2D Array Diagonals

dougal85

I have a 2d array thats fully working

its 8 by 8 but i'll use 2 by 2 to make the example easier

the co-ords are atm...

0,0  0,1  0,2
1,0  1,1  1,2
2,0  2,1  2,2

So want to know if anybody can help me with the login to calculate the diagonas?

i can see here that they are

[B]/ - forward slash direction[/B]
1,0  0,1
2,0  1,1  0,2
2,1  1,2

[B]\ - backward slach direction[/B]
1,0  2,1
0,0  1,1  2,2
0,1  1,2

I can half see a pattern in them but its doing my head in - i wanted a nice neat way to work this out.

scrupul0us

I see 3x3

what do u mean by diagonals

explain what your doing and what your trying to accomplish

You say direction... direction of what, movement, etc?

dougal85

yeh well 3x3 if you count the zero. i think like an array. lol

each of the values in my 2d array have a boolean value, so 1 or 0.

I need to be able to count how many in each diagonal path have a value of 1. and then throw an exception if there is more than 1 in any the diagonals

but in a 8x8 square.

so say the values were

0 0 0
0 0 0
0 0 0

i'd get a result of 0

0 0 0
0 1 0
0 0 0

result of 1, so its ok

0 0 0
0 1 0
0 0 1

diagonal from top left to bottom right gets 2, not ok

0 1 0
0 0 1
0 0 0

diagonal from middle top to liddle right gets 2, not ok

Weedpacket

dougal85 wrote:
yeh well 3x3 if you count the zero. i think like an array. lol

In programming, arrays usually do count the zero coordinate. It makes the maths simpler (if you wanna get technical, it's because it improves the mapping between ordinal and cardinal numbers).

The difference between the x and the y coordinate is the same for all positions on a forward diagonal (x-y=0 for the main diagonal, the adjacent diagonals have x-y=1 and x-y=-1, etc.)

On back diagonals, their sum is a constant.

You can turn all this around of course: starting with the constant and one coordinate, you can determine the corresponding coordinate of the element on the appropriate diagonal.

bpat1434

Hmm... so you're essentially creating an 8x8 matrix and itterating through the matrix axis and seeing there's more than one?

Just trying to clear the air some.....

dougal85

yes thats right bpat1434 althought in the 8x8 its actually more than 2, i just used 1 for my smaller example.

i managed to do the horizontal and vertical quite easily.

now i need to perform the same check for the diagonal axis.

bpat1434

Wouldn't it be possible to say that:

$i=0;
$array1[$i] != $array2[$i+1] != $array3[$i+2] != $array4[$i+3] . . .

and loop through that incrementing $i along the way?

Maybe that's too dumbed down....

Weedpacket

Isn't that what I covered?

dougal85

I'm sorry i'm finding this really hard to follow how i would use that, it may be down to the fact ive hardly slept for 3 days.

i think you gave me the answer weedpacket, but unfortunately my maths is oh so ever rusty.

i'll play around with it tonight - if you have any other tips that would be good 🙂