428 lines
12 KiB
Prolog
428 lines
12 KiB
Prolog
% File : dgraphs.yap
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% Author : Vitor Santos Costa
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% Updated: 2006
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% Purpose: Directed Graph Processing Utilities.
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:- module( dgraphs,
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[
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dgraph_vertices/2,
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dgraph_edge/3,
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dgraph_edges/2,
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dgraph_add_vertex/3,
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dgraph_add_vertices/3,
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dgraph_del_vertex/3,
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dgraph_del_vertices/3,
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dgraph_add_edge/4,
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dgraph_add_edges/3,
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dgraph_del_edge/4,
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dgraph_del_edges/3,
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dgraph_to_ugraph/2,
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ugraph_to_dgraph/2,
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dgraph_neighbors/3,
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dgraph_neighbours/3,
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dgraph_complement/2,
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dgraph_transpose/2,
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dgraph_compose/3,
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dgraph_transitive_closure/2,
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dgraph_symmetric_closure/2,
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dgraph_top_sort/2,
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dgraph_top_sort/3,
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dgraph_min_path/5,
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dgraph_max_path/5,
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dgraph_min_paths/3,
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dgraph_isomorphic/4,
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dgraph_path/3,
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dgraph_leaves/2,
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dgraph_reachable/3
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]).
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:- reexport(library(rbtrees),
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[rb_new/1 as dgraph_new]).
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:- use_module(library(rbtrees),
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[rb_empty/1,
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rb_lookup/3,
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rb_apply/4,
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rb_insert/4,
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rb_visit/2,
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rb_keys/2,
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rb_delete/3,
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rb_map/3,
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rb_clone/3,
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ord_list_to_rbtree/2]).
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:- use_module(library(ordsets),
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[ord_insert/3,
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ord_union/3,
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ord_subtract/3,
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ord_del_element/3,
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ord_memberchk/2]).
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:- use_module(library(wdgraphs),
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[dgraph_to_wdgraph/2,
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wdgraph_min_path/5,
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wdgraph_max_path/5,
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wdgraph_min_paths/3]).
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dgraph_add_edge(Vs0,V1,V2,Vs2) :-
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dgraph_new_edge(V1,V2,Vs0,Vs1),
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dgraph_add_vertex(Vs1,V2,Vs2).
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dgraph_add_edges(V0, Edges, VF) :-
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rb_empty(V0), !,
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sort(Edges,SortedEdges),
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all_vertices_in_edges(SortedEdges,Vertices),
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sort(Vertices,SortedVertices),
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edges2graphl(SortedVertices, SortedEdges, GraphL),
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ord_list_to_rbtree(GraphL, VF).
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dgraph_add_edges(G0, Edges, GF) :-
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sort(Edges,SortedEdges),
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all_vertices_in_edges(SortedEdges,Vertices),
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sort(Vertices,SortedVertices),
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dgraph_add_edges(SortedVertices,SortedEdges, G0, GF).
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all_vertices_in_edges([],[]).
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all_vertices_in_edges([V1-V2|Edges],[V1,V2|Vertices]) :-
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all_vertices_in_edges(Edges,Vertices).
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edges2graphl([], [], []).
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edges2graphl([V|Vertices], [VV-V1|SortedEdges], [V-[V1|Children]|GraphL]) :-
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V == VV, !,
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get_extra_children(SortedEdges,VV,Children,RemEdges),
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edges2graphl(Vertices, RemEdges, GraphL).
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edges2graphl([V|Vertices], SortedEdges, [V-[]|GraphL]) :-
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edges2graphl(Vertices, SortedEdges, GraphL).
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dgraph_add_edges([],[]) --> [].
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dgraph_add_edges([V|Vs],[V0-V1|Es]) --> { V == V0 }, !,
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{ get_extra_children(Es,V,Children,REs) },
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dgraph_update_vertex(V,[V1|Children]),
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dgraph_add_edges(Vs,REs).
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dgraph_add_edges([V|Vs],Es) --> !,
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dgraph_update_vertex(V,[]),
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dgraph_add_edges(Vs,Es).
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get_extra_children([V-C|Es],VV,[C|Children],REs) :- V == VV, !,
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get_extra_children(Es,VV,Children,REs).
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get_extra_children(Es,_,[],Es).
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dgraph_update_vertex(V,Children, Vs0, Vs) :-
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rb_apply(Vs0, V, add_edges(Children), Vs), !.
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dgraph_update_vertex(V,Children, Vs0, Vs) :-
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rb_insert(Vs0,V,Children,Vs).
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add_edges(E0,E1,E) :-
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ord_union(E0,E1,E).
