[erlang-questions] Sunday puzzle - trying to improve my Erlang

[Hynek Vychodil]

On Tue, Jul 8, 2008 at 3:47 AM, Richard A. O'Keefe <ok@REDACTED>
wrote:

> An answer to the puzzle _could_ be something as simple as
>
>        io:format("VIER = 6241, NEUN = 9409\n")


> begin Qs = [integer_to_list(S) || S <- [X*X || X <- lists:seq(32,99)]], Ps
= [{E,{Vr,Nn}} || [N,E,_U,N]=Nn <- Qs, [_V,_I, E1, _R] = Vr <-Qs, E=:=E1,
length(ordsets:from_list(Nn++Vr)) =:= 6], D = lists:foldl(fun ({E,_}, D) ->
dict:update_counter(E,1,D) end, dict:new(), Ps), [{VIER, NEUN}] = [P ||
{E,1} <- dict:to_list(D), {E1,P} <- Ps, E=:=E1], io:format("Neun: ~s, Vier:
~s~n", [NEUN, VIER]) end.
Neun: 9409, Vier: 6241
ok


> *Some* amount of human judgement will be needed to convert
> the problem specification to executable code.  For example,
> one way to find candidates is to enumerate integers in a
> certain range, square them, and check whether the squares
> have a suitable digit pattern.  But what range of integers?
> Looking at it, _we_ see that the range need not be any more
> than 32..99, but given that, the rest is pretty much
> trivial.  (sqrt(VIER) = 79, sqrt(NEUN) = 97, which is quite
> pretty.)  You can get a short list for NEUN thus:
>
> neun_candidates() ->
>     [{N,E,U,NEUN} ||
>        X <- lists:seq(32, 99),
>        NEUN <- [X*X],
>        [N,E,U,N] <- [integer_to_list(NEUN)],
>        N /= E, N /= U, E /= U].
> which returns the list
> [{$1,$5,$2,1521}, {$1,$6,$8,1681}, {$4,$6,$2,4624},
>  {$5,$6,$2,5625}, {$9,$4,$0,9409}].
> The code for vier_candidates() is similar.
> Pasting them together is just
>
> vier_neun_candidates() ->
>    A = vier_candidates(),
>    B = neun_candidates(),
>    [{VIER,NEUN} ||
>        {V,I,E,R,VIER} <- A,
>        {N,E,U,  NUEN} <- B,
>        % some testing goes here
>        ].
>
> Then it's simply a matter of checking the last condition
>
> answer() ->
>     C <- vier_neun_candidates(),
>     [{VIER,NEUN} ||
>         {VIER,NEUN} <- C,
>         X <- [[OOPS || {VIER,OOPS} <- C, OOPS /= NEUN]],
>         X == [],
>         Y <- [[JUNK || {JUNK,NEUN} <- C, JUNK /= VIER]],
>        Y == []].
>
> Finishing the details left for anyone interested.
> One comment I _will_ make is that there is a rather pointless
> restriction in Erlang syntax: the generator of a list
> comprehension *may* include "X <- [expr]" but may *not*
> include "X = expr", which means exactly the same thing.
>
> neun_candidates() ->
>     [{N,E,U,NEUN} ||
>        X <- lists:seq(32, 99),
>        NEUN = X*X,
>        [N,E,U,N] = integer_to_list(NEUN),
>        N /= E, N /= U, E /= U].
>
> would have been much clearer.
>
> More precisely, Erlang *does* allow these expressions
> BUT WITH THE WRONG MEANING!  A qualifier that is
>        <pattern> = <expression>
> should SUCCEED or FAIL, and if it succeeds, the
> value it returns is quite irrelevant and should by NO
> means be restricted to 'true' or 'false'.
>
> Another way to hack around this is to rewrite
>        Pat = Expr
> as      (Pat = Expr, true)
> but that has the wrong semantics too, because when
> the value of Expr doesn't match Pat, we simply want
> that iteration of the list comprehension to fail,
> not to produce an exception in the whole thing.
>
> What could break if this part of Erlang syntax were fixed?
> Let us suppose that nobody writes list comprehensions
> containing
>        Nonvar = Expr
> because they could and should be rewritten to use == or
> =:=.  Would
>        _ = Expr
> make sense?  No, because it would be equivalent to
>        Expr.
> Would
>        X = Expr
> make sense?  No, because it would be equivalent to
>        Expr, X = true
> and what would be the point of that?
>
> It really is past time that something was done about this.
> If the current badly broken semantics cannot be changed,
> then at least a compile-time warning for any list
> comprehension containing Pat = Expr that it is almost
> certainly incorrect would be helpful.
>
>
>
>
>
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>



-- 
--Hynek (Pichi) Vychodil
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