How to check if there are multiple 1s in any diagonal of matrix?

Question

So I have task where I have to check if there are multiple 1s on any diagonal of a 8x8 matrix.

For example if this is the matrix:

0 0 0 0 0 1 0 0
0 0 0 1 0 0 0 0
0 0 0 0 0 0 1 0
1 0 0 0 0 0 0 0
0 0 0 0 0 0 0 1
0 1 0 0 0 0 0 0
0 0 0 0 1 0 0 0
0 0 1 0 0 0 0 0 

Output should be "No", because there isn't a diagonal with multiple 1s.

But for this:

0 0 0 0 0 1 0 0
0 0 0 1 0 0 0 0
0 0 1 0 0 0 1 0
1 0 0 0 0 0 0 0
0 0 0 0 0 0 0 1
0 1 0 0 0 0 0 0
0 0 0 0 1 0 1 0
0 0 1 0 0 0 0 0 

output should be "Yes" since it has two number 1 in one diagonal. I can't quite figure out how to make it check diagonal.

Answer 1

For searching all the diagonals in a matrix you just need to check the difference of the indexes in a for loop for example.

Let's assume i is the index for each element in a row, and j the index for each column of the element

Consider now a matrix 4x4:

[0,0,0,1]
[0,0,1,0]
[0,1,0,0]
[1,0,0,0]

To access each diagonal of this matrix you need to check what is the value for i-j.

Let's build a matrix with the value of i - j for each element:

[ 0, 1, 2, 3]
[-1, 0, 1, 2]
[-2,-1, 0, 1]
[-3,-2,-1, 0]

Now is really easy to see that all we need to do to iterate the diagonals is check the i-j value -> if it's the same value, the element belongs to the same diagonal.

To check the other diagonals just compute i + j :

[ 0, 1, 2, 3]
[ 1, 2, 3, 4]
[ 2, 3, 4, 5]
[ 3, 4, 5, 6]