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dgraph_new_edge(V1,V2,Vs0,Vs) :-
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rb_apply(Vs0, V1, insert_edge(V2), Vs), !.
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dgraph_new_edge(V1,V2,Vs0,Vs) :-
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rb_insert(Vs0,V1,[V2],Vs).
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insert_edge(V2, Children0, Children) :-
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ord_insert(Children0,V2,Children).
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dgraph_add_vertices(G, [], G).
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dgraph_add_vertices(G0, [V|Vs], GF) :-
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dgraph_add_vertex(G0, V, G1),
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dgraph_add_vertices(G1, Vs, GF).
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dgraph_add_vertex(Vs0, V, Vs0) :-
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rb_lookup(V,_,Vs0), !.
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dgraph_add_vertex(Vs0, V, Vs) :-
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rb_insert(Vs0, V, [], Vs).
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dgraph_edges(Vs,Edges) :-
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rb_visit(Vs,L0),
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cvt2edges(L0,Edges).
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dgraph_vertices(Vs,Vertices) :-
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rb_keys(Vs,Vertices).
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cvt2edges([],[]).
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cvt2edges([V-Children|L0],Edges) :-
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children2edges(Children,V,Edges,Edges0),
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cvt2edges(L0,Edges0).
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children2edges([],_,Edges,Edges).
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children2edges([Child|L0],V,[V-Child|EdgesF],Edges0) :-
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children2edges(L0,V,EdgesF,Edges0).
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dgraph_neighbours(V,Vertices,Children) :-
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rb_lookup(V,Children,Vertices).
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dgraph_neighbors(V,Vertices,Children) :-
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rb_lookup(V,Children,Vertices).
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add_vertices(Graph, [], Graph).
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add_vertices(Graph, [V|Vertices], NewGraph) :-
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rb_insert(Graph, V, [], IntGraph),
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add_vertices(IntGraph, Vertices, NewGraph).
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dgraph_complement(Vs0,VsF) :-
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dgraph_vertices(Vs0,Vertices),
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rb_map(Vs0,complement(Vertices),VsF).
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complement(Vs,Children,NewChildren) :-
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ord_subtract(Vs,Children,NewChildren).
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dgraph_del_edge(Vs0,V1,V2,Vs1) :-
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rb_apply(Vs0, V1, delete_edge(V2), Vs1).
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dgraph_del_edges(G0, Edges, Gf) :-
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sort(Edges,SortedEdges),
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continue_del_edges(SortedEdges, G0, Gf).
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continue_del_edges([]) --> [].
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continue_del_edges([V-V1|Es]) --> !,
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{ get_extra_children(Es,V,Children,REs) },
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contract_vertex(V,[V1|Children]),
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continue_del_edges(REs).
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contract_vertex(V,Children, Vs0, Vs) :-
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rb_apply(Vs0, V, del_edges(Children), Vs).
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del_edges(ToRemove,E0,E) :-
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ord_subtract(E0,ToRemove,E).
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dgraph_del_vertex(Vs0, V, Vsf) :-
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rb_delete(Vs0, V, Vs1),
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rb_map(Vs1, delete_edge(V), Vsf).
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delete_edge(Edges0, V, Edges) :-
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ord_del_element(Edges0, V, Edges).
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dgraph_del_vertices(G0, Vs, GF) :-
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sort(Vs,SortedVs),
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delete_all(SortedVs, G0, G1),
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delete_remaining_edges(SortedVs, G1, GF).
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% it would be nice to be able to delete a set of elements from an RB tree
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% but I don't how to do it yet.
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delete_all([]) --> [].
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delete_all([V|Vs],Vs0,Vsf) :-
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rb_delete(Vs0, V, Vsi),
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delete_all(Vs,Vsi,Vsf).
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delete_remaining_edges(SortedVs,Vs0,Vsf) :-
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rb_map(Vs0, del_edges(SortedVs), Vsf).
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dgraph_transpose(Graph, TGraph) :-
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rb_visit(Graph, Edges),
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transpose(Edges, Nodes, TEdges, []),
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dgraph_new(G0),
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% make sure we have all vertices, even if they are unconnected.
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dgraph_add_vertices(G0, Nodes, G1),
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dgraph_add_edges(G1, TEdges, TGraph).
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transpose([], []) --> [].
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transpose([V-Edges|MoreVs], [V|Vs]) -->
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transpose_edges(Edges, V),
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transpose(MoreVs, Vs).
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transpose_edges([], _V) --> [].
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transpose_edges(E.Edges, V) -->
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[E-V],
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transpose_edges(Edges, V).
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dgraph_compose(T1,T2,CT) :-
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rb_visit(T1,Nodes),
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compose(Nodes,T2,NewNodes),
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dgraph_new(CT0),
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dgraph_add_edges(CT0,NewNodes,CT).
