Compatible Doclog docs for library(ugraphs)
This commit is contained in:
Adrián Arroyo Calle
@@ -53,7 +53,7 @@
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connect_ugraph/3 % +Graph1, -Start, -Graph
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connect_ugraph/3 % +Graph1, -Start, -Graph
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]).
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]).
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/** <module> Graph manipulation library
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/** Graph manipulation library
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The S-representation of a graph is a list of (vertex-neighbours) pairs,
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The S-representation of a graph is a list of (vertex-neighbours) pairs,
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where the pairs are in standard order (as produced by keysort) and the
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where the pairs are in standard order (as produced by keysort) and the
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@@ -61,55 +61,50 @@ neighbours of each vertex are also in standard order (as produced by
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sort). This form is convenient for many calculations.
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sort). This form is convenient for many calculations.
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A new UGraph from raw data can be created using
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A new UGraph from raw data can be created using
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vertices_edges_to_ugraph/3.
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vertices\_edges\_to\_ugraph/3.
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Adapted to support some of the functionality of the SICStus ugraphs
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Adapted to support some of the functionality of the SICStus ugraphs
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library by Vitor Santos Costa.
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library by Vitor Santos Costa.
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Ported from YAP 5.0.1 to SWI-Prolog by Jan Wielemaker.
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Ported from YAP 5.0.1 to SWI-Prolog by Jan Wielemaker.
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@author R.A.O'Keefe
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Ported from SWI-Prolog to Scryer by Adrián Arroyo Calle
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@author Vitor Santos Costa
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@author Jan Wielemaker
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License: BSD-2 or Artistic 2.0
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@license BSD-2 or Artistic 2.0
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*/
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*/
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:- use_module(library(lists)).
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:- use_module(library(lists)).
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:- use_module(library(pairs)).
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:- use_module(library(pairs)).
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:- use_module(library(ordsets)).
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:- use_module(library(ordsets)).
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%! vertices(+Graph, -Vertices)
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%% vertices(+Graph, -Vertices)
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%
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%
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% Unify Vertices with all vertices appearing in Graph. Example:
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% Unify Vertices with all vertices appearing in Graph. Example:
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%
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%
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% ?- vertices([1-[3,5],2-[4],3-[],4-[5],5-[]], L).
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% ?- vertices([1-[3,5],2-[4],3-[],4-[5],5-[]], L).
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% L = [1, 2, 3, 4, 5]
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% L = [1, 2, 3, 4, 5]
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vertices([], []) :- !.
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vertices([], []) :- !.
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vertices([Vertex-_|Graph], [Vertex|Vertices]) :-
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vertices([Vertex-_|Graph], [Vertex|Vertices]) :-
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vertices(Graph, Vertices).
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vertices(Graph, Vertices).
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%! vertices_edges_to_ugraph(+Vertices, +Edges, -UGraph) is det.
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%% vertices_edges_to_ugraph(+Vertices, +Edges, -UGraph) is det.
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%
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%
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% Create a UGraph from Vertices and edges. Given a graph with a
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% Create a UGraph from Vertices and edges. Given a graph with a
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% set of Vertices and a set of Edges, Graph must unify with the
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% set of Vertices and a set of Edges, Graph must unify with the
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% corresponding S-representation. Note that the vertices without
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% corresponding S-representation. Note that the vertices without
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% edges will appear in Vertices but not in Edges. Moreover, it is
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% edges will appear in Vertices but not in Edges. Moreover, it is
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% sufficient for a vertice to appear in Edges.
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% sufficient for a vertice to appear in Edges.
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%
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%
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% ==
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% ?- vertices_edges_to_ugraph([],[1-3,2-4,4-5,1-5], L).
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% ?- vertices_edges_to_ugraph([],[1-3,2-4,4-5,1-5], L).
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% L = [1-[3,5], 2-[4], 3-[], 4-[5], 5-[]]
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% L = [1-[3,5], 2-[4], 3-[], 4-[5], 5-[]]
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% ==
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%
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%
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% In this case all vertices are defined implicitly. The next
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% In this case all vertices are defined implicitly. The next
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% example shows three unconnected vertices:
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% example shows three unconnected vertices:
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%
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%
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% ==
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% ?- vertices_edges_to_ugraph([6,7,8],[1-3,2-4,4-5,1-5], L).
