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Ingy döt Net 2023-07-01 11:58:00 -04:00
parent 72d218235f
commit f23f22d71c
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Task/Permutations-Derangements/GAP/permutations-derangements.gap Normal file
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# All of this is built-in
Derangements([1 .. 4]);
# [ [ 2, 1, 4, 3 ], [ 2, 3, 4, 1 ], [ 2, 4, 1, 3 ], [ 3, 1, 4, 2 ], [ 3, 4, 1, 2 ], [ 3, 4, 2, 1 ],
# [ 4, 1, 2, 3 ], [ 4, 3, 1, 2 ], [ 4, 3, 2, 1 ] ]
Size(last);
# 9
NrDerangements([1 .. 4]);
# 9
# An implementation using formula D(n + 1) = n*(D(n) + D(n - 1))
NrDerangementsAlt_memo := [1, 0];
NrDerangementsAlt := function(n)
if not IsBound(NrDerangementsAlt_memo[n + 1]) then
NrDerangementsAlt_memo[n + 1] := (n - 1)*(NrDerangementsAlt(n - 1) + NrDerangementsAlt(n - 2));
fi;
return NrDerangementsAlt_memo[n + 1];
end;
L := List([0 .. 9]);
PrintArray(TransposedMat([L,
List(L, n -> Size(Derangements([1 .. n]))),
List(L, n -> NrDerangements([1 .. n])),
List(L, NrDerangementsAlt)]));
# [ [ 0, 1, 1, 1 ],
# [ 1, 0, 0, 0 ],
# [ 2, 1, 1, 1 ],
# [ 3, 2, 2, 2 ],
# [ 4, 9, 9, 9 ],
# [ 5, 44, 44, 44 ],
# [ 6, 265, 265, 265 ],
# [ 7, 1854, 1854, 1854 ],
# [ 8, 14833, 14833, 14833 ],
# [ 9, 133496, 133496, 133496 ] ]