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Re: Flattening
*To*: mathgroup at yoda.physics.unc.edu
*Subject*: Re: Flattening
*From*: Cetin Cetinkaya <cetin%acm4 at yoda.physics.unc.edu>
*Date*: Fri, 3 Apr 1992 13:32:48 -0600
gaylord at ux1.cso.uiuc.edu writes:
>Subject: elegance vs. 'quick and dirty': a Mathematica expression beauty contest
>a recent discussion of Flattening dealt with going from
startlist = {{a,a,a},{a,a},{{b,b},{b,b,b}},{a,a,a,a},{{b,b},{b}}}
>to
finallist = {{a,a,a},{a,a},{b,b},{b,b,b},{a,a,a,a},{b,b},{b}}
>Three solutions have been proposed:
>#1
>finallist = FixedPoint[
Replace[#,{A___,List[X___List],B___} :> {A,X,B}]&,
startlist]
>Let $A be an unused or local symbol
>finallist = Flatten[List @@ (
startlist /. List[X___List] :> $A[X]
/. {List->$A,$A->List}
)
] /. $A->List
>#2
>f[x_List] :=
> Apply[Join,Map[(If[Head[First[#]] === List, #, {#}] &), x]]
#>3
>f[{x__}] := Sequence[x] /; Not[ And @@ AtomQ /@ {x} ]
>f[{x__}] := {x}
>f /@ startlist
>==========================
>#2 and #3 have been proposed by their authors as being 'quick and dirty'. I
>don't agree at all with the authors. I rank these expressions in terms of
>'elegance in the order
>#2, #3, #1
But I think the true winner is number 1 because it is the only one which works!
Let me explain what I mean:
In[14]:= f[x_List] :=
Apply[Join,Map[(If[Head[First[#]] === List, #, {#}] &), x]]
0. 1317.904 KByte
In[15]:= f[{{{{a,b},{c,d}}}}]
0. 1318.38 KByte
Out[15]= {{{a, b}, {c, d}}}
Thus, number 2 does not work for more general lists. Only "first order" lists
can be handled using it.
In[16]:= f[{x__}] := Sequence[x] /; Not[ And @@ AtomQ /@ {x} ]
0. 1319.276 KByte
In[17]:= f[{x__}] := {x}
0. 1319.988 KByte
In[18]:= f/@{{{{a,b},{c,d}}}}
0. 1320.492 KByte
Out[18]= {{{a, b}, {c, d}}}
And this shows that number 3 does not work,either. However,
In[20]:= FixedPoint[
Replace[#,{A___,List[X___List],B___} :> {A,X,B}]&,
{{{{{{a,b},{c,d}}}}}}]
0.0166667 Second 1322.456 KByte
Out[20]= {{a, b}, {c, d}}
Therefore, the only working one and the winner is number 1.
ccetinkaya
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