Checking 2-dimensional array (like eight queens puzzle)

Question

My problem is very similar to eight queens puzzle.

I've got 2-dimensional array (N x N) that for example, looks like this:

0,0,0,0,1 y
0,0,0,0,0 |
0,0,0,0,0 V
0,0,0,1,0
0,0,0,0,0
x->

I'm checking horizontally, vertically and diagonally for occurrences of 1

\,0,|,0,/
0,\,|,/,0
-,-,1,-,-
0,/,|,\,0
/,0,|,0,\

I'm thinking about storing only the (x,y) postions of "1"'s in a list

[[4,0],[3,3]]

and solving it mathematically, check every position of "1" with another (x1,y1)<->(x2,y2),

if x1 == x2 or y1 == y2 we have a collision! if not check:

x2 == x1 + z;
y2 == y1 + z;
x2 == x1 - z;
y2 == y1 - z;

(???)

where z is +/- that ( x1+z in 0..N ) and ( y1+z in 0..N ) .......

My problem is checking for diagonal collision, is there a better way to do it???

Answer 1

One possible solution:

def collision(x1, y1, x2, y2):
    return x1 == x2 or y1 == y2 or abs(x1-x2) == abs(y1-y2)

i.e. there is a collision if the two points are on the same horizontal row, same vertical row or same diagonal (vertical distance == horizontal distance).