295 lines
7.0 KiB
Prolog
295 lines
7.0 KiB
Prolog
/**
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* @file wundgraphs.yap
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* @author VITOR SANTOS COSTA <vsc@VITORs-MBP.lan>
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* @date 2006
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*
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*
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*/
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:- module( wundgraphs,
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[
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wundgraph_add_edge/5,
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wundgraph_add_edges/3,
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wundgraph_del_edge/5,
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wundgraph_del_edges/3,
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wundgraph_del_vertex/3,
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wundgraph_edges/2,
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wundgraph_neighbours/3,
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wundgraph_neighbors/3,
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wundgraph_wneighbours/3,
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wundgraph_wneighbors/3,
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wundgraph_min_tree/3,
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wundgraph_max_tree/3]).
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/**
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* @defgroup wundgraphs Weighted Undirected Graphs
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* @ingroup library
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*
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* @brief Weighted Undirected Graph Processing Utilities.
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*/
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:- reexport( library(wdgraphs),
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[
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wdgraph_new/1 as wundgraph_new,
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wdgraph_add_vertex/3 as wundgraph_add_vertex,
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wdgraph_add_vertices/3 as wundgraph_add_vertices,
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wdgraph_vertices/2 as wundgraph_vertices,
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wdgraph_del_vertices/3 as wundgraph_del_vertices,
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wdgraph_edge/4 as wundgraph_edge,
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wdgraph_symmetric_closure/2 as wdgraph_to_wundgraph,
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wdgraph_to_dgraph/2 as wundgraph_to_undgraph,
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dgraph_to_wdgraph/2 as undgraph_to_wundgraph,
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wdgraph_min_path/5 as wundgraph_min_path,
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wdgraph_min_paths/3 as wundgraph_min_paths,
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wdgraph_max_path/5 as wundgraph_max_path,
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wdgraph_path/3 as wundgraph_path,
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wdgraph_reachable/3 as wundgraph_reachable
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]).
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:- use_module( library(wdgraphs),
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[
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wdgraph_add_edge/5,
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wdgraph_add_edges/3,
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wdgraph_del_edge/5,
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wdgraph_del_edges/3,
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wdgraph_del_vertex/3,
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wdgraph_edges/2,
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wdgraph_neighbours/3,
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wdgraph_wneighbours/3
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]).
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:- use_module(library(rbtrees),
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[
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rb_new/1,
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rb_delete/4,
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rb_partial_map/4,
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rb_visit/2,
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rb_insert/4,
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rb_lookup/3
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]).
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:- use_module(library(lists),
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[
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reverse/2
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]).
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wundgraph_add_edge(Vs0, V1, V2, K, Vs2) :-
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wdgraphs:wdgraph_new_edge(V1,V2,K,Vs0,Vs1),
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wdgraphs:wdgraph_new_edge(V2,V1,K,Vs1,Vs2).
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wundgraph_add_edges(G0, Edges, GF) :-
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dup_edges(Edges, DupEdges),
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wdgraph_add_edges(G0, DupEdges, GF).
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dup_edges([],[]).
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dup_edges([E1-(E2-K)|Edges], [E1-(E2-K),E2-(E1-K)|DupEdges]) :-
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dup_edges(Edges, DupEdges).
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wundgraph_edges(Vs, Edges) :-
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wdgraph_edges(Vs, DupEdges),
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remove_dups(DupEdges,Edges).
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remove_dups([],[]).
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remove_dups([V1-(V2-K)|DupEdges],NEdges) :- V1 @< V2, !,
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NEdges = [V1-(V2-K)|Edges],
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remove_dups(DupEdges,Edges).
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remove_dups([_|DupEdges],Edges) :-
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remove_dups(DupEdges,Edges).
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wundgraph_neighbours(V,Vertices,Children) :-
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wdgraph_neighbours(V,Vertices,Children0),
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(
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del_me(Children0,V,Children)
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->
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true
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;
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Children = Children0
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).
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wundgraph_neighbors(V,Vertices,Children) :-
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wdgraph_neighbours(V,Vertices,Children0),
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(
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del_me(Children0,V,Children)
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->
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true
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;
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Children = Children0
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).
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wundgraph_wneighbours(V,Vertices,Children) :-
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wdgraph_wneighbours(V,Vertices,Children0),
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(
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wdel_me(Children0,V,Children)
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->
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true
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;
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Children = Children0
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).
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wundgraph_wneighbors(V,Vertices,Children) :-
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wdgraph_wneighbours(V,Vertices,Children0),
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(
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wdel_me(Children0,V,Children)
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->
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true
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;
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Children = Children0
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).
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del_me([], _, []).
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del_me([K|Children], K1, NewChildren) :-
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( K == K1 ->
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Children = NewChildren
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;
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K @< K1 ->
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NewChildren = [K|ChildrenLeft],
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del_me(Children, K1, ChildrenLeft)
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;
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NewChildren = [K|MoreChildren],
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compact(Children, MoreChildren)
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).
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wdel_me([], _, []).
