Talk:Random Latin squares: Difference between revisions
"restarting row" method
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===Non python algorithm===
Apart from selecting from almost none of the possible latin squares the 'python algorithm' has second disadvantage. Considering the above latin square if I move the rightmost column to in front of the leftmost, or the bottom row to above the top I produce the same result. That is there are varying number of ways of producing each of the small number of latin squares that this algorithm can produce. An alternative is to just permute the meaning of 0..4. This would produce a smaller subset of all possible latin squares, but almost none is almost none either way, and they would be uniform. This task was promoted from draft very quickly, I think it needs to go back to draft until this issue is resolved--[[User:Nigel Galloway|Nigel Galloway]] ([[User talk:Nigel Galloway|talk]]) 09:30, 12 June 2019 (UTC)
=="restarting row" method==
To quote the factor solution:<br>
"... generate a random permutation, one row at a time. If a row conflicts with any of the rows above it, generate a new random permutation for that row. The upside is that this is easy to understand and generates uniformly-random Latin squares..."<br>
Does it generate uniformly-random Latin squares? To expose this fallacy let me consider I randomly select 0123 for my first row. Let me first select 1230 with some probability 1/n as my second row. The are now 2 ways to complete this square 2301 as the third row and 3012 as the fourth or 2301 as the fourth row and 3012 as the third. So each of these squares is generated with probability 1/2n, Now again with probability 1/n I select 1032 as my second row. There are now 4 ways to complete this square: 2301 as the third row and
3210 as the fourth; or 3210 as the third row and 2301 as the fourth; or 2310 as the third row and 3201 as the fourth; or 3201 as the third row and 2310 as the fourth. So each of these squares is produced with probability 1/4n.--[[User:Nigel Galloway|Nigel Galloway]] ([[User talk:Nigel Galloway|talk]]) 19:53, 13 July 2019 (UTC)
==Python Algorithm==
I got the mention of Latin squares from a stack-overflow question and a [https://www.academia.edu/29890346/Comparison_of_Seven_Techniques_for_Generating_Random_Latin_Squares link] to some solution methods that I did not read (and so did not add to the task as a reference).
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