Search Paths on a Bidirection Graph

A graph with some nodes (from a to j) and some arcs connecting the nodes are defined. The arcs are bidirectional: For an arc connecting a and b, it means that both a -> b and b -> a are allowed.

This Prolog program can find out all paths between any two nodes. A path is a list of arcs that connects two nodes.

Source Code

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/* /* Title : Bidirectional Graph Searching Remarks : Define a graph and an algorithm to search routes between any two nodes in the graph. Reference : https://www.cpp.edu/~jrfisher/www/prolog_tutorial/2_15.html */ % define the arcs connecting the nodes % of a graph side(a,b). side(a,d). side(b,e). side(b,c). side(d,c). side(e,f). side(c,h). side(c,g). side(f,g). side(f,i). side(i,g). side(g,h). side(g,j). side(h,j). side(d,h). % allow bidirectional arcs path(X,Y) :- side(X,Y). path(X,Y) :- side(Y,X). % define the possible travelling % methods between any two nodes X and Y % 1. there is an arc connecting X and Y % directly. % 2. there is an arc connecting X and Z, % and there is a way to travel from % Z to Y. % Visited - the list for all visited nodes % Path - the list holding the sequence % of nodes from X to Y in a % reversed way. travel(X,Y,P,[Y|P]) :- path(X,Y). travel(X,Y,Visited,Path) :- path(X,Z), Z \== Y, \+member(Z,Visited), travel(Z,Y,[Z|Visited],Path). route(A,B,Path) :- travel(A,B,[A],PathReversed), reverse(PathReversed,Path). % print all items of a list, one item % for each line. printList([]) :- writeln(''). printList([H|T]) :- writeln(H), printList(T). % eg. % 1. To show all routes from a to i: % go(a,i). % 2. To find all routes that can go % to i: % go(X,i). % 3. To find all routes that can go % from a: % go(a,X). go(A,B) :- findall(P,route(A,B,P),PathList), printList(PathList).

Output