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compose([],_,[]).
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compose([V-Children|Nodes],T2,NewNodes) :-
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compose2(Children,V,T2,NewNodes,NewNodes0),
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compose(Nodes,T2,NewNodes0).
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compose2([],_,_,NewNodes,NewNodes).
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compose2([C|Children],V,T2,NewNodes,NewNodes0) :-
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rb_lookup(C, GrandChildren, T2),
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compose3(GrandChildren, V, NewNodes,NewNodesI),
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compose2(Children,V,T2,NewNodesI,NewNodes0).
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compose3([], _, NewNodes, NewNodes).
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compose3([GC|GrandChildren], V, [V-GC|NewNodes], NewNodes0) :-
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compose3(GrandChildren, V, NewNodes, NewNodes0).
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dgraph_transitive_closure(G,Closure) :-
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dgraph_edges(G,Edges),
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continue_closure(Edges,G,Closure).
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continue_closure([], Closure, Closure) :- !.
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continue_closure(Edges, G, Closure) :-
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transit_graph(Edges,G,NewEdges),
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dgraph_add_edges(G, NewEdges, GN),
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continue_closure(NewEdges, GN, Closure).
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transit_graph([],_,[]).
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transit_graph([V-V1|Edges],G,NewEdges) :-
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rb_lookup(V1, GrandChildren, G),
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transit_graph2(GrandChildren, V, G, NewEdges, MoreEdges),
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transit_graph(Edges, G, MoreEdges).
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transit_graph2([], _, _, NewEdges, NewEdges).
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transit_graph2([GC|GrandChildren], V, G, NewEdges, MoreEdges) :-
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is_edge(V,GC,G), !,
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transit_graph2(GrandChildren, V, G, NewEdges, MoreEdges).
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transit_graph2([GC|GrandChildren], V, G, [V-GC|NewEdges], MoreEdges) :-
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transit_graph2(GrandChildren, V, G, NewEdges, MoreEdges).
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is_edge(V1,V2,G) :-
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rb_lookup(V1,Children,G),
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ord_memberchk(V2, Children).
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dgraph_symmetric_closure(G,S) :-
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dgraph_edges(G, Edges),
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invert_edges(Edges, InvertedEdges),
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dgraph_add_edges(G, InvertedEdges, S).
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invert_edges([], []).
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invert_edges([V1-V2|Edges], [V2-V1|InvertedEdges]) :-
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invert_edges(Edges, InvertedEdges).
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dgraph_top_sort(G, Q) :-
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dgraph_top_sort(G, Q, []).
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dgraph_top_sort(G, Q, RQ0) :-
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% O(E)
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rb_visit(G, Vs),
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% O(E)
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invert_and_link(Vs, Links, UnsortedInvertedEdges, AllVs, Q),
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% O(V)
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rb_clone(G, LinkedG, Links),
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% O(Elog(E))
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sort(UnsortedInvertedEdges, InvertedEdges),
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% O(E)
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dgraph_vertices(G, AllVs),
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start_queue(AllVs, InvertedEdges, Q, RQ),
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continue_queue(Q, LinkedG, RQ, RQ0).
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invert_and_link([], [], [], [], []).
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invert_and_link([V-Vs|Edges], [V-NVs|ExtraEdges], UnsortedInvertedEdges, [V|AllVs],[_|Q]) :-
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inv_links(Vs, NVs, V, UnsortedInvertedEdges, UnsortedInvertedEdges0),
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invert_and_link(Edges, ExtraEdges, UnsortedInvertedEdges0, AllVs, Q).
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inv_links([],[],_,UnsortedInvertedEdges,UnsortedInvertedEdges).
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inv_links([V2|Vs],[l(V2,A,B,S,E)|VLnks],V1,[V2-e(A,B,S,E)|UnsortedInvertedEdges],UnsortedInvertedEdges0) :-
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inv_links(Vs,VLnks,V1,UnsortedInvertedEdges,UnsortedInvertedEdges0).
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dup([], []).
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dup([_|AllVs], [_|Q]) :-
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dup(AllVs, Q).
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start_queue([], [], RQ, RQ).
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start_queue([V|AllVs], [VV-e(S,B,S,E)|InvertedEdges], Q, RQ) :- V == VV, !,
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link_edges(InvertedEdges, VV, B, S, E, RemainingEdges),
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start_queue(AllVs, RemainingEdges, Q, RQ).
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start_queue([V|AllVs], InvertedEdges, [V|Q], RQ) :-
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start_queue(AllVs, InvertedEdges, Q, RQ).
