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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