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Run the script by swi-prolog, assume that the name of the script is graph01.pl. # swipl graph01.pl Welcome to SWI-Prolog (Multi-threaded, 64 bits, Version 7.2.3) Copyright (c) 1990-2015 University of Amsterdam, VU Amsterdam SWI-Prolog comes with ABSOLUTELY NO WARRANTY. This is free software, and you are welcome to redistribute it under certain conditions. Please visit http://www.swi-prolog.org for details. For help, use ?- help(Topic). or ?- apropos(Word). /* find all paths from a to d */ ?- go(a,d). [a,d] [a,b,e,f,g,h,d] [a,b,e,f,g,h,c,d] [a,b,e,f,g,j,h,d] [a,b,e,f,g,j,h,c,d] [a,b,e,f,g,c,d] [a,b,e,f,g,c,h,d] [a,b,e,f,i,g,h,d] [a,b,e,f,i,g,h,c,d] [a,b,e,f,i,g,j,h,d] [a,b,e,f,i,g,j,h,c,d] [a,b,e,f,i,g,c,d] [a,b,e,f,i,g,c,h,d] [a,b,c,d] [a,b,c,h,d] [a,b,c,g,h,d] [a,b,c,g,j,h,d] true. /* find all paths that can go to d */ ?- go(X,d). [a,d] [c,d] [h,d] [a,b,e,f,g,h,d] [a,b,e,f,g,h,c,d] [a,b,e,f,g,j,h,d] [a,b,e,f,g,j,h,c,d] [a,b,e,f,g,c,d] [a,b,e,f,g,c,h,d] [a,b,e,f,i,g,h,d] [a,b,e,f,i,g,h,c,d] [a,b,e,f,i,g,j,h,d] [a,b,e,f,i,g,j,h,c,d] [a,b,e,f,i,g,c,d] [a,b,e,f,i,g,c,h,d] [a,b,c,d] [a,b,c,h,d] [a,b,c,g,h,d] [a,b,c,g,j,h,d] [b,e,f,g,h,d] [b,e,f,g,h,c,d] [b,e,f,g,j,h,d] [b,e,f,g,j,h,c,d] [b,e,f,g,c,d] [b,e,f,g,c,h,d] [b,e,f,i,g,h,d] [b,e,f,i,g,h,c,d] [b,e,f,i,g,j,h,d] [b,e,f,i,g,j,h,c,d] [b,e,f,i,g,c,d] [b,e,f,i,g,c,h,d] [b,c,d] [b,c,h,d] [b,c,g,h,d] [b,c,g,j,h,d] [d,c,d] [d,c,h,d] [d,c,h,j,g,f,e,b,a,d] [d,c,h,j,g,i,f,e,b,a,d] [d,c,h,g,f,e,b,a,d] [d,c,h,g,i,f,e,b,a,d] [d,c,g,h,d] [d,c,g,j,h,d] [d,c,g,f,e,b,a,d] [d,c,g,i,f,e,b,a,d] [d,c,b,e,f,g,h,d] [d,c,b,e,f,g,j,h,d] [d,c,b,e,f,i,g,h,d] [d,c,b,e,f,i,g,j,h,d] [d,c,b,a,d] [e,f,g,h,d] [e,f,g,h,c,d] [e,f,g,h,c,b,a,d] [e,f,g,j,h,d] [e,f,g,j,h,c,d] [e,f,g,j,h,c,b,a,d] [e,f,g,c,d] [e,f,g,c,h,d] [e,f,g,c,b,a,d] [e,f,i,g,h,d] [e,