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link_edges([V-e(A,B,S,E)|InvertedEdges], VV, A, S, E, RemEdges) :- V == VV, !,
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link_edges(InvertedEdges, VV, B, S, E, RemEdges).
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link_edges(RemEdges, _, A, _, A, RemEdges).
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continue_queue([], _, RQ0, RQ0).
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continue_queue([V|Q], LinkedG, RQ, RQ0) :-
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rb_lookup(V, Links, LinkedG),
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close_links(Links, RQ, RQI),
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% not clear whether I should deleted V from LinkedG
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continue_queue(Q, LinkedG, RQI, RQ0).
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close_links([], RQ, RQ).
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close_links([l(V,A,A,S,E)|Links], RQ, RQ0) :-
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( S == E -> RQ = [V| RQ1] ; RQ = RQ1),
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close_links(Links, RQ1, RQ0).
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ugraph_to_dgraph(UG, DG) :-
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ord_list_to_rbtree(UG, DG).
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dgraph_to_ugraph(DG, UG) :-
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rb_visit(DG, UG).
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dgraph_edge(N1, N2, G) :-
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rb_lookup(N1, Ns, G),
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ord_memberchk(N2, Ns).
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dgraph_min_path(V1, V2, Graph, Path, Cost) :-
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dgraph_to_wdgraph(Graph, WGraph),
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wdgraph_min_path(V1, V2, WGraph, Path, Cost).
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dgraph_max_path(V1, V2, Graph, Path, Cost) :-
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dgraph_to_wdgraph(Graph, WGraph),
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wdgraph_max_path(V1, V2, WGraph, Path, Cost).
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dgraph_min_paths(V1, Graph, Paths) :-
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dgraph_to_wdgraph(Graph, WGraph),
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wdgraph_min_paths(V1, WGraph, Paths).
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dgraph_path(V, G, [V|P]) :-
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rb_lookup(V, Children, G),
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ord_del_element(Children, V, Ch),
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do_path(Ch, G, [V], P).
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do_path([], _, _, []).
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do_path([C|Children], G, SoFar, Path) :-
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do_children([C|Children], G, SoFar, Path).
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do_children([V|_], G, SoFar, [V|Path]) :-
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rb_lookup(V, Children, G),
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ord_subtract(Children, SoFar, Ch),
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ord_insert(SoFar, V, NextSoFar),
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do_path(Ch, G, NextSoFar, Path).
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do_children([_|Children], G, SoFar, Path) :-
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do_children(Children, G, SoFar, Path).
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dgraph_isomorphic(Vs, Vs2, G1, G2) :-
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rb_new(Map0),
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mapping(Vs,Vs2,Map0,Map),
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dgraph_edges(G1,Edges),
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translate_edges(Edges,Map,TEdges),
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dgraph_new(G20),
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dgraph_add_vertices(Vs2,G20,G21),
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dgraph_add_edges(G21,TEdges,G2).
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mapping([],[],Map,Map).
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mapping([V1|Vs],[V2|Vs2],Map0,Map) :-
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rb_insert(Map0,V1,V2,MapI),
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mapping(Vs,Vs2,MapI,Map).
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translate_edges([],_,[]).
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translate_edges([V1-V2|Edges],Map,[NV1-NV2|TEdges]) :-
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rb_lookup(V1,NV1,Map),
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rb_lookup(V2,NV2,Map),
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translate_edges(Edges,Map,TEdges).
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dgraph_reachable(V, G, Edges) :-
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rb_lookup(V, Children, G),
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ord_list_to_rbtree([V-[]],Done0),
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reachable(Children, Done0, _, G, Edges, []).
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reachable([], Done, Done, _, Edges, Edges).
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reachable([V|Vertices], Done0, DoneF, G, EdgesF, Edges0) :-
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rb_lookup(V,_, Done0), !,
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reachable(Vertices, Done0, DoneF, G, EdgesF, Edges0).
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reachable([V|Vertices], Done0, DoneF, G, [V|EdgesF], Edges0) :-
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rb_lookup(V, Kids, G),
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rb_insert(Done0, V, [], Done1),
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reachable(Kids, Done1, DoneI, G, EdgesF, EdgesI),
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reachable(Vertices, DoneI, DoneF, G, EdgesI, Edges0).
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dgraph_leaves(Graph, Vertices) :-
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rb_visit(Graph, Pairs),
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vertices_without_children(Pairs, Vertices).
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vertices_without_children([], []).
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vertices_without_children((V-[]).Pairs, V.Vertices) :-
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vertices_without_children(Pairs, Vertices).
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vertices_without_children(_V-[_|_].Pairs, Vertices) :-
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vertices_without_children(Pairs, Vertices).
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