A collections of algorithms on (mostly read-only) graph structures. The user provides her own graph structure as a ('v, 'e) CCGraph.t, where 'v is the type of vertices and 'e the type of edges (for instance, 'e = ('v * 'v) is perfectly fine in many cases).
Such a ('v, 'e) CCGraph.t structure is a record containing three functions: two relate edges to their origin and destination, and one maps vertices to their outgoing edges. This abstract notion of graph makes it possible to run the algorithms on any user-specific type that happens to have a graph structure.
Many graph algorithms here take an iterator of vertices as input. The helper module Iter contains basic functions for that, as does the iter library on opam. If the user only has a single vertex (e.g., for a topological sort from a given vertex), they can use Iter.return x to build a iter of one element.
status: unstable
type 'a iter_once = 'a iterIter that should be used only once
module Iter : sig ... endThis interface is designed for oriented graphs with labels on edges
type ('v, 'e) t = 'v -> ('e * 'v) iterDirected graph with vertices of type 'v and edges labeled with e'
type ('v, 'e) graph = ('v, 'e) tTags
Mutable tags from values of type 'v to tags of type bool
type 'a set = ('a, unit) tableMutable set
val mk_table :
eq:('k -> 'k -> bool) ->
?hash:('k -> int) ->
int ->
('k, 'a) tableDefault implementation for Table: a Hashtbl.t.
val mk_map : cmp:('k -> 'k -> int) -> unit -> ('k, 'a) tableUse a Map.S underneath.
val mk_queue : unit -> 'a bagval mk_stack : unit -> 'a bagval mk_heap : leq:('a -> 'a -> bool) -> 'a bagmk_heap ~leq makes a priority queue where leq x y = true means that x is smaller than y and should be prioritary.
module Traverse : sig ... endis_dag ~graph vs returns true if the subset of graph reachable from vs is acyclic.
val topo_sort :
eq:('v -> 'v -> bool) ->
?rev:bool ->
tbl:'v set ->
graph:('v, 'e) t ->
'v iter ->
'v listtopo_sort ~graph seq returns a list of vertices l where each element of l is reachable from seq. The list is sorted in a way such that if v -> v' in the graph, then v comes before v' in the list (i.e. has a smaller index). Basically v -> v' means that v is smaller than v'. See wikipedia.
val topo_sort_tag :
eq:('v -> 'v -> bool) ->
?rev:bool ->
tags:'v tag_set ->
graph:('v, 'e) t ->
'v iter ->
'v listSame as topo_sort but uses an explicit tag set.
module Lazy_tree : sig ... endval spanning_tree :
tbl:'v set ->
graph:('v, 'e) t ->
'v ->
('v, 'e) Lazy_tree.tspanning_tree ~graph v computes a lazy spanning tree that has v as a root. The table tbl is used for the memoization part.
val spanning_tree_tag :
tags:'v tag_set ->
graph:('v, 'e) t ->
'v ->
('v, 'e) Lazy_tree.tHidden state for scc.
Strongly connected components reachable from the given vertices. Each component is a list of vertices that are all mutually reachable in the graph. The components are explored in a topological order (if C1 and C2 are components, and C1 points to C2, then C2 will be yielded before C1). Uses Tarjan's algorithm.
Example (print divisors from 42):
let open CCGraph in
let open Dot in
with_out "/tmp/truc.dot"
(fun out ->
pp ~attrs_v:(fun i -> [`Label (string_of_int i)]) ~graph:divisors_graph out 42
)module Dot : sig ... endtype ('v, 'e) mut_graph = {graph : ('v, 'e) t;add_edge : 'v -> 'e -> 'v -> unit;remove : 'v -> unit;}val mk_mut_tbl :
eq:('v -> 'v -> bool) ->
?hash:('v -> int) ->
int ->
('v, 'a) mut_graphMake a new mutable graph from a Hashtbl. Edges are labelled with type 'a.
A classic implementation of a graph structure on totally ordered vertices, with unlabelled edges. The graph allows to add and remove edges and vertices, and to iterate on edges and vertices.
module type MAP = sig ... endval of_list : eq:('v -> 'v -> bool) -> ('v * 'v) list -> ('v, unit) tof_list l makes a graph from a list of pairs of vertices. Each pair (a,b) is an edge from a to b.
val of_hashtbl : ('v, 'v list) Stdlib.Hashtbl.t -> ('v, unit) tof_hashtbl tbl makes a graph from a hashtable that maps vertices to lists of children.
val of_fun : ('v -> 'v list) -> ('v, unit) tof_fun f makes a graph out of a function that maps a vertex to the list of its children. The function is assumed to be deterministic.
val divisors_graph : (int, unit) tn points to all its strict divisors.