f,i,g,h,c,d] [e,f,i,g,h,c,b,a,d] [e,f,i,g,j,h,d] [e,f,i,g,j,h,c,d] [e,f,i,g,j,h,c,b,a,d] [e,f,i,g,c,d] [e,f,i,g,c,h,d] [e,f,i,g,c,b,a,d] [c,h,d] [c,h,j,g,f,e,b,a,d] [c,h,j,g,i,f,e,b,a,d] [c,h,g,f,e,b,a,d] [c,h,g,i,f,e,b,a,d] [c,g,h,d] [c,g,j,h,d] [c,g,f,e,b,a,d] [c,g,i,f,e,b,a,d] [f,g,h,d] [f,g,h,c,d] [f,g,h,c,b,a,d] [f,g,j,h,d] [f,g,j,h,c,d] [f,g,j,h,c,b,a,d] [f,g,c,d] [f,g,c,h,d] [f,g,c,b,a,d] [f,i,g,h,d] [f,i,g,h,c,d] [f,i,g,h,c,b,a,d] [f,i,g,j,h,d] [f,i,g,j,h,c,d] [f,i,g,j,h,c,b,a,d] [f,i,g,c,d] [f,i,g,c,h,d] [f,i,g,c,b,a,d] [i,g,h,d] [i,g,h,c,d] [i,g,h,c,b,a,d] [i,g,j,h,d] [i,g,j,h,c,d] [i,g,j,h,c,b,a,d] [i,g,c,d] [i,g,c,h,d] [i,g,c,b,a,d] [i,g,f,e,b,c,d] [i,g,f,e,b,c,h,d] [i,g,f,e,b,a,d] [g,h,d] [g,h,c,d] [g,h,c,b,a,d] [g,j,h,d] [g,j,h,c,d] [g,j,h,c,b,a,d] [h,j,g,c,d] [h,j,g,c,b,a,d] [h,j,g,f,e,b,c,d] [h,j,g,f,e,b,a,d] [h,j,g,i,f,e,b,c,d] [h,j,g,i,f,e,b,a,d] [d,h,d] [d,h,j,g,c,d] [d,h,j,g,c,b,a,d] [d,h,j,g,f,e,b,c,d] [d,h,j,g,f,e,b,a,d] [d,h,j,g,i,f,e,b,c,d] [d,h,j,g,i,f,e,b,a,d] [d,h,c,d] [d,h,c,g,f,e,b,a,d] [d,h,c,g,i,f,e,b,a,d] [d,h,c,b,a,d] [d,h,g,c,d] [d,h,g,c,b,a,d] [d,h,g,f,e,b,c,d] [d,h,g,f,e,b,a,d] [d,h,g,i,f,e,b,c,d] [d,h,g,i,f,e,b,a,d] [b,a,d] [d,a,d] [d,a,b,e,f,g,h,d] [d,a,b,e,f,g,h,c,d] [d,a,b,e,f,g,j,h,d] [d,a,b,e,f,g,j,h,c,d] [d,a,b,e,f,g,c,d] [d,a,b,e,f,g,c,h,d] [d,a,b,e,f,i,g,h,d] [d,a,b,e,f,i,g,h,c,d] [d,a,b,e,f,i,g,j,h,d] [d,a,b,e,f,i,g,j,h,c,d] [d,a,b,e,f,i,g,c,d] [d,a,b,e,f,i,g,c,h,d] [d,a,b,c,d] [d,a,b,c,h,d] [d,a,b,c,g,h,d] [d,a,b,c,g,j,h,d] [e,b,c,d] [e,b,c,h,d] [e,b,c,g,h,d] [e,b,c,g,j,h,d] [e,b,a,d] [c,b,e,f,g,h,d] [c,b,e,f,g,j,h,d] [c,b,e,f,i,g,h,d] [c,b,e,f,i,g,j,h,d] [c,b,a,d] [f,e,b,c,d] [f,e,b,c,h,d] [f,e,b,c,g,h,d] [f,e,b,c,g,j,h,d] [f,e,b,a,d] [h,c,d] [h,c,g,f,e,b,a,d] [h,c,g,i,f,e,b,a,d] [h,c,b,a,d] [g,c,d] [g,c,h,d] [g,c,b,a,d] [g,f,e,b,c,d] [g,f,e,b,c,h,d] [g,f,e,b,a,d] [i,