--- /dev/null
+! See http://factorcode.org/license.txt for BSD licence.
+USING: help.markup help.syntax ;
+
+IN: graph-theory
+
+ARTICLE: "graph-protocol" "Graph protocol"
+"All graphs must be instances of the graph mixin:"
+{ $subsections graph }
+"All graphs must implement a method on the following generic word:"
+{ $subsections vertices }
+"At least one of the following two generic words must have a method; the " { $link graph } " mixin has default definitions which are mutually recursive:"
+{ $subsections
+ adjlist
+ adj?
+}
+"All mutable graphs must implement a method on the following generic word:"
+{ $subsections add-blank-vertex }
+"All mutable undirected graphs must implement a method on the following generic word:"
+{ $subsections add-edge }
+"Mutable directed graphs should not implement the above word, as it has a default definition defined in terms of the following generic word:"
+{ $subsections add-edge* }
+"The following two words have default definitions, but are available as generics to allow implementations to optimize them:"
+{ $subsections
+ num-vertices
+ num-edges
+} ;
+
+HELP: graph
+{ $class-description "A mixin class whose instances are graphs. Custom implementations of the graph protocol should be declared as instances of this mixin for all graph functionality to work correctly:"
+ { $code "INSTANCE: hex-board graph" }
+} ;
+
+{ vertices num-vertices num-edges } related-words
+
+HELP: vertices
+{ $values { "graph" graph } { "seq" "The vertices" } }
+{ $description "Returns the vertices of the graph." } ;
+
+HELP: num-vertices
+{ $values { "graph" graph } { "n" "The number of vertices" } }
+{ $description "Returns the number of vertices in the graph." } ;
+
+HELP: num-edges
+{ $values { "graph" "A graph" } { "n" "The number of edges" } }
+{ $description "Returns the number of edges in the graph." } ;
+
+{ adjlist adj? } related-words
+
+HELP: adjlist
+{ $values
+ { "from" "The index of a vertex" }
+ { "graph" "The graph to be examined" }
+ { "seq" "The adjacency list" } }
+{ $description "Returns a sequence of vertices that this vertex links to" } ;
+
+HELP: adj?
+{ $values
+ { "from" "The index of a vertex" }
+ { "to" "The index of a vertex" }
+ { "graph" "A graph" }
+ { "?" "A boolean" } }
+{ $description "Returns a boolean describing whether there is an edge in the graph between from and to." } ;
+
+{ add-blank-vertex add-blank-vertices add-edge add-edge* } related-words
+
+HELP: add-blank-vertex
+{ $values
+ { "index" "A vertex index" }
+ { "graph" "A graph" } }
+{ $description "Adds a vertex to the graph." } ;
+
+HELP: add-blank-vertices
+{ $values
+ { "seq" "A sequence of vertex indices" }
+ { "graph" "A graph" } }
+{ $description "Adds vertices with indices in seq to the graph." } ;
+
+HELP: add-edge*
+{ $values
+ { "from" "The index of a vertex" }
+ { "to" "The index of another vertex" }
+ { "graph" "A graph" } }
+{ $description "Adds a one-way edge to the graph, between " { $snippet "from" } " and " { $snippet "to" } "."
+ $nl
+ "If you want to add a two-way edge, use " { $link add-edge } " instead." } ;
+
+HELP: add-edge
+{ $values
+ { "u" "The index of a vertex" }
+ { "v" "The index of another vertex" }
+ { "graph" "A graph" } }
+{ $description "Adds a two-way edge to the graph, between " { $snippet "u" } " and " { $snippet "v" } "."
+ $nl
+ "If you want to add a one-way edge, use " { $link add-edge* } " instead." } ;
+
+{ depth-first full-depth-first dag? topological-sort } related-words
+
+HELP: depth-first
+{ $values
+ { "v" "The vertex to start the search at" }
+ { "graph" "The graph to search" }
+ { "pre" "A quotation of the form ( n -- )" }
+ { "post" "A quotation of the form ( n -- )" }
+ { "?list" "A list of booleans describing the vertices visited in the search" }
+ { "?" "A boolean describing whether or not the end-search error was thrown" } }
+{ $description "Performs a depth-first search on " { $emphasis "graph" } ". The variable " { $emphasis "graph" } " can be accessed in both quotations."
+ $nl
+ "The " { $emphasis "pre" } " quotation is run before the recursive application of depth-first."
+ $nl
+ "The " { $emphasis "post" } " quotation is run after the recursive application of depth-first."
+ $nl
+ { $emphasis "?list" } " is a list of booleans, " { $link t } " for every vertex visted during the search, and " { $link f } " for every vertex not visited." } ;
+
+HELP: full-depth-first
+{ $values
+ { "graph" "The graph to search" }
+ { "pre" "A quotation of the form ( n -- )" }
+ { "post" "A quotation of the form ( n -- )" }
+ { "tail" "A quotation of the form ( -- )" }
+ { "?" "A boolean describing whether or not the end-search error was thrown" } }
+{ $description "Performs a depth-first search on " { $emphasis "graph" } ". The variable " { $emphasis "graph" } "can be accessed in both quotations."
+ $nl
+ "The " { $emphasis "pre" } " quotation is run before the recursive application of depth-first."
+ $nl
+ "The " { $emphasis "post" } " quotation is run after the recursive application of depth-first."
+ $nl
+ "The " { $emphasis "tail" } " quotation is run after each time the depth-first search runs out of nodes. On an undirected graph this will be each connected subgroup but on a directed graph it can be more complex." } ;
+
+HELP: dag?
+{ $values
+ { "graph" graph }
+ { "?" "A boolean indicating if the graph is acyclic" } }
+{ $description "Using a depth-first search, determines if the specified directed graph is a directed acyclic graph. An undirected graph will produce a false result, as the algorithm does not eliminate cycles of length 2, which will include any edge that goes both ways." } ;
+
+HELP: topological-sort
+{ $values
+ { "graph" graph }
+ { "seq/f" "Either a sequence of values or f" } }
+{ $description "Using a depth-first search, topologically sorts the specified directed graph. Returns f if the graph contains any cycles, and a topologically sorted sequence otherwise." } ;
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