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% ?- vertices_edges_to_ugraph([6,7,8],[1-3,2-4,4-5,1-5], L).
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% L = [1-[3,5], 2-[4], 3-[], 4-[5], 5-[], 6-[], 7-[], 8-[]]
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% L = [1-[3,5], 2-[4], 3-[], 4-[5], 5-[], 6-[], 7-[], 8-[]]
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% ==
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vertices_edges_to_ugraph(Vertices, Edges, Graph) :-
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vertices_edges_to_ugraph(Vertices, Edges, Graph) :-
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sort(Edges, EdgeSet),
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sort(Edges, EdgeSet),
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@@ -119,15 +114,13 @@ vertices_edges_to_ugraph(Vertices, Edges, Graph) :-
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p_to_s_group(VertexSet, EdgeSet, Graph).
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p_to_s_group(VertexSet, EdgeSet, Graph).
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%! add_vertices(+Graph, +Vertices, -NewGraph)
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%% add_vertices(+Graph, +Vertices, -NewGraph)
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%
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%
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% Unify NewGraph with a new graph obtained by adding the list of
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% Unify NewGraph with a new graph obtained by adding the list of
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% Vertices to Graph. Example:
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% Vertices to Graph. Example:
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%
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%
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% ```
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% ?- add_vertices([1-[3,5],2-[]], [0,1,2,9], NG).
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% ?- add_vertices([1-[3,5],2-[]], [0,1,2,9], NG).
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% NG = [0-[], 1-[3,5], 2-[], 9-[]]
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% NG = [0-[], 1-[3,5], 2-[], 9-[]]
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% ```
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% replace with real msort/2 when available
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% replace with real msort/2 when available
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msort_(List, Sorted) :-
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msort_(List, Sorted) :-
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@@ -159,23 +152,16 @@ add_empty_vertices([], []).
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add_empty_vertices([V|G], [V-[]|NG]) :-
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add_empty_vertices([V|G], [V-[]|NG]) :-
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add_empty_vertices(G, NG).
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add_empty_vertices(G, NG).
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%! del_vertices(+Graph, +Vertices, -NewGraph) is det.
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%% del_vertices(+Graph, +Vertices, -NewGraph) is det.
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%
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%
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% Unify NewGraph with a new graph obtained by deleting the list of
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% Unify NewGraph with a new graph obtained by deleting the list of
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% Vertices and all the edges that start from or go to a vertex in
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% Vertices and all the edges that start from or go to a vertex in
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% Vertices to the Graph. Example:
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% Vertices to the Graph. Example:
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%
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%
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% ==
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% ?- del_vertices([1-[3,5],2-[4],3-[],4-[5],5-[],6-[],7-[2,6],8-[]],
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% ?- del_vertices([1-[3,5],2-[4],3-[],4-[5],5-[],6-[],7-[2,6],8-[]],
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% [2,1],
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% [2,1],
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% NL).
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% NL).
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% NL = [3-[],4-[5],5-[],6-[],7-[6],8-[]]
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% NL = [3-[],4-[5],5-[],6-[],7-[6],8-[]]
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% ==
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%
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% @compat Upto 5.6.48 the argument order was (+Vertices, +Graph,
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% -NewGraph). Both YAP and SWI-Prolog have changed the argument
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% order for compatibility with recent SICStus as well as
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% consistency with del_edges/3.
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del_vertices(Graph, Vertices, NewGraph) :-
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del_vertices(Graph, Vertices, NewGraph) :-
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sort(Vertices, V1), % JW: was msort
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sort(Vertices, V1), % JW: was msort
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@@ -204,32 +190,28 @@ split_on_del_vertices(>, V, Edges, [_|Vs], Vs, V1, [V-NEdges|NG], NG) :-
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ord_subtract(Edges, V1, NEdges).
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ord_subtract(Edges, V1, NEdges).
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split_on_del_vertices(=, _, _, [_|Vs], Vs, _, NG, NG).
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split_on_del_vertices(=, _, _, [_|Vs], Vs, _, NG, NG).