f,g,h,d] [i,f,g,h,c,d] [i,f,g,h,c,b,a,d] [i,f,g,j,h,d] [i,f,g,j,h,c,d] [i,f,g,j,h,c,b,a,d] [i,f,g,c,d] [i,f,g,c,h,d] [i,f,g,c,b,a,d] [i,f,e,b,c,d] [i,f,e,b,c,h,d] [i,f,e,b,c,g,h,d] [i,f,e,b,c,g,j,h,d] [i,f,e,b,a,d] [g,i,f,e,b,c,d] [g,i,f,e,b,c,h,d] [g,i,f,e,b,a,d] [h,g,c,d] [h,g,c,b,a,d] [h,g,f,e,b,c,d] [h,g,f,e,b,a,d] [h,g,i,f,e,b,c,d] [h,g,i,f,e,b,a,d] [j,g,h,d] [j,g,h,c,d] [j,g,h,c,b,a,d] [j,g,c,d] [j,g,c,h,d] [j,g,c,b,a,d] [j,g,f,e,b,c,d] [j,g,f,e,b,c,h,d] [j,g,f,e,b,a,d] [j,g,i,f,e,b,c,d] [j,g,i,f,e,b,c,h,d] [j,g,i,f,e,b,a,d] [j,h,d] [j,h,c,d] [j,h,c,g,f,e,b,a,d] [j,h,c,g,i,f,e,b,a,d] [j,h,c,b,a,d] [j,h,g,c,d] [j,h,g,c,b,a,d] [j,h,g,f,e,b,c,d] [j,h,g,f,e,b,a,d] [j,h,g,i,f,e,b,c,d] [j,h,g,i,f,e,b,a,d] true. /* find all paths that can go from d */ ?- go(d,X). [d,c] [d,h] [d,a] [d,c,h] [d,c,g] [d,c,b] [d,c,d] [d,c,h,j] [d,c,h,c] [d,c,h,g] [d,c,h,d] [d,c,h,j,g] [d,c,h,j,h] [d,c,h,j,g,h] [d,c,h,j,g,j] [d,c,h,j,g,c] [d,c,h,j,g,f] [d,c,h,j,g,i] [d,c,h,j,g,f,g] [d,c,h,j,g,f,i] [d,c,h,j,g,f,e] [d,c,h,j,g,f,i,g] [d,c,h,j,g,f,i,f] [d,c,h,j,g,f,e,f] [d,c,h,j,g,f,e,b] [d,c,h,j,g,f,e,b,e] [d,c,h,j,g,f,e,b,c] [d,c,h,j,g,f,e,b,a] [d,c,h,j,g,f,e,b,a,b] [d,c,h,j,g,f,e,b,a,d] [d,c,h,j,g,i,g] [d,c,h,j,g,i,f] [d,c,h,j,g,i,f,g] [d,c,h,j,g,i,f,i] [d,c,h,j,g,i,f,e] [d,c,h,j,g,i,f,e,f] [d,c,h,j,g,i,f,e,b] [d,c,h,j,g,i,f,e,b,e] [d,c,h,j,g,i,f,e,b,c] [d,c,h,j,g,i,f,e,b,a] [d,c,h,j,g,i,f,e,b,a,b] [d,c,h,j,g,i,f,e,b,a,d] [d,c,h,g,h] [d,c,h,g,j] [d,c,h,g,c] [d,c,h,g,f] [d,c,h,g,i] [d,c,h,g,j,g] [d,c,h,g,j,h] [d,c,h,g,f,g] [d,c,h,g,f,i] [d,c,h,g,f,e] [d,c,h,g,f,i,g] [d,c,h,g,f,i,f] [d,c,h,g,f,e,f] [d,c,h,g,f,e,b] [d,c,h,g,f,e,b,e] [d,c,h,g,f,e,b,c] [d,c,h,g,f,e,b,a] [d,c,h,g,f,e,b,a,b] [d,c,h,g,f,e,b,a,d] [d,c,h,g,i,g] [d,c,h,g,i,f] [d,c,h,g,i,f,g] [d,c,h,g,i,f,i] [d,c,h,g,i,f,e] [d,c,h,g,i,f,e,f] [d,c,h,g,i,f,e,b] [d,c,h,g,i,f,e,b,e] [d,c,