connect_ugraph/3 % +Graph1, -Start, -Graph
]).
-/** <module> Graph manipulation library
+/** Graph manipulation library
The S-representation of a graph is a list of (vertex-neighbours) pairs,
where the pairs are in standard order (as produced by keysort) and the
sort). This form is convenient for many calculations.
A new UGraph from raw data can be created using
-vertices_edges_to_ugraph/3.
+vertices\_edges\_to\_ugraph/3.
Adapted to support some of the functionality of the SICStus ugraphs
library by Vitor Santos Costa.
Ported from YAP 5.0.1 to SWI-Prolog by Jan Wielemaker.
-@author R.A.O'Keefe
-@author Vitor Santos Costa
-@author Jan Wielemaker
-@license BSD-2 or Artistic 2.0
+Ported from SWI-Prolog to Scryer by Adrián Arroyo Calle
+
+License: BSD-2 or Artistic 2.0
*/
:- use_module(library(lists)).
:- use_module(library(pairs)).
:- use_module(library(ordsets)).
-%! vertices(+Graph, -Vertices)
+%% vertices(+Graph, -Vertices)
%
-% Unify Vertices with all vertices appearing in Graph. Example:
+% Unify Vertices with all vertices appearing in Graph. Example:
%
-% ?- vertices([1-[3,5],2-[4],3-[],4-[5],5-[]], L).
-% L = [1, 2, 3, 4, 5]
+% ?- vertices([1-[3,5],2-[4],3-[],4-[5],5-[]], L).
+% L = [1, 2, 3, 4, 5]
vertices([], []) :- !.
vertices([Vertex-_|Graph], [Vertex|Vertices]) :-
vertices(Graph, Vertices).
-%! vertices_edges_to_ugraph(+Vertices, +Edges, -UGraph) is det.
+%% vertices_edges_to_ugraph(+Vertices, +Edges, -UGraph) is det.
%
-% Create a UGraph from Vertices and edges. Given a graph with a
-% set of Vertices and a set of Edges, Graph must unify with the
-% corresponding S-representation. Note that the vertices without
-% edges will appear in Vertices but not in Edges. Moreover, it is
-% sufficient for a vertice to appear in Edges.
+% Create a UGraph from Vertices and edges. Given a graph with a
+% set of Vertices and a set of Edges, Graph must unify with the
+% corresponding S-representation. Note that the vertices without
+% edges will appear in Vertices but not in Edges. Moreover, it is
+% sufficient for a vertice to appear in Edges.
%
-% ==
-% ?- vertices_edges_to_ugraph([],[1-3,2-4,4-5,1-5], L).
-% L = [1-[3,5], 2-[4], 3-[], 4-[5], 5-[]]
-% ==
+% ?- vertices_edges_to_ugraph([],[1-3,2-4,4-5,1-5], L).
+% L = [1-[3,5], 2-[4], 3-[], 4-[5], 5-[]]
%
-% In this case all vertices are defined implicitly. The next
-% example shows three unconnected vertices:
+% In this case all vertices are defined implicitly. The next
+% example shows three unconnected vertices:
%
-% ==
-% ?- vertices_edges_to_ugraph([6,7,8],[1-3,2-4,4-5,1-5], L).
-% L = [1-[3,5], 2-[4], 3-[], 4-[5], 5-[], 6-[], 7-[], 8-[]]
-% ==
+% ?- vertices_edges_to_ugraph([6,7,8],[1-3,2-4,4-5,1-5], L).
+% L = [1-[3,5], 2-[4], 3-[], 4-[5], 5-[], 6-[], 7-[], 8-[]]
vertices_edges_to_ugraph(Vertices, Edges, Graph) :-
sort(Edges, EdgeSet),
p_to_s_group(VertexSet, EdgeSet, Graph).
-%! add_vertices(+Graph, +Vertices, -NewGraph)
+%% add_vertices(+Graph, +Vertices, -NewGraph)
%
-% Unify NewGraph with a new graph obtained by adding the list of
-% Vertices to Graph. Example:
+% Unify NewGraph with a new graph obtained by adding the list of
+% Vertices to Graph. Example:
%
-% ```
-% ?- add_vertices([1-[3,5],2-[]], [0,1,2,9], NG).
-% NG = [0-[], 1-[3,5], 2-[], 9-[]]
-% ```
+% ?- add_vertices([1-[3,5],2-[]], [0,1,2,9], NG).
