Multifactorial: Difference between revisions
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{1,2,3,4,5,6,14,24,36,50}
</pre>
=={{header|Picat}}==
<lang Picat>import util.
go =>
foreach(D in 1..15)
println(D=[multifactorial(I,D) : I in 1..15])
end,
nl.
% using prod/1
multifactorial(N,Degree) = prod([ I : I in N..-Degree..1]).
% Some other variants
% reduce/2
multifactorial2(N,Degree) = reduce(*, [I : I in N..-Degree..1]).
% while loop
multifactorial3(N,Degree) = M =>
M = 1, I = N,
while(I > 0)
M := M*I,
I := I - Degree
end.
% some recursive variants
multifactorial4(N,_D) = 1, N <= 0 => true.
multifactorial4(N,D) = N*multifactorial4(N-D,D).
multifactorial5(N,D) = M =>
N <= 0 -> M = 1 ; M = N*multifactorial4(N-D,D).
multifactorial6(N,D) = cond(N <= 0, 1, N*multifactorial6(N-D,D)).</lang>
Output:
<pre>1 = [1,2,6,24,120,720,5040,40320,362880,3628800,39916800,479001600,6227020800,87178291200,1307674368000]
2 = [1,2,3,8,15,48,105,384,945,3840,10395,46080,135135,645120,2027025]
3 = [1,2,3,4,10,18,28,80,162,280,880,1944,3640,12320,29160]
4 = [1,2,3,4,5,12,21,32,45,120,231,384,585,1680,3465]
5 = [1,2,3,4,5,6,14,24,36,50,66,168,312,504,750]
6 = [1,2,3,4,5,6,7,16,27,40,55,72,91,224,405]
7 = [1,2,3,4,5,6,7,8,18,30,44,60,78,98,120]
8 = [1,2,3,4,5,6,7,8,9,20,33,48,65,84,105]
9 = [1,2,3,4,5,6,7,8,9,10,22,36,52,70,90]
10 = [1,2,3,4,5,6,7,8,9,10,11,24,39,56,75]
11 = [1,2,3,4,5,6,7,8,9,10,11,12,26,42,60]
12 = [1,2,3,4,5,6,7,8,9,10,11,12,13,28,45]
13 = [1,2,3,4,5,6,7,8,9,10,11,12,13,14,30]
14 = [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]
15 = [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]</pre>
Using constraint modelling for a reversible variant (i.e. all parameters can be inputs or outputs); here shown by identifying all the valid N and the degree given the multifactorial (M).
<lang Picat>import cp.
%
% Reversible: find Degree and N given M
%
go2 =>
Ms = [4,20,105], % The multifactorials to identify
foreach(M in Ms)
println(m=M),
Degree :: 1..10, % limit of the degree
N :: 1..100, % limit of N
All = findall([N,Degree,M], (multifactorial_reversible(N,Degree,M),
solve([M,N,Degree]))),
foreach([NN,DD,MM] in All.sort)
printf("n=%d degree=%d m=%d\n",NN,DD,MM)
end,
nl
end,
nl.
% reversible variant (using CP)
multifactorial_reversible(N,_D,M) :-
N #<= 0, M #= 1.
multifactorial_reversible(N,D,M) :-
D #> 0,
N #> 0,
ND #= N-D,
multifactorial_reversible(ND,D,M1),
M #= N*M1.</lang>
Output:
<pre>Reversible: find Degree and N given M:
m = 4
n=4 degree=3 m=4
n=4 degree=4 m=4
n=4 degree=5 m=4
n=4 degree=6 m=4
n=4 degree=7 m=4
n=4 degree=8 m=4
n=4 degree=9 m=4
n=4 degree=10 m=4
m = 20
n=10 degree=8 m=20
m = 105
n=7 degree=2 m=105
n=15 degree=8 m=105</pre>
=={{header|PicoLisp}}==
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