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%! add_edges(+Graph, +Edges, -NewGraph)
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%% add_edges(+Graph, +Edges, -NewGraph)
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%
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%
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% Unify NewGraph with a new graph obtained by adding the list of Edges
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% Unify NewGraph with a new graph obtained by adding the list of Edges
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% to Graph. Example:
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% to Graph. Example:
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%
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%
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% ```
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% ?- add_edges([1-[3,5],2-[4],3-[],4-[5],
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% ?- add_edges([1-[3,5],2-[4],3-[],4-[5],
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% 5-[],6-[],7-[],8-[]],
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% 5-[],6-[],7-[],8-[]],
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% [1-6,2-3,3-2,5-7,3-2,4-5],
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% [1-6,2-3,3-2,5-7,3-2,4-5],
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% NL).
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% NL).
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% NL = [1-[3,5,6], 2-[3,4], 3-[2], 4-[5],
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% NL = [1-[3,5,6], 2-[3,4], 3-[2], 4-[5],
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% 5-[7], 6-[], 7-[], 8-[]]
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% 5-[7], 6-[], 7-[], 8-[]]
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% ```
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add_edges(Graph, Edges, NewGraph) :-
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add_edges(Graph, Edges, NewGraph) :-
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p_to_s_graph(Edges, G1),
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p_to_s_graph(Edges, G1),
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ugraph_union(Graph, G1, NewGraph).
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ugraph_union(Graph, G1, NewGraph).
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%! ugraph_union(+Graph1, +Graph2, -NewGraph)
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%% ugraph_union(+Graph1, +Graph2, -NewGraph)
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%
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%
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% NewGraph is the union of Graph1 and Graph2. Example:
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% NewGraph is the union of Graph1 and Graph2. Example:
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%
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%
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% ```
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% ?- ugraph_union([1-[2],2-[3]],[2-[4],3-[1,2,4]],L).
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% ?- ugraph_union([1-[2],2-[3]],[2-[4],3-[1,2,4]],L).
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% L = [1-[2], 2-[3,4], 3-[1,2,4]]
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% L = [1-[2], 2-[3,4], 3-[1,2,4]]
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% ```
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ugraph_union(Set1, [], Set1) :- !.
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ugraph_union(Set1, [], Set1) :- !.
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ugraph_union([], Set2, Set2) :- !.
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ugraph_union([], Set2, Set2) :- !.
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@@ -245,25 +227,23 @@ ugraph_union(<, Head1, Tail1, Head2, Tail2, [Head1|Union]) :-
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ugraph_union(>, Head1, Tail1, Head2, Tail2, [Head2|Union]) :-
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ugraph_union(>, Head1, Tail1, Head2, Tail2, [Head2|Union]) :-
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ugraph_union([Head1|Tail1], Tail2, Union).
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ugraph_union([Head1|Tail1], Tail2, Union).
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%! del_edges(+Graph, +Edges, -NewGraph)
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%% del_edges(+Graph, +Edges, -NewGraph)
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%
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%
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% Unify NewGraph with a new graph obtained by removing the list of
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% Unify NewGraph with a new graph obtained by removing the list of
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% Edges from Graph. Notice that no vertices are deleted. Example:
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% Edges from Graph. Notice that no vertices are deleted. Example:
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%
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%
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% ```
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% ?- del_edges([1-[3,5],2-[4],3-[],4-[5],5-[],6-[],7-[],8-[]],
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% ?- del_edges([1-[3,5],2-[4],3-[],4-[5],5-[],6-[],7-[],8-[]],
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% [1-6,2-3,3-2,5-7,3-2,4-5,1-3],
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% [1-6,2-3,3-2,5-7,3-2,4-5,1-3],
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% NL).
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% NL).
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% NL = [1-[5],2-[4],3-[],4-[],5-[],6-[],7-[],8-[]]
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% NL = [1-[5],2-[4],3-[],4-[],5-[],6-[],7-[],8-[]]
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% ```
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del_edges(Graph, Edges, NewGraph) :-
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del_edges(Graph, Edges, NewGraph) :-
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p_to_s_graph(Edges, G1),
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p_to_s_graph(Edges, G1),
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graph_subtract(Graph, G1, NewGraph).
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graph_subtract(Graph, G1, NewGraph).
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%! graph_subtract(+Set1, +Set2, ?Difference)
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%% graph_subtract(+Set1, +Set2, ?Difference)
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%
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%
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% Is based on ord_subtract
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% Is based on ord_subtract
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graph_subtract(Set1, [], Set1) :- !.
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graph_subtract(Set1, [], Set1) :- !.
