zacjl

solutions to https://golf.cucats.org/contest/8/problems

cartography

rotate a matrix m clockwise n times.

f=lambda m,n:m*(n<1)or[*zip(*f(m,n-1)[::-1])]

zacjl

partition[n_,l_]:=partition[n,l]=FrobeniusSolve[ConstantArray[1,l],n];
coeff=Compile[{{r,_Real},{l,_Integer},{succ,_Integer},{g,_Integer}},(r^(succ-g)*(1-r)^(11-succ))/l^succ]

cycle[r_,a_:1][n_Integer,t_List]:=(*arguments
r_ rate (fixed)
a_ add (what are we counting by?) default 1=#steps. should be the same (cycle)
n_ number of r5s to reach
t_ current state
*)
Which[n<=0,0,(*reached goal*)

zacjl

partition[n_,l_]:=partition[n,l]=IntegerPartitions[n+l+1,{l+1}]-1
coeff=Compile[{{r,_Real},{l,_Integer},{v,_Integer},{g,_Integer}},(r/l)^(11-g-v)*(1-r)^v*(1/l)^g]

cycle[r_,a_:1][n_,t_]:=(*arguments
r_ rate (fixed)
a_ add (what are we counting by?) default 1=steps. should be the same (cycle)
n_ number of r5s to reach
t_ current state
*)
Which[n<=0,0,(*reached goal*)

zacjl

PartitionsOf[n_,l_]:=PartitionsOf[n,l]=Flatten[Permutations/@IntegerPartitions[n+l+1,{l+1}]-1,1]
PartitionsBy[n_,l_,f_]:=PartitionsBy[n,l,f]=Select[PartitionsOf[n,l],f@*Most]
CaseWeight[state_]:=CaseWeight[state]=Multinomial@@state(*cache multinomials*)

ExpectedCycle[n_,t_,r_,a_:1]:=(*
n_ number to reach
t_ current state
r_ rate (fixed)
a_ add (what are we counting?) default 1=steps *)
Module[{st=Sort@t,mt=Min@t,l=Length@t},

zacjl

FilterBy[m_]:=Cases[x_/;m[Total@Most@x]]

PartitionsOf[n_,l_]:=PartitionsOf[n,l]=Flatten[Permutations/@IntegerPartitions[n+l+1,{l+1}]-1,1]

CycleExpectedMulti[n_,t_,r_,a_:1]:=(*
n_ number to reach
t_ current state
r_ rate (fixed)
a_ add (what are we counting?) default 1=steps*)
Module[{st=Sort@t,mt=Min@t,l=Length@t},(*self explanatory*)