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yap-6.3/library/wundgraphs.yap
Vitor Santos Costa faf3c930c8 docs
2017-04-07 23:10:59 +01:00

295 lines
7.0 KiB
Prolog

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