87 lines
2.9 KiB
Prolog
87 lines
2.9 KiB
Prolog
% :- table step_at/2.
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% :- table node_at/3.
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:- table reachable_endnode/2.
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:- op(700, xfx, l).
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:- op(700, xfx, r).
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From l To :- From to To-_.
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From r To :- From to _-To.
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answer(Answer) :-
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starts(Starts),
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routes(Starts, [Route1 | RestOfRoutes]),
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foldl(unify2, RestOfRoutes, Route1, _-(_-Answer-_)).
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% unify2 combines 2 routes into one with its own stride-offsets-dests
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unify2(Route1, Route2, NewRoute) :-
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once(findnsols(2, S, converge(Route1, Route2, S), SolutionPair)),
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SolutionPair = [NewA-LenA-NewZ, _-LenB-_],
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NewStride is LenB - LenA,
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NewRoute = NewA-(NewStride-LenA-[0-NewZ]).
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% Len = Stride1*X1 + Offset1 + Dest1 = Stride2*X2 + Offset2 + Dest2
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% For performance, Route1's Stride should =< Route2's Stride
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converge(Route1, Route2, NewA-Len-NewZ) :-
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writef('Combining %t - %t\n', [Route1, Route2]),
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Route1 = A1-(Stride1-Offset1-Dests1),
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Route2 = A2-(Stride2-Offset2-Dests2),
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natnum(X2),
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pick([Dests1, Dests2], [Dest1-Z1, Dest2-Z2]),
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0 is (Stride2*X2 + Offset2 + Dest2 - Offset1 - Dest1) mod Stride1,
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Len is Stride2*X2 + Offset2 + Dest2,
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atom_concat(A1, A2, NewA), atom_concat(Z1, Z2, NewZ).
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routes(Starts, Routes) :-
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maplist([S, S-Route]>>(route(S, Route)), Starts, Routes).
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% route builds a route (Stride-Offset-Internals) for a particular starting node.
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route(Start, Stride-FirstN-[0-FirstDest | Dests]) :-
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direction_len(DirLen),
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once(reachable_endnode(Start, FirstN-FirstDest)),
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findall(ShiftedN-Dest,
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( reachable_endnode(Start, N-Dest),
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ShiftedN is N - FirstN,
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ShiftedN =\= 0,
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(0 is ShiftedN mod DirLen -> !; true)),
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TmpDests),
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last(TmpDests, Stride-LastDest),
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append(Dests, [Stride-LastDest], TmpDests).
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% Dest is reachable from Start after N steps
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reachable_endnode(Start, N-Dest) :-
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natnum(N),
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node_at(N, Start, Dest),
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is_end(Dest).
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starts(Starts) :- findall(X, X to _, Nodes), include(is_start, Nodes, Starts).
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is_start(Node) :- atom_chars(Node, [_, _, a]).
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is_end(Node) :- atom_chars(Node, [_, _, z]).
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% node_at(N, Dir, From, Dest) :- Dest is reached after moving N step from From.
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node_at(0, Start, Start).
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node_at(N, From, Dest) :-
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N > 0,
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PrevN is N - 1,
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step_at(PrevN, PrevStep),
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G =.. [PrevStep, PrevNode, Dest], G,
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node_at(PrevN, From, PrevNode).
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% Step is the N-th step (counting starts from 0).
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step_at(N, Step) :-
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direction_list(Dir),
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length(Dir, DirLen),
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divmod(N, DirLen, _, Remainder),
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nth0(Remainder, Dir, Step).
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direction_list(Dir) :- direction(Str), atom_chars(Str, Dir).
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direction_len(Len) :- direction_list(D), length(D, Len).
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% pick one item from each sublist of ListOfLists & put them into Items in order.
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% [[1,2,3], [4], [5,6]] -> [1,4,5]; [1,4,6]; [2,4,5]; [2,4,6]; [3,4,5]; [3,4,6].
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pick(ListOfLists, Items) :-
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maplist([SubList, X]>>(member(X, SubList)), ListOfLists, Items).
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natnum(0).
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natnum(N) :- natnum(N0), N is N0 + 1.
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