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DeleteRepetitions summary

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  • Subject: [mg23724] DeleteRepetitions summary
  • From: Preston Nichols <pnichols at>
  • Date: Mon, 5 Jun 2000 01:09:17 -0400 (EDT)
  • Sender: owner-wri-mathgroup at


Last week requested ideas for prgramming a function which extracts, in
order, the first instance of each distinct element of a list.

Many thanks to Allan Hayes and David Park, who sent me Carl Woll's method
(so many thanks to Carl, too) and to Bob Hanlon, who documented (again)
Mathematica's power and flexibility by proposing five additional versions
of the function.

Here again is Carl Woll's solution:

DeleteRepetitions[X_] :=
  Block[{t}, t[n_] := (t[n] = Sequence[]; n); t /@ X]

Allan calls this a "neat solution", and David calls it a "very ingenious
routine"; I certainly agree.

I was also very happy to see Bob's

DeleteRepetitions4[x_List] := x //. {a___, b_, c___, b_, d___} -> {a, b, c, d}

because the code is so transparent, once you understand the simplest things
about pattern matching.  That's a valuable feature in some contexts, even
though it is inefficient on long lists (as Bob pointed out).

In constrast, Carl's solution has a stunning "economy of action", but
understanding how it works requires thinking about such things as the
precedence of the operators := and ; (that's an operator?!), the internal
ordering of user-defined rules for functions, and the semi-magical
properties of Sequence[].

I intend to add both of these methods to my bag of tricks.  I sure learn a
lot from this group!

Preston Nichols
Mathematics and Computer Science
Wittenberg University

At 11:09 PM 05/28/2000 -0400, you wrote:
>Dear Mathematica Wizards:
>Below I give a function which removes duplicates from a list (as Union
>does), but without sorting the result (as Union also does).  More
>specifically, it extracts, in order, the first instance of each distinct
>element of the list.
>Is there any simpler way to do this?  It's a simple idea, but I seem to
>need seven different list-manipulation functions, including 3 uses of Map!
>DeleteRepetitions[X_] :=
>  Take[X, #] & /@
>      Sort[First /@
>          (Position[X, #] & /@
>              Union[X])] // Flatten
>For example,
>In[2] := DeleteRepetitions[{3,1,2,3,3,2,4,1}]
>Out[2] = {3,1,2,4}
>In[3] := DeleteRepetitions[{b,a,b,a,c,a}]
>Out[3] = {b,a,c}
>I don't need to use this function on lists longer that 20 or so elements,
>so speed is not a critical concern.
>Also, my version happens to work on expressions with heads other than List
>(because Take, Position, Union, and Flatten all do so), but I don't really
>need that feature.
>How would you implement this function?
>Preston Nichols
>Mathematics and Computer Science
>Wittenberg University

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