Here is a quick reference as to why it is not possible to efficiently
generate all possible latin squares for one given size, let alone all of
them from 1 to 50: https://en.wikipedia.org/wiki/Latin_square.
See specifically the Number section. There are 1.5*10^86 possible Latin
squares of size 15; That's not counting the squares of size 16-50.
On Tuesday, April 7, 2020 at 12:55:57 PM UTC-4, Shivanjan Chakravorty wrote:
>
> I had a different approach to solving this problem. I generated all the
> possible orthogonal latin squares of all possible sizes and for every size
> cached the mattrices based on their trace. So that way it was like. Now for
> 1 to 50 this thing is done in less than 3 seconds and now all you have to
> do is read the input, check if the keys pair exists and print the answer. I
> do not have any idea why it wasn't accepted. Can anyone tell where was I
> missing the corner case?
>
> {
> "1": {},
> "2": {
> "2": [[ 1, 2],
> [ 2, 1]]
> },
> "3": {
> "3": [[ 1, 2, 3],
> [ 3, 1, 2],
> [ 2, 3, 1]],
>
> "6": [[ 1, 2, 3],
> [ 2, 3, 1],
> [ 3, 1, 2]]
> },
> "4": {
> "4": [[ 1, 2, 3, 4],
> [ 4, 1, 2, 3],
> [ 3, 4, 1, 2],
> [ 2, 3, 4, 1]],
>
> "8": [[ 1, 2, 3, 4],
> [ 2, 3, 4, 1],
> [ 3, 4, 1, 2],
> [ 4, 1, 2, 3]],
>
> "10": [[ 1, 2, 3, 4],
> [ 3, 4, 1, 2],
> [ 1, 2, 3, 4],
> [ 3, 4, 1, 2]]
> }
> }
>
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