h,g,i,f,e,b,c] [d,c,h,g,i,f,e,b,a] [d,c,h,g,i,f,e,b,a,b] [d,c,h,g,i,f,e,b,a,d] [d,c,g,h] [d,c,g,j] [d,c,g,c] [d,c,g,f] [d,c,g,i] [d,c,g,h,j] [d,c,g,h,c] [d,c,g,h,g] [d,c,g,h,d] [d,c,g,h,j,g] [d,c,g,h,j,h] [d,c,g,j,g] [d,c,g,j,h] [d,c,g,j,h,j] [d,c,g,j,h,c] [d,c,g,j,h,g] [d,c,g,j,h,d] [d,c,g,f,g] [d,c,g,f,i] [d,c,g,f,e] [d,c,g,f,i,g] [d,c,g,f,i,f] [d,c,g,f,e,f] [d,c,g,f,e,b] [d,c,g,f,e,b,e] [d,c,g,f,e,b,c] [d,c,g,f,e,b,a] [d,c,g,f,e,b,a,b] [d,c,g,f,e,b,a,d] [d,c,g,i,g] [d,c,g,i,f] [d,c,g,i,f,g] [d,c,g,i,f,i] [d,c,g,i,f,e] [d,c,g,i,f,e,f] [d,c,g,i,f,e,b] [d,c,g,i,f,e,b,e] [d,c,g,i,f,e,b,c] [d,c,g,i,f,e,b,a] [d,c,g,i,f,e,b,a,b] [d,c,g,i,f,e,b,a,d] [d,c,b,e] [d,c,b,c] [d,c,b,a] [d,c,b,e,f] [d,c,b,e,b] [d,c,b,e,f,g] [d,c,b,e,f,i] [d,c,b,e,f,e] [d,c,b,e,f,g,h] [d,c,b,e,f,g,j] [d,c,b,e,f,g,c] [d,c,b,e,f,g,f] [d,c,b,e,f,g,i] [d,c,b,e,f,g,h,j] [d,c,b,e,f,g,h,c] [d,c,b,e,f,g,h,g] [d,c,b,e,f,g,h,d] [d,c,b,e,f,g,h,j,g] [d,c,b,e,f,g,h,j,h] [d,c,b,e,f,g,j,g] [d,c,b,e,f,g,j,h] [d,c,b,e,f,g,j,h,j] [d,c,b,e,f,g,j,h,c] [d,c,b,e,f,g,j,h,g] [d,c,b,e,f,g,j,h,d] [d,c,b,e,f,g,i,g] [d,c,b,e,f,g,i,f] [d,c,b,e,f,i,g] [d,c,b,e,f,i,f] [d,c,b,e,f,i,g,h] [d,c,b,e,f,i,g,j] [d,c,b,e,f,i,g,c] [d,c,b,e,f,i,g,f] [d,c,b,e,f,i,g,i] [d,c,b,e,f,i,g,h,j] [d,c,b,e,f,i,g,h,c] [d,c,b,e,f,i,g,h,g] [d,c,b,e,f,i,g,h,d] [d,c,b,e,f,i,g,h,j,g] [d,c,b,e,f,i,g,h,j,h] [d,c,b,e,f,i,g,j,g] [d,c,b,e,f,i,g,j,h] [d,c,b,e,f,i,g,j,h,j] [d,c,b,e,f,i,g,j,h,c] [d,c,b,e,f,i,g,j,h,g] [d,c,b,e,f,i,g,j,h,d] [d,c,b,a,b] [d,c,b,a,d] [d,h,j] [d,h,c] [d,h,g] [d,h,d] [d,h,j,g] [d,h,j,h] [d,h,j,g,h] [d,h,j,g,j] [d,h,j,g,c] [d,h,j,g,f] [d,h,j,g,i] [d,h,j,g,c,h] [d,h,j,g,c,g] [d,h,j,g,c,b] [d,h,j,g,c,d] [d,h,j,g,c,b,e] [d,h,j,g,c,b,c] [d,h,j,g,c,b,a] [d,h,j,g,c,b,e,f] [d,h,j,g,c,b,e,b] [d,h,j,g,c,b,e,f,g] [d,h,j,g,c,b,e,f,i] [d,h,j,g,c,b,e,f,e] [d,h,j,g,c,b,e,f,i,g] [d,h,j,g,c,b,e,f,i,f