+% NG = [0-[], 1-[3,5], 2-[], 9-[]]
% replace with real msort/2 when available
msort_(List, Sorted) :-
add_empty_vertices([V|G], [V-[]|NG]) :-
add_empty_vertices(G, NG).
-%! del_vertices(+Graph, +Vertices, -NewGraph) is det.
+%% del_vertices(+Graph, +Vertices, -NewGraph) is det.
%
-% Unify NewGraph with a new graph obtained by deleting the list of
-% Vertices and all the edges that start from or go to a vertex in
-% Vertices to the Graph. Example:
+% Unify NewGraph with a new graph obtained by deleting the list of
+% Vertices and all the edges that start from or go to a vertex in
+% Vertices to the Graph. Example:
%
-% ==
-% ?- del_vertices([1-[3,5],2-[4],3-[],4-[5],5-[],6-[],7-[2,6],8-[]],
+% ?- del_vertices([1-[3,5],2-[4],3-[],4-[5],5-[],6-[],7-[2,6],8-[]],
% [2,1],
% NL).
-% NL = [3-[],4-[5],5-[],6-[],7-[6],8-[]]
-% ==
-%
-% @compat Upto 5.6.48 the argument order was (+Vertices, +Graph,
-% -NewGraph). Both YAP and SWI-Prolog have changed the argument
-% order for compatibility with recent SICStus as well as
-% consistency with del_edges/3.
+% NL = [3-[],4-[5],5-[],6-[],7-[6],8-[]]
del_vertices(Graph, Vertices, NewGraph) :-
sort(Vertices, V1), % JW: was msort
ord_subtract(Edges, V1, NEdges).
split_on_del_vertices(=, _, _, [_|Vs], Vs, _, NG, NG).
-%! add_edges(+Graph, +Edges, -NewGraph)
+%% add_edges(+Graph, +Edges, -NewGraph)
%
-% Unify NewGraph with a new graph obtained by adding the list of Edges
-% to Graph. Example:
+% Unify NewGraph with a new graph obtained by adding the list of Edges
+% to Graph. Example:
%
-% ```
-% ?- add_edges([1-[3,5],2-[4],3-[],4-[5],
+% ?- add_edges([1-[3,5],2-[4],3-[],4-[5],
% 5-[],6-[],7-[],8-[]],
% [1-6,2-3,3-2,5-7,3-2,4-5],
% NL).
-% NL = [1-[3,5,6], 2-[3,4], 3-[2], 4-[5],
+% NL = [1-[3,5,6], 2-[3,4], 3-[2], 4-[5],
% 5-[7], 6-[], 7-[], 8-[]]
-% ```
add_edges(Graph, Edges, NewGraph) :-
p_to_s_graph(Edges, G1),
ugraph_union(Graph, G1, NewGraph).
-%! ugraph_union(+Graph1, +Graph2, -NewGraph)
+%% ugraph_union(+Graph1, +Graph2, -NewGraph)
%
-% NewGraph is the union of Graph1 and Graph2. Example:
+% NewGraph is the union of Graph1 and Graph2. Example:
%
-% ```
-% ?- ugraph_union([1-[2],2-[3]],[2-[4],3-[1,2,4]],L).
-% L = [1-[2], 2-[3,4], 3-[1,2,4]]
-% ```
+% ?- ugraph_union([1-[2],2-[3]],[2-[4],3-[1,2,4]],L).
+% L = [1-[2], 2-[3,4], 3-[1,2,4]]
ugraph_union(Set1, [], Set1) :- !.
ugraph_union([], Set2, Set2) :- !.
ugraph_union(>, Head1, Tail1, Head2, Tail2, [Head2|Union]) :-
ugraph_union([Head1|Tail1], Tail2, Union).
-%! del_edges(+Graph, +Edges, -NewGraph)
+%% del_edges(+Graph, +Edges, -NewGraph)
%
-% Unify NewGraph with a new graph obtained by removing the list of
-% Edges from Graph. Notice that no vertices are deleted. Example:
+% Unify NewGraph with a new graph obtained by removing the list of
+% Edges from Graph. Notice that no vertices are deleted. Example:
%
-% ```
-% ?- del_edges([1-[3,5],2-[4],3-[],4-[5],5-[],6-[],7-[],8-[]],
+% ?- del_edges([1-[3,5],2-[4],3-[],4-[5],5-[],6-[],7-[],8-[]],
% [1-6,2-3,3-2,5-7,3-2,4-5,1-3],
% NL).
