Sunday puzzle - trying to improve my Erlang
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Sunday puzzle - trying to improve my Erlang
by Toby Thain-2
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Hi list,
I stumbled on this simple 'puzzle'[0] posted some years ago on comp.lang.tcl (originally to an Icon mailing list). After solving it in Icon[1] and SQL[2] I decided to see what an Erlang solution would look like. I'm posting here firstly because other people's solutions would be interesting, and also I'd like to see how my own solution[3] could be improved. Any takers over the weekend? :-) --Toby [0] http://groups.google.com/group/comp.lang.tcl/msg/8846d9f7491ba0ba [1] http://telegraphics.com.au/svn/puzzles/trunk/vier-neun/vn.icn [2] http://telegraphics.com.au/svn/puzzles/trunk/vier-neun/Makefile [3] http://telegraphics.com.au/svn/puzzles/trunk/vier-neun/erlang/ _______________________________________________ erlang-questions mailing list erlang-questions@... http://www.erlang.org/mailman/listinfo/erlang-questions |
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Re: Sunday puzzle - trying to improve my Erlang
by Richard Carlsson-2
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Toby Thain wrote:
> Hi list, > > I stumbled on this simple 'puzzle'[0] posted some years ago on > comp.lang.tcl (originally to an Icon mailing list). > > After solving it in Icon[1] and SQL[2] I decided to see what an > Erlang solution would look like. I'm posting here firstly because > other people's solutions would be interesting, and also I'd like to > see how my own solution[3] could be improved. > > Any takers over the weekend? :-) > > --Toby > > [0] http://groups.google.com/group/comp.lang.tcl/msg/8846d9f7491ba0ba > [1] http://telegraphics.com.au/svn/puzzles/trunk/vier-neun/vn.icn > [2] http://telegraphics.com.au/svn/puzzles/trunk/vier-neun/Makefile > [3] http://telegraphics.com.au/svn/puzzles/trunk/vier-neun/erlang/ stages of list processing (mapreduce etc.), instead of inserting and looking up in dictionaries. I tag each generated pair with the E element, just to make the list easier to work with later. /Richard %% File: solve.erl %% @author Richard Carlsson -module(solve). -export([it/0]). %% Problem: VIER and NEUN are 4-digit squares; determine distinct V, I, %% E, R, N, and U, such that there is a unique solution (VIER,NEUN) for %% some particular E. it() -> 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), [P || {E,1} <- dict:to_list(D), {E1,P} <- Ps, E=:=E1]. _______________________________________________ erlang-questions mailing list erlang-questions@... http://www.erlang.org/mailman/listinfo/erlang-questions |
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Re: Sunday puzzle - trying to improve my Erlang
by Toby Thain-2
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On 6-Jul-08, at 9:17 AM, Richard Carlsson wrote: > Toby Thain wrote: >> Hi list, >> I stumbled on this simple 'puzzle'[0] ... >> [0] http://groups.google.com/group/comp.lang.tcl/msg/8846d9f7491ba0ba ... > %% File: solve.erl > %% @author Richard Carlsson Wonderful, that's just the kind of brain-melting variation I was after. Those who can't get enough of this puzzle, there's another thread about it: http://groups.google.ca/group/comp.lang.apl/browse_thread/thread/ 8a1abe807d1eda3c/ _______________________________________________ erlang-questions mailing list erlang-questions@... http://www.erlang.org/mailman/listinfo/erlang-questions |
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Re: Sunday puzzle - trying to improve my Erlang
by Edwin Fine
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Richard,
Lovely solution! It's stuff like this that helps newcomers to Erlang like myself to learn how to write better Erlang. I'm curious, though; what is the reason for writing Qs = [integer_to_list(S) || S <- [X*X || X <- lists:seq(32,99)]] instead of Qs = [integer_to_list(X*X) || X <- lists:seq(32,99)] ? 2008/7/6 Richard Carlsson <richardc@...>:
-- The great enemy of the truth is very often not the lie -- deliberate, contrived and dishonest, but the myth, persistent, persuasive, and unrealistic. Belief in myths allows the comfort of opinion without the discomfort of thought. John F. Kennedy 35th president of US 1961-1963 (1917 - 1963) _______________________________________________ erlang-questions mailing list erlang-questions@... http://www.erlang.org/mailman/listinfo/erlang-questions |
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Re: Sunday puzzle - trying to improve my Erlang
by Richard Carlsson-2
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Edwin Fine wrote:
> Richard, > > Lovely solution! It's stuff like this that helps newcomers to Erlang > like myself to learn how to write better Erlang. > > I'm curious, though; what is the reason for writing > > Qs = [integer_to_list(S) || S <- [X*X || X <- lists:seq(32,99)]] > > instead of > > Qs = [integer_to_list(X*X) || X <- lists:seq(32,99)] Oh, right... Sorry. It's just a remnant of a refactoring. I started out working on lists on the form [S div 1000, ..., S rem 10], but realized that I could just use the lists of character codes instead. But I didn't tidy up after changing to integer_to_list(S). Improved version attached. /Richard %% File: solve.erl %% @author Richard Carlsson -module(solve). -export([it/0]). %% Problem: VIER and NEUN are 4-digit squares; determine distinct V, I, %% E, R, N, and U, such that (given the choice of E) there exists a %% unique solution (VIER,NEUN). it() -> Qs = [integer_to_list(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), [P || {E,1} <- dict:to_list(D), {E1,P} <- Ps, E=:=E1]. _______________________________________________ erlang-questions mailing list erlang-questions@... http://www.erlang.org/mailman/listinfo/erlang-questions |
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Re: Sunday puzzle - trying to improve my Erlang
by Matthias Lang