] [d,h,j,g,c,b,a,b] [d,h,j,g,c,b,a,d] [d,h,j,g,f,g] [d,h,j,g,f,i] [d,h,j,g,f,e] [d,h,j,g,f,i,g] [d,h,j,g,f,i,f] [d,h,j,g,f,e,f] [d,h,j,g,f,e,b] [d,h,j,g,f,e,b,e] [d,h,j,g,f,e,b,c] [d,h,j,g,f,e,b,a] [d,h,j,g,f,e,b,c,h] [d,h,j,g,f,e,b,c,g] [d,h,j,g,f,e,b,c,b] [d,h,j,g,f,e,b,c,d] [d,h,j,g,f,e,b,a,b] [d,h,j,g,f,e,b,a,d] [d,h,j,g,i,g] [d,h,j,g,i,f] [d,h,j,g,i,f,g] [d,h,j,g,i,f,i] [d,h,j,g,i,f,e] [d,h,j,g,i,f,e,f] [d,h,j,g,i,f,e,b] [d,h,j,g,i,f,e,b,e] [d,h,j,g,i,f,e,b,c] [d,h,j,g,i,f,e,b,a] [d,h,j,g,i,f,e,b,c,h] [d,h,j,g,i,f,e,b,c,g] [d,h,j,g,i,f,e,b,c,b] [d,h,j,g,i,f,e,b,c,d] [d,h,j,g,i,f,e,b,a,b] [d,h,j,g,i,f,e,b,a,d] [d,h,c,h] [d,h,c,g] [d,h,c,b] [d,h,c,d] [d,h,c,g,h] [d,h,c,g,j] [d,h,c,g,c] [d,h,c,g,f] [d,h,c,g,i] [d,h,c,g,j,g] [d,h,c,g,j,h] [d,h,c,g,f,g] [d,h,c,g,f,i] [d,h,c,g,f,e] [d,h,c,g,f,i,g] [d,h,c,g,f,i,f] [d,h,c,g,f,e,f] [d,h,c,g,f,e,b] [d,h,c,g,f,e,b,e] [d,h,c,g,f,e,b,c] [d,h,c,g,f,e,b,a] [d,h,c,g,f,e,b,a,b] [d,h,c,g,f,e,b,a,d] [d,h,c,g,i,g] [d,h,c,g,i,f] [d,h,c,g,i,f,g] [d,h,c,g,i,f,i] [d,h,c,g,i,f,e] [d,h,c,g,i,f,e,f] [d,h,c,g,i,f,e,b] [d,h,c,g,i,f,e,b,e] [d,h,c,g,i,f,e,b,c] [d,h,c,g,i,f,e,b,a] [d,h,c,g,i,f,e,b,a,b] [d,h,c,g,i,f,e,b,a,d] [d,h,c,b,e] [d,h,c,b,c] [d,h,c,b,a] [d,h,c,b,e,f] [d,h,c,b,e,b] [d,h,c,b,e,f,g] [d,h,c,b,e,f,i] [d,h,c,b,e,f,e] [d,h,c,b,e,f,g,h] [d,h,c,b,e,f,g,j] [d,h,c,b,e,f,g,c] [d,h,c,b,e,f,g,f] [d,h,c,b,e,f,g,i] [d,h,c,b,e,f,g,j,g] [d,h,c,b,e,f,g,j,h] [d,h,c,b,e,f,g,i,g] [d,h,c,b,e,f,g,i,f] [d,h,c,b,e,f,i,g] [d,h,c,b,e,f,i,f] [d,h,c,b,e,f,i,g,h] [d,h,c,b,e,f,i,g,j] [d,h,c,b,e,f,i,g,c] [d,h,c,b,e,f,i,g,f] [d,h,c,b,e,f,i,g,i] [d,h,c,b,e,f,i,g,j,g] [d,h,c,b,e,f,i,g,j,h] [d,h,c,b,a,b] [d,h,c,b,a,d] [d,h,g,h] [d,h,g,j] [d,h,g,c] [d,h,g,f] [d,h,g,i] [d,h,g,j,g] [d,h,g,j,h] [d,h,g,c,h] [d,h,g,c,g] [d,h,g,c,b] [d,h,g,c,d] [d,h,g,c,b,e] [d,h,g,c,b,c] [d,h,g,c,b,a] [d,h,g,c,b,e,f] [d,h,g,c,b