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Talk:Random Latin squares: Difference between revisions
→Python Algorithm: Randomness
Line 19:
If you read the reference mentioned in the first sentence and think it is of use, then please add it to the task.
- --[[User:Paddy3118|Paddy3118]] ([[User talk:Paddy3118|talk]]) 11:44, 9 June 2019 (UTC)
==="Randomness"===
I don't actually use the algorithm in earnest, but several of the references mention the randomness of the generation.
I have no measure of the randomness, but thought that any number should be as likely to appear in any position in the square so I created a counter of how many times each symbol appeared in each cell of the square grid and present the counts for a million runs:
Additional Python:
<lang python>def distributions(n, count):
counters = [[defaultdict(int) for _ in range(n)] for __ in range(n)]
range_n = range(n)
for _ in range(count):
square = rls(n)
for r in range_n:
for c in range_n:
counters[r][c][ square[r][c] ] += 1
for symbol in range_n:
symcounts = [[counters[r][c][symbol] for c in range_n] for r in range_n]
mx = max(cnt for row in symcounts for cnt in row)
mn = min(cnt for row in symcounts for cnt in row)
print(f'\n{symbol} distribution: from {mn} to {mx}\n==')
print(_to_text(symcounts))
distributions(5, 1000_000)</lang>
{{out}}
<pre>0 distribution: from 199123 to 200657
==
199758 200268 199123 200194 200657
199878 200137 200165 199932 199888
200447 199564 200602 200024 199363
200094 200412 200266 199659 199569
199823 199619 199844 200191 200523
1 distribution: from 198960 to 200500
==
200057 200135 200085 199825 199898
200144 200249 199308 200118 200181
199297 200500 200268 200380 199555
200441 198960 200000 200317 200282
200061 200156 200339 199360 200084
2 distribution: from 198983 to 200849
==
200849 200156 200034 199978 198983
199747 199808 200144 200054 200247
199796 200405 199650 199895 200254
199820 199935 200178 199872 200195
199788 199696 199994 200201 200321
3 distribution: from 199433 to 200820
==
199816 199452 200527 200133 200072
200820 200003 199749 199598 199830
199769 199985 200143 199664 200439
199739 200558 199545 199932 200226
199856 200002 200036 200673 199433
4 distribution: from 199337 to 200691
==
199520 199989 200231 199870 200390
199411 199803 200634 200298 199854
200691 199546 199337 200037 200389
199906 200135 200011 200220 199728
200472 200527 199787 199575 199639</pre>
--[[User:Paddy3118|Paddy3118]] ([[User talk:Paddy3118|talk]]) 14:10, 9 June 2019 (UTC)
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