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wdel_me([K-A|Children], K1, NewChildren) :-
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( K == K1 ->
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Children = NewChildren
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;
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K @< K1 ->
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NewChildren = [K-A|ChildrenLeft],
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wdel_me(Children, K1, ChildrenLeft)
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;
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NewChildren = [K-A|MoreChildren],
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compact(Children, MoreChildren)
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).
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wundgraph_del_edge(Vs0,V1,V2,K,VsF) :-
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wdgraph_del_edge(Vs0,V1,V2,K,Vs1),
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wdgraph_del_edge(Vs1,V2,V1,K,VsF).
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wundgraph_del_edges(G0, Edges, GF) :-
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dup_edges(Edges,DupEdges),
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wdgraph_del_edges(G0, DupEdges, GF).
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wundgraph_del_vertex(Vs0, V, Vsf) :-
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rb_delete(Vs0, V, BackEdges, Vsi),
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del_and_compact(BackEdges,V,BackVertices),
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rb_partial_map(Vsi, BackVertices, del_edge(V), Vsf).
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del_and_compact([], _, []).
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del_and_compact([K-_|Children], K1, NewChildren) :-
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( K == K1 ->
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compact(Children, NewChildren)
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;
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K @< K1 ->
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NewChildren = [K|ChildrenLeft],
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del_and_compact(Children, K1, ChildrenLeft)
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;
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NewChildren = [K|CompactChildren],
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compact(Children, CompactChildren)
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).
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compact([], []).
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compact([K-_|Children], [K|CompactChildren]) :-
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compact(Children, CompactChildren).
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del_edge(_, [], []).
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del_edge(K1, [K-W|Children], NewChildren) :-
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( K == K1 ->
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Children = NewChildren
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;
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K @< K1 ->
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NewChildren = [K-W|ChildrenLeft],
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del_edge(K1, Children, ChildrenLeft)
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;
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NewChildren = [K-W|Children]
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).
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wundgraph_to_wdgraph(G, G).
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% simplistic algorithm to build a minimal spanning tree.
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% Just sort edges and then walk over each one.
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wundgraph_min_tree(G, T, C) :-
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rb_visit(G, Els0),
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generate_min_tree(Els0, T, C).
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generate_min_tree([], T, 0) :- !,
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wundgraph_new(T).
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generate_min_tree([El-_], T, 0) :- !,
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wundgraph_new(T0),
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wundgraph_add_vertex(T0, El, T).
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generate_min_tree(Els0, T, C) :-
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mk_list_of_edges(Els0, Edges),
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keysort(Edges, SortedEdges),
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rb_new(V0),
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rb_new(T0),
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add_sorted_edges(SortedEdges, V0, TreeEdges, 0, C),
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wundgraph_add_edges(T0, TreeEdges, T).
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wundgraph_max_tree(G, T, C) :-
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rb_visit(G, Els0),
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generate_max_tree(Els0, T, C).
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generate_max_tree([], T, 0) :- !,
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wundgraph_new(T).
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generate_max_tree([El-_], T, 0) :- !,
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wundgraph_new(T0),
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wundgraph_add_vertex(T0, El, T).
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generate_max_tree(Els0, T, C) :-
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mk_list_of_edges(Els0, Edges),
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keysort(Edges, SortedEdges),
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reverse(SortedEdges, ReversedEdges),
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rb_new(V0),
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rb_new(T0),
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add_sorted_edges(ReversedEdges, V0, TreeEdges, 0, C),
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wundgraph_add_edges(T0, TreeEdges, T).
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mk_list_of_edges([], []).
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mk_list_of_edges([V-Els|Els0], Edges) :-
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add_neighbs(Els, V, Edges, Edges0),
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mk_list_of_edges(Els0, Edges0).
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add_neighbs([], _, Edges, Edges).
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add_neighbs([V-W|Els], V0, [W-(V0-V)|Edges], Edges0) :-
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V0 @< V, !,
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add_neighbs(Els, V0, Edges, Edges0).
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add_neighbs([_|Els], V0, Edges, Edges0) :-
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add_neighbs(Els, V0, Edges, Edges0).
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add_sorted_edges([], _, [], C, C).
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add_sorted_edges([W-(V0-V)|SortedEdges], T0, NewTreeEdges, C0, C) :-
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( rb_lookup(V0, Component, T0) ->
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( rb_lookup(V, Component1, T0) ->
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( Component \== Component1 ->
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/* edge that links two separate sub-trees (components) */
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Component = Component1,
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Ti = T0
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;
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/* same component, can't add edge */
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fail
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)
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;
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/* V is new */
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rb_insert(T0, V, Component, Ti)
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)
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;
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( rb_lookup(V, Component1, T0) ->
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/* V0 is new */
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rb_insert(T0, V0, Component1, Ti)
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;
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/* new edges, new tree */
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rb_insert(T0, V0, NewComponent, T1),
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rb_insert(T1, V, NewComponent, Ti)
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)
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),
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!,
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NewTreeEdges = [(V0-(V-W)),(V-(V0-W))|TreeEdges],
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Ci is C0+W,
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add_sorted_edges(SortedEdges, Ti, TreeEdges, Ci, C).
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add_sorted_edges([_|SortedEdges], T0, NewTreeEdges, C0, C) :-
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add_sorted_edges(SortedEdges, T0, NewTreeEdges, C0, C).
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