More fun with APL

Note: see the rest of the series so far.

 

I stumbled across this post the other day and problem 2 seems like something I can easily do in APL since it essentially requires you to interleave two arrays.

The problem is:

Write a function that combines two lists by alternatingly taking elements. For example: given the two lists [a, b, c] and [1, 2, 3], the function should return [a, 1, b, 2, c, 3].

Here’s the solution I have come up with:

p2

since it uses both \omega (right argument) and \alpha (left argument) so it’s a dyadic function, let’s test it out:

'a' \ 'b' \ 'c' \ p2 \ 1 \ 2 \ 3

=> a 1 b 2 c 3

Here’s how it works:

  • concatenate the two arguments together, with the left argument first (\alpha, \omega)
  • reshape \rho the concatenated vector into 2 rows, so that you have effectively placed \alpha and \omega into a matrix, i.e.

a \ b \ c\\*    1 \ 2 \ 3

  • transpose that matrix

a \ 1\\*    b \ 2\\*    c \ 3

  • reshape \rho the transposed matrix into a vector, and that’s it!

 

7 Comments

  1. Aaron Hsu   •  

    Assuming that you have only vectors, my solution to this would be `,?,??`.

  2. Andy Shiers   •  

    Strictly speaking your result is a one row matrix rather than a vector. If it’s truly a vector that you want, then your code can be simplified by using ravel rather than reshape (and some of the parentheses can be removed too):

    s1?{,?(2,??)??,?}

    These days I prefer to use the monadic function Tally (?) rather than monadic ?: Tally returns the length of the leading axis, which in the case of a vector is its length. Tally has the benefit of always returning a scalar.

    s2?{,?(2,??)??,?}

    A more traditional solution would be to use Catenate (,) with fractional axis:

    s3?{,?,[?io+.5]?}

    although unless you use the slightly awkward ?io+.5 the expression is ?IO dependent.

    Recent versions of Dyalog include Table (?) which has been in Sharp APL and J for many years. Using Table allows the following solution:

    s4?{,?,??}

    The last expression is the fastest, but as to which is “best” .. well that is in the eye of the beholder !

  3. Yan Cui   •  

    that’s amazing ;-)

  4. Yan Cui   •  

    Thanks for these, that’s one of the things I like above APL – there’s always so many different ways to approach a given problem!

  5. Yan Cui   •  

    Thanks Fiona :-)

  6. Nechemyeh Ben Tzien Brudzewsky   •  

    Now that we have function trains, I like:
    s5?,,[1.5]

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