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graph_subtract([], _, []).
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graph_subtract([], _, []).
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@@ -279,12 +259,12 @@ graph_subtract(<, Head1, Tail1, Head2, Tail2, [Head1|Difference]) :-
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graph_subtract(>, Head1, Tail1, _, Tail2, Difference) :-
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graph_subtract(>, Head1, Tail1, _, Tail2, Difference) :-
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graph_subtract([Head1|Tail1], Tail2, Difference).
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graph_subtract([Head1|Tail1], Tail2, Difference).
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%! edges(+Graph, -Edges)
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%% edges(+Graph, -Edges)
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%
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%
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% Unify Edges with all edges appearing in Graph. Example:
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% Unify Edges with all edges appearing in Graph. Example:
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%
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%
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% ?- edges([1-[3,5],2-[4],3-[],4-[5],5-[]], L).
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% ?- edges([1-[3,5],2-[4],3-[],4-[5],5-[]], L).
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% L = [1-3, 1-5, 2-4, 4-5]
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% L = [1-3, 1-5, 2-4, 4-5]
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edges(Graph, Edges) :-
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edges(Graph, Edges) :-
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s_to_p_graph(Graph, Edges).
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s_to_p_graph(Graph, Edges).
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@@ -324,15 +304,13 @@ s_to_p_graph([], _, P_Graph, P_Graph) :- !.
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s_to_p_graph([Neib|Neibs], Vertex, [Vertex-Neib|P], Rest_P) :-
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s_to_p_graph([Neib|Neibs], Vertex, [Vertex-Neib|P], Rest_P) :-
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s_to_p_graph(Neibs, Vertex, P, Rest_P).
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s_to_p_graph(Neibs, Vertex, P, Rest_P).
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%! transitive_closure(+Graph, -Closure)
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%% transitive_closure(+Graph, -Closure)
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%
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%
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% Generate the graph Closure as the transitive closure of Graph.
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% Generate the graph Closure as the transitive closure of Graph.
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% Example:
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% Example:
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%
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%
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% ```
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% ?- transitive_closure([1-[2,3],2-[4,5],4-[6]],L).
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% ?- transitive_closure([1-[2,3],2-[4,5],4-[6]],L).
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% L = [1-[2,3,4,5,6], 2-[4,5,6], 4-[6]]
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% L = [1-[2,3,4,5,6], 2-[4,5,6], 4-[6]]
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% ```
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transitive_closure(Graph, Closure) :-
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transitive_closure(Graph, Closure) :-
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warshall(Graph, Graph, Closure).
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warshall(Graph, Graph, Closure).
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@@ -354,23 +332,16 @@ warshall([X-Neibs|G], V, Y, [X-Neibs|NewG]) :-
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warshall(G, V, Y, NewG).
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warshall(G, V, Y, NewG).
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warshall([], _, _, []).
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warshall([], _, _, []).
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%! transpose_ugraph(Graph, NewGraph) is det.
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%% transpose_ugraph(Graph, NewGraph) is det.
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%
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%
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% Unify NewGraph with a new graph obtained from Graph by replacing
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% Unify NewGraph with a new graph obtained from Graph by replacing
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% all edges of the form V1-V2 by edges of the form V2-V1. The cost
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% all edges of the form V1-V2 by edges of the form V2-V1. The cost
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% is O(|V|*log(|V|)). Notice that an undirected graph is its own
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% is O(|V|*log(|V|)). Notice that an undirected graph is its own
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% transpose. Example:
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% transpose. Example:
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%
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%
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% ==
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% ?- transpose([1-[3,5],2-[4],3-[],4-[5],
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% ?- transpose([1-[3,5],2-[4],3-[],4-[5],
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% 5-[],6-[],7-[],8-[]], NL).
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% 5-[],6-[],7-[],8-[]], NL).
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% NL = [1-[],2-[],3-[1],4-[2],5-[1,4],6-[],7-[],8-[]]
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% NL = [1-[],2-[],3-[1],4-[2],5-[1,4],6-[],7-[],8-[]]
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% ==
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%
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% @compat This predicate used to be known as transpose/2.
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% Following SICStus 4, we reserve transpose/2 for matrix
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% transposition and renamed ugraph transposition to
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% transpose_ugraph/2.
