74 lines
1.3 KiB
Prolog
74 lines
1.3 KiB
Prolog
% Three = [[0,14,10,35],[14,_,_,_],[15,_,_,_],[28,_,1,_]], puzzle_solution(Three)
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% Three = [[0, 14, 10, 35], [14, 7, 2, 1], [15, 3, 7, 5], [28, 4, 1, 7]].
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:- use_module(library(clpfd)).
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%% puzzle_solution(+Puzzle)
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%
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puzzle_solution(Puzzle) :-
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Puzzle = [_|Rows],
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unify_diagonal(Puzzle),
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maplist(valid_row, Rows),
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transpose(Puzzle, TransposedPuzzle),
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TransposedPuzzle = [_|Columns],
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maplist(valid_row, Columns).
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%% valid(+Row)
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%
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valid_row([Head|Row]) :-
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Row ins 1..9,
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all_distinct(Row),
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valid_head(Head, Row),
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label(Row).
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%% valid_head(+Head, +Tail)
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%
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valid_head(Head, List) :-
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sum(List, #=, Head)
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; product(List, Head).
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%% product(+List, -Product)
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%
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product(List, Product) :-
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foldl(times, List, 1, Product).
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%% times(?Int1, ?Int2, ?Int3)
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%
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% true if Int3 #= Int1 * Int2
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times(Int1, Int2, Int3) :-
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Int3 #= Int1 * Int2.
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%% unify_diagonal(+Puzzle)
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%
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unify_diagonal(Puzzle) :-
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main_diagonal(Puzzle, [_|Diag]),
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all_same(Diag).
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%% main_diagonal(+Matrix, -Diag)
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%
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main_diagonal(Matrix, Diag) :-
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main_diagonal(Matrix, 0, Diag).
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main_diagonal([], _, []).
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main_diagonal([M|Ms], I, [D|Ds]) :-
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nth0(I, M, D),
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I1 is I + 1,
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main_diagonal(Ms, I1, Ds).
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%% all_same(+List)
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%
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all_same([Head|Tail]) :-
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all_same(Head, Tail).
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all_same(X, [X]).
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all_same(Head, [X|Xs]) :-
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Head #= X,
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all_same(Head, Xs).
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