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On Saturday, July 05, Toby Thain wrote:
> I stumbled on this simple 'puzzle'[0] posted some years ago on > comp.lang.tcl (originally to an Icon mailing list). After reading the description four times, I still wasn't completely sure what 'uniquely determines' means, but ploughed ahead, assuming it'd become obvious when I saw the solutions, which it did. I wrote the solution below before looking at the other solutions, but was coward enough to peek at Richard's much shorter one before posting. The obvious advantage of my solution is that I understand it ;-) Matt -------------------- -module(sq). -export([go/0]). go() -> All = all_answers(), Unique_viers = [ Vier || {Vier, _} <- All, length([X || {X, _} <- All, X == Vier]) == 1], Unique_neuns = [ Neun || {_, Neun} <- All, length([X || {_, X} <- All, X == Neun]) == 1], [ {Vier, Neun} || {Vier, Neun} <- All, lists:member(Vier, Unique_viers), lists:member(Neun, Unique_neuns)]. all_answers() -> [ {{V,I,E1,R}, {N,E2,U,N}} || {V,I,E1,R} <- possible_viers(), {N,E2,U,N} <- possible_neuns(), E1 == E2, all_unique([V,I,R,N,U])]. square_digits() -> Squares = [ X * X || X <- lists:seq(30, 100)], [ {X div 1000, (X div 100) rem 10, (X div 10) rem 10, X rem 10} || X <- Squares]. possible_neuns() -> [ X || X = {N,E,U,N} <- square_digits(), all_unique([N,E,U])]. possible_viers() -> [ X || X = {V,I,E,R} <- square_digits(), all_unique([V,I,E,R])]. all_unique([]) -> true; all_unique([H|T]) -> not lists:member(H, T) andalso all_unique(T). _______________________________________________ erlang-questions mailing list erlang-questions@... http://www.erlang.org/mailman/listinfo/erlang-questions |
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Re: Sunday puzzle - trying to improve my Erlang
by Toby Thain-2
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On 6-Jul-08, at 7:25 PM, Matthias Lang wrote: > On Saturday, July 05, Toby Thain wrote: > >> I stumbled on this simple 'puzzle'[0] posted some years ago on >> comp.lang.tcl (originally to an Icon mailing list). > > After reading the description four times, I still wasn't completely > sure what 'uniquely determines' means, but ploughed ahead, assuming > it'd become obvious when I saw the solutions, which it did. I didn't find the wording very clear either :) Tried to reword it but abandoned the effort. I notice Richard restated it in comments. --Toby _______________________________________________ erlang-questions mailing list erlang-questions@... http://www.erlang.org/mailman/listinfo/erlang-questions |
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Re: Sunday puzzle - trying to improve my Erlang
by Edwin Fine
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On Sun, Jul 6, 2008 at 5:39 PM, Richard Carlsson <richardc@...> wrote:
Oh, thank goodness!! I thought it was some expert optimization or technique that I just couldn't understand :)
-- The great enemy of the truth is very often not the lie -- deliberate, contrived and dishonest, but the myth, persistent, persuasive, and unrealistic. Belief in myths allows the comfort of opinion without the discomfort of thought. John F. Kennedy 35th president of US 1961-1963 (1917 - 1963) _______________________________________________ erlang-questions mailing list erlang-questions@... http://www.erlang.org/mailman/listinfo/erlang-questions |
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Re: Sunday puzzle - trying to improve my Erlang
by Richard Carlsson-2
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Toby Thain wrote:
> On 6-Jul-08, at 7:25 PM, Matthias Lang wrote: >> After reading the description four times, I still wasn't completely >> sure what 'uniquely determines' means, but ploughed ahead, assuming >> it'd become obvious when I saw the solutions, which it did. > > I didn't find the wording very clear either :) Tried to reword it but > abandoned the effort. I notice Richard restated it in comments. I also found that the greatest snag was understanding the exact specification of the problem. I eventually had to peek at the Icon solution to see what it was generating. /Richard _______________________________________________ erlang-questions mailing list erlang-questions@... http://www.erlang.org/mailman/listinfo/erlang-questions |
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Re: Sunday puzzle - trying to improve my Erlang
by Richard O'Keefe
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An answer to the puzzle _could_ be something as simple as
io:format("VIER = 6241, NEUN = 9409\n") *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. _______________________________________________ erlang-questions mailing list erlang-questions@... http://www.erlang.org/mailman/listinfo/erlang-questions |
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Re: Sunday puzzle - trying to improve my Erlang
by Hynek Vychodil
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On Tue, Jul 8, 2008 at 3:47 AM, Richard A. O'Keefe <ok@...> wrote: An answer to the puzzle _could_ be something as simple as neun_candidates() -> [{N,E,U,NEUN} || X <- lists:seq(32, 99), begin NEUN = X*X, [N,E,U,N1] = integer_to_list(NEUN), N =:= N1 andalso N /= E andalso N /= U andalso E /= U end].
-- --Hynek (Pichi) Vychodil _______________________________________________ erlang-questions mailing list erlang-questions@... http://www.erlang.org/mailman/listinfo/erlang-questions |
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Re: Sunday puzzle - trying to improve my Erlang
by Hynek Vychodil
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On Tue, Jul 8, 2008 at 3:47 AM, Richard A. O'Keefe <ok@...> wrote: An answer to the puzzle _could_ be something as simple as > 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
-- --Hynek (Pichi) Vychodil _______________________________________________ erlang-questions mailing list erlang-questions@... http://www.erlang.org/mailman/listinfo/erlang-questions |
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