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transpose_ugraph(Graph, NewGraph) :-
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transpose_ugraph(Graph, NewGraph) :-
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edges(Graph, Edges),
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edges(Graph, Edges),
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@@ -382,13 +353,13 @@ flip_edges([], []).
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flip_edges([Key-Val|Pairs], [Val-Key|Flipped]) :-
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flip_edges([Key-Val|Pairs], [Val-Key|Flipped]) :-
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flip_edges(Pairs, Flipped).
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flip_edges(Pairs, Flipped).
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%! compose(+LeftGraph, +RightGraph, -NewGraph)
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%% compose(+LeftGraph, +RightGraph, -NewGraph)
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%
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%
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% Compose NewGraph by connecting the _drains_ of LeftGraph to the
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% Compose NewGraph by connecting the _drains_ of LeftGraph to the
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% _sources_ of RightGraph. Example:
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% _sources_ of RightGraph. Example:
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%
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%
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% ?- compose([1-[2],2-[3]],[2-[4],3-[1,2,4]],L).
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% ?- compose([1-[2],2-[3]],[2-[4],3-[1,2,4]],L).
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% L = [1-[4], 2-[1,2,4], 3-[]]
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% L = [1-[4], 2-[1,2,4], 3-[]]
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compose(G1, G2, Composition) :-
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compose(G1, G2, Composition) :-
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vertices(G1, V1),
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vertices(G1, V1),
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@@ -423,21 +394,15 @@ compose1(=, V1, Vs1, V1, N2, G2, SoFar, Comp) :-
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ord_union(N2, SoFar, Next),
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ord_union(N2, SoFar, Next),
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compose1(Vs1, G2, Next, Comp).
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compose1(Vs1, G2, Next, Comp).
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%! top_sort(+Graph, -Sorted) is semidet.
|
%% top_sort(+Graph, -Sorted) is semidet.
|
||||||
%! top_sort(+Graph, -Sorted, ?Tail) is semidet.
|
|
||||||
%
|
%
|
||||||
% Sorted is a topological sorted list of nodes in Graph. A
|
% Sorted is a topological sorted list of nodes in Graph. A
|
||||||
% toplogical sort is possible if the graph is connected and
|
% toplogical sort is possible if the graph is connected and
|
||||||
% acyclic. In the example we show how topological sorting works
|
% acyclic. In the example we show how topological sorting works
|
||||||
% for a linear graph:
|
% for a linear graph:
|
||||||
%
|
%
|
||||||
% ==
|
% ?- top_sort([1-[2], 2-[3], 3-[]], L).
|
||||||
% ?- top_sort([1-[2], 2-[3], 3-[]], L).
|
% L = [1, 2, 3]
|
||||||
% L = [1, 2, 3]
|
|
||||||
% ==
|
|
||||||
%
|
|
||||||
% The predicate top_sort/3 is a difference list version of
|
|
||||||
% top_sort/2.
|
|
||||||
|
|
||||||
top_sort(Graph, Sorted) :-
|
top_sort(Graph, Sorted) :-
|
||||||
vertices_and_zeros(Graph, Vertices, Counts0),
|
vertices_and_zeros(Graph, Vertices, Counts0),
|
||||||
@@ -445,6 +410,11 @@ top_sort(Graph, Sorted) :-
|
|||||||
select_zeros(Counts1, Vertices, Zeros),
|
select_zeros(Counts1, Vertices, Zeros),
|
||||||
top_sort(Zeros, Sorted, Graph, Vertices, Counts1).
|
top_sort(Zeros, Sorted, Graph, Vertices, Counts1).
|
||||||
|
|
||||||
|
%% top_sort(+Graph, -Sorted, ?Tail) is semidet.
|
||||||
|
%
|
||||||
|
% The predicate top\_sort/3 is a difference list version of
|
||||||
|
% top\_sort/2.
|
||||||
|
|
||||||
top_sort(Graph, Sorted0, Sorted) :-
|
top_sort(Graph, Sorted0, Sorted) :-
|
||||||
vertices_and_zeros(Graph, Vertices, Counts0),
|
vertices_and_zeros(Graph, Vertices, Counts0),
|
||||||
count_edges(Graph, Vertices, Counts0, Counts1),
|
count_edges(Graph, Vertices, Counts0, Counts1),
|
||||||
@@ -520,17 +490,19 @@ decr_list(Neibs, [_|Vertices], [N|Counts1], [N|Counts2], Zi, Zo) :-
|
|||||||
decr_list(Neibs, Vertices, Counts1, Counts2, Zi, Zo).
