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Cryptogram Puzzle with Prolog CLPFD

I recently found a small game in the Google Play app store called Cryptogram . There are dozens of apps like this one. The idea is to match the number with the colors, so that all the equations sound believable.

I was able to quickly overcome problems 1-8 and problem 10, but problem 9 turned out to be more difficult for me.

Problem 9 Problem 9

, . Prolog/Datalog , Project Euler. 15 line Sudoku solver, Prolog Constraint Logic Programming over Finite Domains (clpfd), . SWI-Prolog.

:- use_module(library(clpfd)).
problem(Colors) :-
    Colors = [Pink, Cyan, Yellow, Green, Purple, Red, Brown, White, Lime],
    Colors ins 0..9,
    all_distinct(Colors),
    % The leading digit of a number can't be 0
    Pink #\= 0,
    Red #\= 0,
    White #\= 0,
    Green #\= 0,
    Lime #\= 0,
    Cyan #\= 0,
    % I originally tried to write a predicate generalizing numbers and a list of digits
    % but got in way over my head with CLPFD.
    Number1_1 #= (Pink * 1000) + (Cyan * 100) + (Pink * 10) + Yellow,
    Number1_2 #= (Green * 10) + Purple,
    Number1_3 #= (Cyan * 100) + (Red * 10) + Purple,
    Number2_1 #= (Red * 1000) + (Brown * 100) + (White * 10) + Red,
    Number2_2 #= (Lime * 10) + Yellow,
    Number2_3 #= (Red * 1000) + (Lime * 100) + (Purple * 10) + Pink,
    Number3_1 #= (White * 1000) + (Purple * 100) + (Cyan * 10) + White,
    Number3_2 #= (Green * 1000) + (Cyan * 100) + (Yellow * 10) + Purple,
    Number3_3 #= (Cyan * 1000) + (Red * 100) + (Yellow * 10) + Red,
    % I'm not 100% sure whether to use floored or truncated division here.
    % I thought the difference would be a float vs integer output,
    % but that doesn't make sense with finite domains.
    Number1_1 // Number1_2 #= Number1_3,
    Number1_1 rem Number1_2 #= 0,
    Number2_3 #= Number2_1 + Number2_2,
    Number3_3 #= Number3_1 - Number3_2,
    Number3_1 #= Number1_1 - Number2_1,
    Number3_2 #= Number1_2 * Number2_2,
    Number3_3 #= Number1_3 + Number2_3.

, SWI-Prolog, , CLPFD:

?- problem([Pink, Cyan, Yellow, Green, Purple, Red, Brown, White, Lime]).
Pink in 3..9,
_7756#=Pink+10*Purple+1000*Red+100*Lime,
_7810#=1010*Pink+100*Cyan+Yellow,
all_distinct([Pink, Cyan, Yellow, Green, Purple, Red, Brown, White|...]),
Cyan in 1..7,
_7946#=1000*Cyan+10*Yellow+101*Red,
_7994#=100*Cyan+10*Yellow+1000*Green+Purple,
_8048#=10*Cyan+100*Purple+1001*White,
_8096#=100*Cyan+Purple+10*Red,
Yellow in 0..9,
_8162#=Yellow+10*Lime,
Green in 1..7,
_8216#=10*Green+Purple,
Purple in 0..9,
Red in 1..7,
_8294#=1001*Red+100*Brown+10*White,
Brown in 0..9,
White in 2..8,
Lime in 1..9,
_7756 in 1103..7568,
_8096+_7756#=_7946,
_8294+_8162#=_7756,
_8096 in 110..779,
_7810//_8216#=_8096,
_7810 in 3334..9799,
_8048+_8294#=_7810,
_7810 rem _8216#=0,
_8048 in 2313..8778,
_7946+_7994#=_8048,
_7946 in 1213..7678,
_7994 in 1100..7565,
_8216*_8162#=_7994,
_8216 in 12..79,
_8162 in 14..99,
_8294 in 1021..7486.

, 0..9, , . ?

, , . Cyan, 1.