-% NL = [1-[5],2-[4],3-[],4-[],5-[],6-[],7-[],8-[]]
-% ```
+% NL = [1-[5],2-[4],3-[],4-[],5-[],6-[],7-[],8-[]]
del_edges(Graph, Edges, NewGraph) :-
p_to_s_graph(Edges, G1),
graph_subtract(Graph, G1, NewGraph).
-%! graph_subtract(+Set1, +Set2, ?Difference)
+%% graph_subtract(+Set1, +Set2, ?Difference)
%
-% Is based on ord_subtract
+% Is based on ord_subtract
graph_subtract(Set1, [], Set1) :- !.
graph_subtract([], _, []).
graph_subtract(>, Head1, Tail1, _, Tail2, Difference) :-
graph_subtract([Head1|Tail1], Tail2, Difference).
-%! edges(+Graph, -Edges)
+%% edges(+Graph, -Edges)
%
-% Unify Edges with all edges appearing in Graph. Example:
+% Unify Edges with all edges appearing in Graph. Example:
%
-% ?- edges([1-[3,5],2-[4],3-[],4-[5],5-[]], L).
-% L = [1-3, 1-5, 2-4, 4-5]
+% ?- edges([1-[3,5],2-[4],3-[],4-[5],5-[]], L).
+% L = [1-3, 1-5, 2-4, 4-5]
edges(Graph, Edges) :-
s_to_p_graph(Graph, Edges).
s_to_p_graph([Neib|Neibs], Vertex, [Vertex-Neib|P], Rest_P) :-
s_to_p_graph(Neibs, Vertex, P, Rest_P).
-%! transitive_closure(+Graph, -Closure)
+%% transitive_closure(+Graph, -Closure)
%
-% Generate the graph Closure as the transitive closure of Graph.
-% Example:
+% Generate the graph Closure as the transitive closure of Graph.
+% Example:
%
-% ```
-% ?- transitive_closure([1-[2,3],2-[4,5],4-[6]],L).
-% L = [1-[2,3,4,5,6], 2-[4,5,6], 4-[6]]
-% ```
+% ?- transitive_closure([1-[2,3],2-[4,5],4-[6]],L).
+% L = [1-[2,3,4,5,6], 2-[4,5,6], 4-[6]]
transitive_closure(Graph, Closure) :-
warshall(Graph, Graph, Closure).
warshall(G, V, Y, NewG).
warshall([], _, _, []).
-%! transpose_ugraph(Graph, NewGraph) is det.
+%% transpose_ugraph(Graph, NewGraph) is det.
%
-% Unify NewGraph with a new graph obtained from Graph by replacing
-% all edges of the form V1-V2 by edges of the form V2-V1. The cost
-% is O(|V|*log(|V|)). Notice that an undirected graph is its own
-% transpose. Example:
+% Unify NewGraph with a new graph obtained from Graph by replacing
+% all edges of the form V1-V2 by edges of the form V2-V1. The cost
+% is O(|V|*log(|V|)). Notice that an undirected graph is its own
+% transpose. Example:
%
-% ==
% ?- transpose([1-[3,5],2-[4],3-[],4-[5],
% 5-[],6-[],7-[],8-[]], NL).
-% NL = [1-[],2-[],3-[1],4-[2],5-[1,4],6-[],7-[],8-[]]
-% ==
-%
-% @compat This predicate used to be known as transpose/2.
-% Following SICStus 4, we reserve transpose/2 for matrix
-% transposition and renamed ugraph transposition to
-% transpose_ugraph/2.
+% NL = [1-[],2-[],3-[1],4-[2],5-[1,4],6-[],7-[],8-[]]
transpose_ugraph(Graph, NewGraph) :-
edges(Graph, Edges),
flip_edges([Key-Val|Pairs], [Val-Key|Flipped]) :-
flip_edges(Pairs, Flipped).