|
decr_list(Neibs, Vertices, Counts1, Counts2, Zi, Zo).
|
||||||
|
|
||||||
|
|
||||||
%! neighbors(+Vertex, +Graph, -Neigbours) is det.
|
|
||||||
%! neighbours(+Vertex, +Graph, -Neigbours) is det.
|
%% neighbours(+Vertex, +Graph, -Neigbours) is det.
|
||||||
%
|
%
|
||||||
% Neigbours is a sorted list of the neighbours of Vertex in Graph.
|
% Neigbours is a sorted list of the neighbours of Vertex in Graph.
|
||||||
% Example:
|
% Example:
|
||||||
%
|
%
|
||||||
% ```
|
% ?- neighbours(4,[1-[3,5],2-[4],3-[],
|
||||||
% ?- neighbours(4,[1-[3,5],2-[4],3-[],
|
|
||||||
% 4-[1,2,7,5],5-[],6-[],7-[],8-[]], NL).
|
% 4-[1,2,7,5],5-[],6-[],7-[],8-[]], NL).
|
||||||
% NL = [1,2,7,5]
|
% NL = [1,2,7,5]
|
||||||
% ```
|
|
||||||
|
%% neighbors(+Vertex, +Graph, -Neigbours) is det.
|
||||||
|
%
|
||||||
|
% Same as neighbours/3
|
||||||
|
|
||||||
neighbors(Vertex, Graph, Neig) :-
|
neighbors(Vertex, Graph, Neig) :-
|
||||||
neighbours(Vertex, Graph, Neig).
|
neighbours(Vertex, Graph, Neig).
|
||||||
@@ -542,24 +514,22 @@ neighbours(V,[_|G],Neig) :-
|
|||||||
neighbours(V,G,Neig).
|
neighbours(V,G,Neig).
|
||||||
|
|
||||||
|
|
||||||
%! connect_ugraph(+UGraphIn, -Start, -UGraphOut) is det.
|
%% connect_ugraph(+UGraphIn, -Start, -UGraphOut) is det.
|
||||||
%
|
%
|
||||||
% Adds Start as an additional vertex that is connected to all vertices
|
% Adds Start as an additional vertex that is connected to all vertices
|
||||||
% in UGraphIn. This can be used to create an topological sort for a
|
% in UGraphIn. This can be used to create an topological sort for a
|
||||||
% not connected graph. Start is before any vertex in UGraphIn in the
|
% not connected graph. Start is before any vertex in UGraphIn in the
|
||||||
% standard order of terms. No vertex in UGraphIn can be a variable.
|
% standard order of terms. No vertex in UGraphIn can be a variable.
|
||||||
%
|
%
|
||||||
% Can be used to order a not-connected graph as follows:
|
% Can be used to order a not-connected graph as follows:
|
||||||
%
|
%
|
||||||
% ```
|
% top_sort_unconnected(Graph, Vertices) :-
|
||||||
% top_sort_unconnected(Graph, Vertices) :-
|
|
||||||
% ( top_sort(Graph, Vertices)
|
% ( top_sort(Graph, Vertices)
|
||||||
% -> true
|
% -> true
|
||||||
% ; connect_ugraph(Graph, Start, Connected),
|
% ; connect_ugraph(Graph, Start, Connected),
|
||||||
% top_sort(Connected, Ordered0),
|
% top_sort(Connected, Ordered0),
|
||||||
% Ordered0 = [Start|Vertices]
|
% Ordered0 = [Start|Vertices]
|
||||||
% ).
|
% ).
|
||||||
% ```
|
|
||||||
|
|
||||||
connect_ugraph([], 0, []) :- !.
|
connect_ugraph([], 0, []) :- !.
|
||||||
connect_ugraph(Graph, Start, [Start-Vertices|Graph]) :-
|
connect_ugraph(Graph, Start, [Start-Vertices|Graph]) :-
|
||||||
@@ -567,12 +537,12 @@ connect_ugraph(Graph, Start, [Start-Vertices|Graph]) :-
|
|||||||
Vertices = [First|_],
|
Vertices = [First|_],
|
||||||
before(First, Start).
