording the problem correctly in the title. Basically, in a chess board, I need to find the diagonals a bishop can move on, and more specifically, the coordinates of those squares. So, given a grid of any size and a position in that grid (expressed in coordinates within the grid), I have to compute the coordinates of the diagonals of that initial position.

I'm using zero-based indexing, and the (row, column) notation for coordinates.

For example, on a 8x8 grid, with starting position of (0, 0), the returned list should be [(0, 0), (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6), (7, 7)].

On a 8x8 grid, with starting position of (3, 4), the returned list should be [(3, 4), (2, 3), (1, 2), (0, 1), (4, 5), (5, 6), (6, 7), (4, 3), (5, 2), (6, 1), (7, 0), (2, 5), (1, 6), (0, 7)]

This is my working program in Python 3:

def diagonals(coord, size):
    limit = size - 1
    coords = [coord]
    row = coord[0]
    col = coord[1]

    while row > 0 and col > 0:
        row -= 1
        col -= 1
        coords.append((row, col))

    row = coord[0]
    col = coord[1]

    while row < limit and col < limit:
        row += 1
        col += 1
        coords.append((row, col))

    row = coord[0]
    col = coord[1]

    while row < limit and col > 0:
        row += 1
        col -= 1
        coords.append((row, col))

    row = coord[0]
    col = coord[1]

    while row > 0 and col < limit:
        row -= 1
        col += 1
        coords.append((row, col))

    return coords

coord = (3, 4)
size = 8
print(diagonals(coord, size))

Depending on the diagonal (4 cases), row and column are added or subtracted by one until the last square is reached, and everything is kept in a list, which in the end is returned.

It works, but it left me wondering if there's a simpler, different, better way of doing this, probably using linear algebra or something? And how about idiomatically, how can this be more Pythonic?