-%! compose(+LeftGraph, +RightGraph, -NewGraph)
+%% compose(+LeftGraph, +RightGraph, -NewGraph)
%
-% Compose NewGraph by connecting the _drains_ of LeftGraph to the
-% _sources_ of RightGraph. Example:
+% Compose NewGraph by connecting the _drains_ of LeftGraph to the
+% _sources_ of RightGraph. Example:
%
-% ?- compose([1-[2],2-[3]],[2-[4],3-[1,2,4]],L).
-% L = [1-[4], 2-[1,2,4], 3-[]]
+% ?- compose([1-[2],2-[3]],[2-[4],3-[1,2,4]],L).
+% L = [1-[4], 2-[1,2,4], 3-[]]
compose(G1, G2, Composition) :-
vertices(G1, V1),
ord_union(N2, SoFar, Next),
compose1(Vs1, G2, Next, Comp).
-%! top_sort(+Graph, -Sorted) is semidet.
-%! top_sort(+Graph, -Sorted, ?Tail) is semidet.
+%% top_sort(+Graph, -Sorted) is semidet.
%
-% Sorted is a topological sorted list of nodes in Graph. A
-% toplogical sort is possible if the graph is connected and
-% acyclic. In the example we show how topological sorting works
-% for a linear graph:
+% Sorted is a topological sorted list of nodes in Graph. A
+% toplogical sort is possible if the graph is connected and
+% acyclic. In the example we show how topological sorting works
+% for a linear graph:
%
-% ==
-% ?- top_sort([1-[2], 2-[3], 3-[]], L).
-% L = [1, 2, 3]
-% ==
-%
-% The predicate top_sort/3 is a difference list version of
-% top_sort/2.
+% ?- top_sort([1-[2], 2-[3], 3-[]], L).
+% L = [1, 2, 3]
top_sort(Graph, Sorted) :-
vertices_and_zeros(Graph, Vertices, Counts0),
select_zeros(Counts1, Vertices, Zeros),
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) :-
vertices_and_zeros(Graph, Vertices, Counts0),
count_edges(Graph, Vertices, Counts0, Counts1),
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.
-% Example:
+% Neigbours is a sorted list of the neighbours of Vertex in Graph.
+% 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).
-% NL = [1,2,7,5]
-% ```
+% NL = [1,2,7,5]
+
+%% neighbors(+Vertex, +Graph, -Neigbours) is det.
+%
+% Same as neighbours/3
neighbors(Vertex, Graph, Neig) :-
neighbours(Vertex, Graph, 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
-% 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
-% standard order of terms. No vertex in UGraphIn can be a variable.
+% 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
+% not connected graph. Start is before any vertex in UGraphIn in the
+% 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)
% -> true
% ; connect_ugraph(Graph, Start, Connected),
% top_sort(Connected, Ordered0),
% Ordered0 = [Start|Vertices]
% ).
-% ```
connect_ugraph([], 0, []) :- !.
connect_ugraph(Graph, Start, [Start-Vertices|Graph]) :-
Vertices = [First|_],
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
-% order of terms.
+% Unify Before to a term that comes before Term in the standard
+% order of terms.
%
-% @error instantiation_error if Term is unbound.
+% Throws instantiation_error if Term is unbound.
before(X, _) :-
var(X),
before(_, 0).
-%! complement(+UGraphIn, -UGraphOut)
+%% complement(+UGraphIn, -UGraphOut)
%
-% UGraphOut is a ugraph with an edge between all vertices that are
-% _not_ connected in UGraphIn and all edges from UGraphIn removed.
-% Example:
+% UGraphOut is a ugraph with an edge between all vertices that are
+% _not_ connected in UGraphIn and all edges from UGraphIn removed.
+% 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).
-% 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],
% 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) :-
vertices(G,Vs),
ord_subtract(Vs,Ns1,INs),
complement(G, Vs, NG).
-%! reachable(+Vertex, +UGraph, -Vertices)
+%% reachable(+Vertex, +UGraph, -Vertices)
%
-% True when Vertices is an ordered set of vertices reachable in
-% UGraph, including Vertex. Example:
+% True when Vertices is an ordered set of vertices reachable in
+% UGraph, including Vertex. Example:
%
-% ?- reachable(1,[1-[3,5],2-[4],3-[],4-[5],5-[]],V).
-% V = [1, 3, 5]
+% ?- reachable(1,[1-[3,5],2-[4],3-[],4-[5],5-[]],V).
+% V = [1, 3, 5]
reachable(N, G, Rs) :-
reachable([N], G, [N], Rs).
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