,e,b] [d,h,g,c,b,e,f,g] [d,h,g,c,b,e,f,i] [d,h,g,c,b,e,f,e] [d,h,g,c,b,e,f,i,g] [d,h,g,c,b,e,f,i,f] [d,h,g,c,b,a,b] [d,h,g,c,b,a,d] [d,h,g,f,g] [d,h,g,f,i] [d,h,g,f,e] [d,h,g,f,i,g] [d,h,g,f,i,f] [d,h,g,f,e,f] [d,h,g,f,e,b] [d,h,g,f,e,b,e] [d,h,g,f,e,b,c] [d,h,g,f,e,b,a] [d,h,g,f,e,b,c,h] [d,h,g,f,e,b,c,g] [d,h,g,f,e,b,c,b] [d,h,g,f,e,b,c,d] [d,h,g,f,e,b,a,b] [d,h,g,f,e,b,a,d] [d,h,g,i,g] [d,h,g,i,f] [d,h,g,i,f,g] [d,h,g,i,f,i] [d,h,g,i,f,e] [d,h,g,i,f,e,f] [d,h,g,i,f,e,b] [d,h,g,i,f,e,b,e] [d,h,g,i,f,e,b,c] [d,h,g,i,f,e,b,a] [d,h,g,i,f,e,b,c,h] [d,h,g,i,f,e,b,c,g] [d,h,g,i,f,e,b,c,b] [d,h,g,i,f,e,b,c,d] [d,h,g,i,f,e,b,a,b] [d,h,g,i,f,e,b,a,d] [d,a,b] [d,a,d] [d,a,b,e] [d,a,b,c] [d,a,b,a] [d,a,b,e,f] [d,a,b,e,b] [d,a,b,e,f,g] [d,a,b,e,f,i] [d,a,b,e,f,e] [d,a,b,e,f,g,h] [d,a,b,e,f,g,j] [d,a,b,e,f,g,c] [d,a,b,e,f,g,f] [d,a,b,e,f,g,i] [d,a,b,e,f,g,h,j] [d,a,b,e,f,g,h,c] [d,a,b,e,f,g,h,g] [d,a,b,e,f,g,h,d] [d,a,b,e,f,g,h,j,g] [d,a,b,e,f,g,h,j,h] [d,a,b,e,f,g,h,c,h] [d,a,b,e,f,g,h,c,g] [d,a,b,e,f,g,h,c,b] [d,a,b,e,f,g,h,c,d] [d,a,b,e,f,g,j,g] [d,a,b,e,f,g,j,h] [d,a,b,e,f,g,j,h,j] [d,a,b,e,f,g,j,h,c] [d,a,b,e,f,g,j,h,g] [d,a,b,e,f,g,j,h,d] [d,a,b,e,f,g,j,h,c,h] [d,a,b,e,f,g,j,h,c,g] [d,a,b,e,f,g,j,h,c,b] [d,a,b,e,f,g,j,h,c,d] [d,a,b,e,f,g,c,h] [d,a,b,e,f,g,c,g] [d,a,b,e,f,g,c,b] [d,a,b,e,f,g,c,d] [d,a,b,e,f,g,c,h,j] [d,a,b,e,f,g,c,h,c] [d,a,b,e,f,g,c,h,g] [d,a,b,e,f,g,c,h,d] [d,a,b,e,f,g,c,h,j,g] [d,a,b,e,f,g,c,h,j,h] [d,a,b,e,f,g,i,g] [d,a,b,e,f,g,i,f] [d,a,b,e,f,i,g] [d,a,b,e,f,i,f] [d,a,b,e,f,i,g,h] [d,a,b,e,f,i,g,j] [d,a,b,e,f,i,g,c] [d,a,b,e,f,i,g,f] [d,a,b,e,f,i,g,i] [d,a,b,e,f,i,g,h,j] [d,a,b,e,f,i,g,h,c] [d,a,b,e,f,i,g,h,g] [d,a,b,e,f,i,g,h,d] [d,a,b,e,f,i,g,h,j,g] [d,a,b,e,f,i,g,h,j,h] [d,a,b,e,f,i,g,h,c,h] [d,a,b,e,f,i,g,h,c,g] [d,a,b,e,f,i,g,h,c,b] [d,a,b,e,f,i,g,h,c,d] [d,a,b,e,f,i,g,j,g] [d,a,b,e,f,i,g,j,h] [d,a,b,e,f,i,g,j,h,j] [d,a,b,e,f,i,g,j,h,c] [d,a,b,e,f,i,g,j,h,g] [d,a,b,e,f,i,g,j,h,d] [d,a,b,e,f,i,g,j,h,c,h] [d,a,b,e,f,i,g,j,h,c,g] [d,a,b,e,f,i,g,j,h,c,b] [d,a,b,e,f,i,g,j,h,c,d] [d,a,b,e,f,i,g,c,h] [d,a,b,e,f,i,g,c,g] [d,a,b,e,f,i,g,c,b] [d,a,b,e,f,i,g,c,d] [d,a,b,e,f,i,g,c,h,j] [d,a,b,e,f,i,g,c,h,c] [d,a,b,e,f,i,g,c,h,g] [d,a,b,e,f,i,g,c,h,d] [d,a,b,e,f,i,g,c,h,j,g] [d,a,b,e,f,i,g,c,h,j,h] [d,a,b,c,h] [d,a,b,c,g] [d,a,b,c,b] [d,a,b,c,d] [d,a,b,c,h,j] [d,a,b,c,h,c] [d,a,b,c,h,g] [d,a,b,c,h,d] [d,a,b,c,h,j,g] [d,a,b,c,h,j,h] [d,a,b,c,h,j,g,h] [d,a,b,c,h,j,g,j] [d,a,b,c,h,j,g,c] [d,a,b,c,h,j,g,f] [d,a,b,c,h,j,g,i] [d,a,b,c,h,j,g,f,g] [d,a,b,c,h,j,g,f,i] [d,a,b,c,h,j,g,f,e] [d,a,b,c,h,j,g,f,i,g] [d,a,b,c,h,j,g,f,i,f] [d,a,b,c,h,j,g,f,e,f] [d,a,b,c,h,j,g,f,e,b] [d,a,b,c,h,j,g,i,g] [d,a,b,c,h,j,g,i,f] [d,a,b,c,h,j,g,i,f,g] [d,a,b,c,h,j,g,i,f,i] [d,a,b,c,h,j,g,i,f,e] [d,a,b,c,h,j,g,i,f,e,f] [d,a,b,c,h,j,g,i,f,e,b] [d,a,b,c,h,g,h] [d,a,b,c,h,g,j] [d,a,b,c,h,g,c] [d,a,b,c,h,g,f] [d,a,b,c,h,g,i] [d,a,b,c,h,g,j,g] [d,a,b,c,h,g,j,h] [d,a,b,c,h,g,f,g] [d,a,b,c,h,g,f,i] [d,a,b,c,h,g,f,e] [d,a,b,c,h,g,f,i,g] [d,a,b,c,h,g,f,i,f] [d,a,b,c,h,g,f,e,f] [d,a,b,c,h,g,f,e,b] [d,a,b,c,h,g,i,g] [d,a,b,c,h,g,i,f] [d,a,b,c,h,g,i,f,g] [d,a,b,c,h,g,i,f,i] [d,a,b,c,h,g,i,f,e] [d,a,b,c,h,g,i,f,e,f] [d,a,b,c,h,g,i,f,e,b] [d,a,b,c,g,h] [d,a,b,c,g,j] [d,a,b,c,g,c] [d,a,b,c,g,f] [d,a,b,c,g,i] [d,a,b,c,g,h,j] [d,a,b,c,g,h,c] [d,a,b,c,g,h,g] [d,a,b,c,g,h,d] [d,a,b,c,g,h,j,g] [d,a,b,c,g,h,j,h] [d,a,b,c,g,j,g] [d,a,b,c,g,j,h] [d,a,b,c,g,j,h,j] [d,a,b,c,g,j,h,c] [d,a,b,c,g,j,h,g] [d,a,b,c,g,j,h,d] [d,a,b,c,g,f,g] [d,a,b,c,g,f,i] [d,a,b,c,g,f,e] [d,a,b,c,g,f,i,g] [d,a,b,c,g,f,i,f] [d,a,b,c,g,f,e,f] [d,a,b,c,g,f,e,b] [d,a,b,c,g,i,g] [d,a,b,c,g,i,f] [d,a,b,c,g,i,f,g] [d,a,b,c,g,i,f,i] [d,a,b,c,g,i,f,e] [d,a,b,c,g,i,f,e,f] [d,a,b,c,g,i,f,e,b] true. ?-