Dominoes: Difference between revisions
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===Extra credit task === |
===Extra credit task === |
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<lang julia>""" From https:// |
<lang julia>""" From https://www.math.cmu.edu/~bwsulliv/domino-tilings.pdf |
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The number of ways to cover an m X n rectangle with m * n / 2 dominoes, calculated |
The number of ways to cover an m X n rectangle with m * n / 2 dominoes, calculated |
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independently by Temperley & Fisher (1961) and Kasteleyn (1961), is given by |
independently by Temperley & Fisher (1961) and Kasteleyn (1961), is given by |
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""" |
""" |
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function dominotilingcount(m, n) |
function dominotilingcount(m, n) |
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return BigInt(floor(prod( |
return BigInt(floor(prod([prod( |
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[abs(big"2.0" * cospi(j / (m + 1)) + 2 * im * cospi(k / (n + 1))) for k in 1:n]) |
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[prod( |
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for j in 1:m] |
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) for j in 1:(m+1)÷2] |
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))) |
))) |
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end |
end |
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</lang>{{out}} |
</lang>{{out}} |
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<pre> |
<pre> |
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Arrangements ignoring values: |
Arrangements ignoring values: 1671065533809 |
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Permutations of 28 dominos: 304888344611713860501504000000 |
Permutations of 28 dominos: 304888344611713860501504000000 |
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Permuted arrangements ignoring flipping dominos: |
Permuted arrangements ignoring flipping dominos: 509488404340715971133309942207348736000000 |
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Possible flip configurations: 268435456 |
Possible flip configurations: 268435456 |
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Possible permuted arrangements with flips: |
Possible permuted arrangements with flips: 136764752145912471077652891125763304499183616000000 |
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</pre> |
</pre> |
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