comment on

The solution for the 7x7 problem using my combination of constraints and backtracking (I prefer to see it as just a custom labeling algorithm). The only optimization used is forcing the last five rows to be in lexicographic order.

:- use_module(library(clpfd)).

different_lists([A|TA], [B|TB]) :-
        (   A #\= B
        ;   A #= B,
            different_lists(TA, TB) ).

all_different_lists([]).
all_different_lists([A|T]) :-
        all_different_lists(T, A),
        all_different_lists(T).

all_different_lists([], _).
all_different_lists([B|T], A) :-
        different_lists(A, B),
        all_different_lists(T, A).

list_sequence([]).
list_sequence([H|T]) :-
        list_sequence(T, H).

list_sequence([], _).
list_sequence([B|T], A) :-
        list_lt(A, B),
        list_sequence(T, B).
    
list_lt([A|TA], [B|TB]) :-
        (   A #< B
        ;   A #= B,
            list_lt(TA, TB) ).

solve([Row1, Row2, Row3, Row4, Row5, Row6, Row7]) :-
    
        Row1 = [A1, A2, A3, A4, A5, A6, A7],
        Row2 = [B1, B2, B3, B4, B5, B6, B7],
        Row3 = [C1, C2, C3, C4, C5, C6, C7],
        Row4 = [D1, D2, D3, D4, D5, D6, D7],
        Row5 = [E1, E2, E3, E4, E5, E6, E7],
        Row6 = [F1, F2, F3, F4, F5, F6, F7],
        Row7 = [G1, G2, G3, G4, G5, G6, G7],

        Col1 = [A1, B1, C1, D1, E1, F1, G1],
        Col2 = [A2, B2, C2, D2, E2, F2, G2],
        Col3 = [A3, B3, C3, D3, E3, F3, G3],
        Col4 = [A4, B4, C4, D4, E4, F4, G4],
        Col5 = [A5, B5, C5, D5, E5, F5, G5],
        Col6 = [A6, B6, C6, D6, E6, F6, G6],
        Col7 = [A7, B7, C7, D7, E7, F7, G7],

        global_cardinality(Row1, [0-2, 1-2, 2-3]),
        global_cardinality(Row2, [0-2, 1-2, 2-3]),
        global_cardinality(Row3, [0-2, 1-2, 2-3]),
        global_cardinality(Row4, [0-2, 1-2, 2-3]),
        global_cardinality(Row5, [0-2, 1-2, 2-3]),
        global_cardinality(Row6, [0-2, 1-2, 2-3]),
        global_cardinality(Row7, [0-2, 1-2, 2-3]),

        global_cardinality(Col1, [0-2, 1-2, 2-3]),
        global_cardinality(Col2, [0-2, 1-2, 2-3]),
        global_cardinality(Col3, [0-2, 1-2, 2-3]),
        global_cardinality(Col4, [0-2, 1-2, 2-3]),
        global_cardinality(Col5, [0-2, 1-2, 2-3]),
        global_cardinality(Col6, [0-2, 1-2, 2-3]),
        global_cardinality(Col7, [0-2, 1-2, 2-3]),

        all_different_lists([Row3, Row4, Row5, Row6, Row7], Row1),
        all_different_lists([Row3, Row4, Row5, Row6, Row7], Row2),

        list_sequence([Row3, Row4, Row5, Row6, Row7]),
        
        all_different_lists([Col1, Col2, Col3, Col4, Col5, Col6, Col7]
+),

        label([A1, A2, A3, A4, A5, A6, A7, B1, B2, B3, B4, B5, B6, B7,
               C1, C2, C3, C4, C5, C6, C7, D1, D2, D3, D4, D5, D6, D7,
               E1, E2, E3, E4, E5, E6, E7, F1, F2, F3, F4, F5, F6, F7,
               G1, G2, G3, G4, G5, G6, G7]).

solve(R1, R2, L) :-
        findall(-, solve([R1, R2 | _]), All),
        length(All, L).

tryme([]).
tryme([H|T]) :-
        H = [R1, R2],
        write('searching...'), nl,
        time(solve(R1, R2, L)),
        L120 is L * 120,
        write(solve(R1, R2, L, L120)), nl,
        tryme(T).

tryme :-
        tryme([[[2, 1, 0, 0, 2, 2, 1], [0, 2, 2, 1, 1, 0, 2]],
               [[2, 0, 0, 2, 2, 1, 1], [2, 0, 1, 2, 2, 1, 0]],
               [[2, 1, 0, 1, 2, 0, 2], [2, 2, 1, 1, 2, 0, 0]],
               [[2, 1, 0, 1, 2, 2, 0], [1, 2, 0, 2, 1, 2, 0]],
               [[0, 2, 0, 1, 2, 1, 2], [1, 2, 0, 2, 1, 0, 2]],
               [[2, 0, 0, 1, 2, 2, 1], [2, 1, 1, 0, 2, 2, 0]],
               [[1, 2, 2, 0, 0, 2, 1], [2, 0, 1, 0, 1, 2, 2]],
               [[2, 2, 1, 1, 0, 2, 0], [1, 0, 2, 1, 2, 0, 2]],
               [[2, 0, 1, 1, 2, 0, 2], [0, 1, 2, 2, 0, 1, 2]],
               [[0, 2, 2, 0, 1, 2, 1], [1, 0, 1, 2, 2, 2, 0]]]).
[download]

running it (on my several years old computer)...

% 813,486,620 inferences, 296.670 CPU in 298.033 seconds (100% CPU, 27
+42059 Lips)
solve([2, 1, 0, 0, 2, 2, 1], [0, 2, 2, 1, 1, 0, 2], 40916, 4909920)
searching...
% 76,087,028 inferences, 25.970 CPU in 26.092 seconds (100% CPU, 29298
+05 Lips)
solve([2, 0, 0, 2, 2, 1, 1], [2, 0, 1, 2, 2, 1, 0], 4230, 507600)
searching...
% 126,148,718 inferences, 43.040 CPU in 43.119 seconds (100% CPU, 2930
+965 Lips)
solve([2, 1, 0, 1, 2, 0, 2], [2, 2, 1, 1, 2, 0, 0], 6049, 725880)
searching...
% 177,009,601 inferences, 60.300 CPU in 60.680 seconds (99% CPU, 29354
+83 Lips)
solve([2, 1, 0, 1, 2, 2, 0], [1, 2, 0, 2, 1, 2, 0], 8372, 1004640)
searching...
% 392,855,329 inferences, 132.700 CPU in 133.397 seconds (99% CPU, 296
+0477 Lips)
solve([0, 2, 0, 1, 2, 1, 2], [1, 2, 0, 2, 1, 0, 2], 11227, 1347240)
...
[download]

So it is not too bad, specially considering that the program is almost a direct translation of the problem wording to prolog, fully declarative.

Also, SWI-Prolog is not exactly the fastest prolog available and its clpfd module is not exactly the fastest CLP(FD) library either... I would not be surprised if some other prolog could run the same program more than an order of magnitude faster!

BTW, it requires the git version of SWI-Prolog to run... there was a bug on the global_cardinality/2 constraint.

In reply to Re^4: Seven by seven farming puzzle by salva
in thread Seven by seven farming puzzle by ambrus

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