|
before(First, Start).
|
||||||
|
|
||||||
%! before(+Term, -Before) is det.
|
%% before(+Term, -Before) is det.
|
||||||
%
|
%
|
||||||
% Unify Before to a term that comes before Term in the standard
|
% Unify Before to a term that comes before Term in the standard
|
||||||
% order of terms.
|
% order of terms.
|
||||||
%
|
%
|
||||||
% @error instantiation_error if Term is unbound.
|
% Throws instantiation_error if Term is unbound.
|
||||||
|
|
||||||
before(X, _) :-
|
before(X, _) :-
|
||||||
var(X),
|
var(X),
|
||||||
@@ -585,21 +555,21 @@ before(Number, Start) :-
|
|||||||
before(_, 0).
|
before(_, 0).
|
||||||
|
|
||||||
|
|
||||||
%! complement(+UGraphIn, -UGraphOut)
|
%% complement(+UGraphIn, -UGraphOut)
|
||||||
%
|
%
|
||||||
% UGraphOut is a ugraph with an edge between all vertices that are
|
% UGraphOut is a ugraph with an edge between all vertices that are
|
||||||
% _not_ connected in UGraphIn and all edges from UGraphIn removed.
|
% _not_ connected in UGraphIn and all edges from UGraphIn removed.
|
||||||
% Example:
|
% Example:
|
||||||
%
|
%
|
||||||
% ```
|
% ?- complement([1-[3,5],2-[4],3-[],
|
||||||
% ?- complement([1-[3,5],2-[4],3-[],
|
|
||||||
% 4-[1,2,7,5],5-[],6-[],7-[],8-[]], NL).
|
% 4-[1,2,7,5],5-[],6-[],7-[],8-[]], NL).
|
||||||
% NL = [1-[2,4,6,7,8],2-[1,3,5,6,7,8],3-[1,2,4,5,6,7,8],
|
% NL = [1-[2,4,6,7,8],2-[1,3,5,6,7,8],3-[1,2,4,5,6,7,8],
|
||||||
% 4-[3,5,6,8],5-[1,2,3,4,6,7,8],6-[1,2,3,4,5,7,8],
|
% 4-[3,5,6,8],5-[1,2,3,4,6,7,8],6-[1,2,3,4,5,7,8],
|
||||||
% 7-[1,2,3,4,5,6,8],8-[1,2,3,4,5,6,7]]
|
% 7-[1,2,3,4,5,6,8],8-[1,2,3,4,5,6,7]]
|
||||||
% ```
|
|
||||||
%
|
%
|
||||||
% @tbd Simple two-step algorithm. You could be smarter, I suppose.
|
|
||||||
|
|
||||||
|
% TODO: Simple two-step algorithm. You could be smarter, I suppose.
|
||||||
|
|
||||||
complement(G, NG) :-
|
complement(G, NG) :-
|
||||||
vertices(G,Vs),
|
vertices(G,Vs),
|
||||||
@@ -611,13 +581,13 @@ complement([V-Ns|G], Vs, [V-INs|NG]) :-
|
|||||||
ord_subtract(Vs,Ns1,INs),
|
ord_subtract(Vs,Ns1,INs),
|
||||||
complement(G, Vs, NG).
|
complement(G, Vs, NG).
|
||||||
|
|
||||||
%! reachable(+Vertex, +UGraph, -Vertices)
|
%% reachable(+Vertex, +UGraph, -Vertices)
|
||||||
%
|
%
|
||||||
% True when Vertices is an ordered set of vertices reachable in
|
% True when Vertices is an ordered set of vertices reachable in
|
||||||
% UGraph, including Vertex. Example:
|
% UGraph, including Vertex. Example:
|
||||||
%
|
%
|
||||||
% ?- reachable(1,[1-[3,5],2-[4],3-[],4-[5],5-[]],V).
|
% ?- reachable(1,[1-[3,5],2-[4],3-[],4-[5],5-[]],V).
|
||||||
% V = [1, 3, 5]
|
% V = [1, 3, 5]
|
||||||
|
|
||||||
reachable(N, G, Rs) :-
|
reachable(N, G, Rs) :-
|
||||||
reachable([N], G, [N], Rs).
|
reachable([N], G, [N], Rs).
|
||||||
|
|||||||
Reference in New Issue
Block a user