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MathGroup Archive 1995

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Re: Programming: List Structure Manipulation

  • To: mathgroup at christensen.cybernetics.net
  • Subject: [mg930] Re: Programming: List Structure Manipulation
  • From: Count Dracula <lk3a at kelvin.seas.virginia.edu>
  • Date: Wed, 3 May 1995 00:09:15 -0400
  • Organization: University of Virginia

In article 250 of comp.soft-sys.math.mathematica 
rubin at msu.edu (Paul A. Rubin) writes:

> In article <3nck7m$a07 at news0.cybernetics.net>,
>    Xah Y Lee  <xyl10060 at fhda.edu> wrote:
> ->Can anyone show me better ways to write the following function?
> ->
> ->fun[listA_, styleList_]:=
> ->   Table[
> ->      Append[
> ->          Flatten@{ First@RotateLeft[styleList,t-1] },  listA[[t]]
> ->      ],
> ->      {t, Length@listA}
> ->  ]
> ->
> [snip]
> The following, somewhat cumbersome, definitions produce a function "fun" 
> (defined, for convenience, in terms of another function "fun1") which 
> matches all your examples and seems tolerably quick.  There is probably a 
> more efficient way of coding it, but at the moment this is the best that 
> comes to mind.
> 
> Clear[ fun, fun1 ];
> fun1[ x_List, y_List ] := MapThread[ fun1, {x, y} ] /; 
>   Length[ x ] == Length[ y ]
> fun1[ x_List, y_List ] := 
>   Module[
>     {z = Partition[ x, Length[ y ] ], w},
>     w = Drop[ x, Length[ Flatten[ z, 1 ] ] ];
>     If[ w != {}, z = Append[ z, w ] ];
>     fun1[ #, y ]& /@ z
>   ]/; Length[ x ] > Length[ y ]
> fun1[ x_List, y_List ] := 
>   fun1[ x, Take[ y, Length[ x ] ] ] /; Length[ x ] < Length[ y ]
> fun1[ x_, y_ ] := Flatten[ {y, x} ] /; Head[ x ] =!= List
> fun[ x_, y_ ] := Flatten[ fun1[ x, y ], 1 ]
> 

An alternative definition is:

func[index_, letters_] :=
    Flatten /@ Inner[List, Take[Join @@ Array[letters &, 
          Ceiling[Length[index]/Length[letters]]],  Length[index]], index, List]

The following are the test cases offered by  Xah Y Lee:

test1 := func[Range[0,5],  {a}] == {{a, 0}, {a, 1}, {a, 2}, {a, 3}, {a, 4}, {a, 5}}

test2 := func[Range[0,5],  {a,b,c}] == {{a, 0}, {b, 1}, {c, 2}, {a, 3}, {b, 4}, {c, 5}}

test3 := func[Range[0,10],  {{a1, a2}, b}] == 
{{a1, a2, 0}, {b, 1}, {a1, a2, 2}, {b, 3}, {a1, a2, 4}, {b, 5}, {a1, a2, 
6}, {b, 7}, {a1, a2, 8}, {b, 9}, {a1, a2, 10}}



test4 := func[Range[0,10],  {{a1, a2}, {{b}}, {c1,c2} }]  == 
{{a1, a2, 0}, {b, 1}, {c1, c2, 2}, {a1, a2, 3}, {b, 4}, {c1, c2, 5}, 
   {a1, a2, 6}, {b, 7}, {c1, c2, 8}, {a1, a2, 9}, {b, 10}}


The function works as needed (at least for these tests):

In[3]:= {test1, test2, test3, test4}

Out[3]= {True, True, True, True}
-- 
 ___________________________________________________________________________________
 Levent Kitis           lk3a at cars.mech.virginia.edu    lk3a at kelvin.seas.virginia.edu
 University of Virginia  Department of Mechanical, Aerospace and Nuclear Engineering  
 ___________________________________________________________________________________


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