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Dimitri Lozeve 2020-07-21 17:33:54 +02:00
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posts/dyalog-apl-competition-2020.org
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@ -18,20 +18,26 @@ Write a function that, given a right argument ~Y~ which is a scalar or
a non-empty vector and a left argument ~X~ which is a single non-zero a non-empty vector and a left argument ~X~ which is a single non-zero
integer so that its absolute value is less or equal to ~≢Y~, splits integer so that its absolute value is less or equal to ~≢Y~, splits
~Y~ into a vector of two vectors according to ~X~, as follows: ~Y~ into a vector of two vectors according to ~X~, as follows:
- If ~X>0~, the first vector contains the first ~X~ elements of ~Y~
and the second vector contains the remaining elements. If ~X>0~, the first vector contains the first ~X~ elements of ~Y~ and
- If ~X<0~, the second vector contains the last ~|X~ elements of ~Y~ the second vector contains the remaining elements.
and the first vector contains the remaining elements.
If ~X<0~, the second vector contains the last ~|X~ elements of ~Y~ and
the first vector contains the remaining elements.
#+end_quote #+end_quote
*Solution:* ~(0>⊣)⌽((⊂↑),(⊂↓))~ *Solution:* ~(0>⊣)⌽((⊂↑),(⊂↓))~
There are three nested trains here. The first one, ~((⊂↑),(⊂↓))~, uses There are three nested trains here[fn:trains]. The first one,
the two functions [[https://help.dyalog.com/18.0/index.htm#Language/Primitive%20Functions/Take.htm][Take]] (~↑~) and [[https://help.dyalog.com/18.0/index.htm#Language/Primitive%20Functions/Drop.htm][Drop]] (~↓~) to build a nested array ~((⊂↑),(⊂↓))~, uses the two functions [[https://help.dyalog.com/18.0/index.htm#Language/Primitive%20Functions/Take.htm][Take]] (~↑~) and [[https://help.dyalog.com/18.0/index.htm#Language/Primitive%20Functions/Drop.htm][Drop]] (~↓~) to
consisting of the two outputs we need. (Take and Drop already have the build a nested array consisting of the two outputs we need. (Take and
behaviour needed regarding negative arguments.) However, if the left Drop already have the behaviour needed regarding negative arguments.)
argument is positive, the two arrays will not be in the correct However, if the left argument is positive, the two arrays will not be
order. So we need a way to reverse them if ~X<0~. in the correct order. So we need a way to reverse them if ~X<0~.
[fn:trains] Trains are nice to read (even if they are easy to abuse),
and generally make for shorter dfns, which is better for Phase I.
The second train ~(0>⊣)~ will return 1 if its left argument is The second train ~(0>⊣)~ will return 1 if its left argument is
positive. From this, we can use [[https://help.dyalog.com/18.0/index.htm#Language/Primitive%20Functions/Rotate.htm][Rotate]] (~⌽~) to correctly order the positive. From this, we can use [[https://help.dyalog.com/18.0/index.htm#Language/Primitive%20Functions/Rotate.htm][Rotate]] (~⌽~) to correctly order the
@ -136,7 +142,9 @@ the second, inclusively.
First, we have to compute the range of the output, which is the First, we have to compute the range of the output, which is the
absolute value of the difference between the two integers ~|-/⍵~. From absolute value of the difference between the two integers ~|-/⍵~. From
this, we compute the actual sequence, including zero: ~0,⍳|-/⍵~. this, we compute the actual sequence, including zero[fn::If we had
~⎕IO←0~, we could have written ~⍳|1+-/⍵~, but this is the same number
of characters.]: ~0,⍳|-/⍵~.
This sequence will always be nondecreasing, but we have to make it This sequence will always be nondecreasing, but we have to make it
decreasing if needed, so we multiply it by the opposite of the sign of decreasing if needed, so we multiply it by the opposite of the sign of
@ -261,11 +269,15 @@ right argument.
*Solution:* ~{↑⊃,/↓¨⍕¨⍵}~ *Solution:* ~{↑⊃,/↓¨⍕¨⍵}~
So this is a little bit by trial-and-error. The first step is to The first step is to [[https://help.dyalog.com/latest/#Language/Primitive%20Functions/Format%20Monadic.htm][Format]] (~⍕~) everything to get
[[https://help.dyalog.com/latest/#Language/Primitive%20Functions/Format%20Monadic.htm][Format]] (~⍕~) everything to get strings. The next step would be to strings.[fn:trial-error] The next step would be to "stack everything
"stack everything vertically", so we will need [[https://help.dyalog.com/latest/#Language/Primitive%20Functions/Mix.htm][Mix]] (~↑~) at some vertically", so we will need [[https://help.dyalog.com/latest/#Language/Primitive%20Functions/Mix.htm][Mix]] (~↑~) at some point. However, if we
point. However, if we do it immediately we don't get the correct do it immediately we don't get the correct result:
result:
[fn:trial-error] {-} A lot of trial-and-error is always necessary when
dealing with nested arrays, and this being about formatting
exacerbates the problem.
#+begin_src default #+begin_src default
{↑⍕¨⍵}(3 3⍴⍳9)(↑'Adam' 'Michael') {↑⍕¨⍵}(3 3⍴⍳9)(↑'Adam' 'Michael')
@ -280,7 +292,8 @@ Michael
Mix is padding with spaces both horizontally (necessary as we want the Mix is padding with spaces both horizontally (necessary as we want the
output to be a simple array of characters) and vertically (not what we output to be a simple array of characters) and vertically (not what we
want). We will have to decompose everything line by line, and then mix want). We will have to decompose everything line by line, and then mix
all the lines together. This is exactly what [[https://help.dyalog.com/latest/#Language/Primitive%20Functions/Split.htm][Split]] (~↓~) does: all the lines together. This is exactly what [[https://help.dyalog.com/latest/#Language/Primitive%20Functions/Split.htm][Split]][fn::Split is the
dual of Mix.] (~↓~) does:
#+begin_src default #+begin_src default
{↓¨⍕¨⍵}(3 3⍴⍳9)(↑'Adam' 'Michael')(⍳10) '*'(5 5⍴⍳25) {↓¨⍕¨⍵}(3 3⍴⍳9)(↑'Adam' 'Michael')(⍳10) '*'(5 5⍴⍳25)