?- problem([Pink, 1, Yellow, Green, Purple, Red, Brown, White, Lime]).
false.

. "" "Cyan in 1..7", , , , . , Cyan:

?- problem([Pink, 2, Yellow, Green, Purple, Red, Brown, White, Lime]).
Pink = 7,
Yellow = 6,
Green = 3,
Purple = 4,
Red = 1,
Brown = 8,
White = 5,
Lime = 9.

, . , , Prolog CLPFD .

2

. , . .

:- use_module(library(clpfd)).

digit_number(0, [], 1).

digit_number(Number, [Digit|Tail], DigitPlace) :-
    digit_number(NextNumber, Tail, NextDigitPlace),
    DigitPlace #= NextDigitPlace * 10,
    PlaceNumber #= Digit * (NextDigitPlace),
    Number #= PlaceNumber + NextNumber.

digit_number(Number, ColorList) :-
    digit_number(Number, ColorList, _).

problem(Colors) :-
    Colors = [Pink, Cyan, Yellow, Green, Purple, Red, Brown, White, Lime],
    Colors ins 0..9,
    all_distinct(Colors),
    digit_number(Number1_1, [Pink, Cyan, Pink, Yellow]),
    digit_number(Number1_2, [Green, Purple]),
    digit_number(Number1_3, [Cyan, Red, Purple]),
    digit_number(Number2_1, [Red, Brown, White, Red]),
    digit_number(Number2_2, [Lime, Yellow]),
    digit_number(Number2_3, [Red, Lime, Purple, Pink]),
    digit_number(Number3_1, [White, Purple, Cyan, White]),
    digit_number(Number3_2, [Green, Cyan, Yellow, Purple]),
    digit_number(Number3_3, [Cyan, Red, Yellow, Red]),
    Number1_1 // Number1_2 #= Number1_3,
    Number1_1 rem Number1_2 #= 0,
    Number2_1 + Number2_2 #= Number2_3,
    Number3_1 - Number3_2 #= Number3_3,
    Number1_1 - Number2_1 #= Number3_1,
    Number1_2 * Number2_2 #= Number3_2,
    Number1_3 + Number2_3 #= Number3_3,
    label(Colors).
+4
2

, .

, Prolog CLPFD .

Prolog - , ( , ) , , , . , , . . :

?- between(1, 99999999, N), N > 99999998.
N = 99999999.  % correct but slooooow

?- N > 99999998, between(1, 99999999, N).
ERROR: >/2: Arguments are not sufficiently instantiated

CLP (FD) :

?- N in 1..99999999, N #> 99999998.
N = 99999999.  % correct and fast!

?- N #> 99999998, N in 1..99999999.
N = 99999999.  % also correct, also fast!

CLP (FD) , , , , .

, Prolog, CLP (FD) . CLP (FD) , , , Cyan in 1..7 , . .

: . , , , ! , .

, , , . SWI-Prolog indomain/1 label/1; labeling/2. , , .

"" "Cyan in 1..7", , , , .

: , Cyan, 1 7. , . :

?- X in 1..5, Y in 1..5, X #< Y.
X in 1..4,
X#=<Y+ -1,
Y in 2..5.

3 1..4, 3 2..5, X = 3 Y = 3. - . , , .

. : fooobar.com/questions/1207991/...

Edit:

% I'm not 100% sure whether to use floored or truncated division here.
% I thought the difference would be a float vs integer output,
% but that doesn't make sense with finite domains.
Number1_1 // Number1_2 #= Number1_3,

, , Prolog :

?- X in 1..5, Y in 1..5, Z #= X // Y.
X in 1..5,
X//Y#=Z,
Y in 1..5,
Z in 0..5.

?- X in 1..5, Y in 1..5, Z #= X / Y.
ERROR: Domain error: `clpfd_expression' expected, found `_G6388/_G6412'
+4

, (C):

?- problem(C), label(C).
C = [7, 2, 6, 3, 4, 1, 8, 5, 9] .
+4

Source: https://habr.com/ru/post/1696191/

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