CCGraph: more functions, better interface for traversals

src/data/CCGraph.ml

@@ -35,6 +35,7 @@ module Seq = struct
   let return x k = k x
   let (>>=) a f k = a (fun x -> f x k)
   let map f a k = a (fun x -> k (f x))
+  let filter_map f a k = a (fun x -> match f x with None -> () | Some y -> k y)
   let iter f a = a f
   let fold f acc a =
     let acc = ref acc in
@@ -51,10 +52,12 @@ type ('v, 'e) t = {
   dest: 'e -> 'v;
 }
 
+type ('v, 'e) graph = ('v, 'e) t
+
 (** Mutable bitset for values of type ['v] *)
 type 'v tag_set = {
   get_tag: 'v -> bool;
-  set_tag: 'v -> unit; (** Set tag to [true] for the given element *)
+  set_tag: 'v -> unit; (** Set tag for the given element *)
 }
 
 (** Mutable table with keys ['k] and values ['a] *)
@@ -81,7 +84,19 @@ let mk_table (type k) ?(eq=(=)) ?(hash=Hashtbl.hash) size =
   ; size=(fun () -> H.length tbl)
   }
 
-(** {2 Traversals} *)
+let mk_map (type k) ?(cmp=Pervasives.compare) () =
+  let module M = Map.Make(struct
+    type t = k
+    let compare = cmp
+  end) in
+  let tbl = ref M.empty in
+  { mem=(fun k -> M.mem k !tbl)
+  ; find=(fun k -> M.find k !tbl)
+  ; add=(fun k v -> tbl := M.add k v !tbl)
+  ; size=(fun () -> M.cardinal !tbl)
+  }
+
+(** {2 Bags} *)
 
 type 'a bag = {
   push: 'a -> unit;
@@ -140,73 +155,243 @@ let mk_heap ~leq =
     )
   }
 
-let traverse ?tbl:(mk_tbl=mk_table ?eq:None ?hash:None) ~bag:mk_bag ~graph seq =
+(** {2 Traversals} *)
-  fun k ->
-    let bag = mk_bag() in
-    Seq.iter bag.push seq;
-    let tbl = mk_tbl 128 in
-    let bag = mk_bag () in
-    while not (bag.is_empty ()) do
-      let x = bag.pop () in
-      if not (tbl.mem x) then (
-        k x;
-        tbl.add x ();
-        Seq.iter
-          (fun e -> bag.push (graph.dest e))
-          (graph.children x)
-      )
-    done
 
-let traverse_tag ~tags ~bag ~graph seq =
+module Traverse = struct
-  let first = ref true in
+  let generic_tag ~tags ~bag ~graph seq =
-  fun k ->
+    let first = ref true in
-    (* ensure linearity *)
+    fun k ->
-    if !first then first := false else raise Sequence_once;
+      (* ensure linearity *)
-    Seq.iter bag.push seq;
+      if !first then first := false else raise Sequence_once;
-    while not (bag.is_empty ()) do
+      Seq.iter bag.push seq;
-      let x = bag.pop () in
+      while not (bag.is_empty ()) do
-      if not (tags.get_tag x) then (
+        let x = bag.pop () in
-        k x;
+        if not (tags.get_tag x) then (
-        tags.set_tag x;
+          k x;
-        Seq.iter
+          tags.set_tag x;
-          (fun e -> bag.push (graph.dest e))
+          Seq.iter
-          (graph.children x)
+            (fun e -> bag.push (graph.dest e))
-      )
+            (graph.children x)
-    done
+        )
+      done
 
-let bfs ?tbl ~graph seq =
+  let generic ?(tbl=mk_table 128) ~bag ~graph seq =
-  traverse ?tbl ~bag:mk_queue ~graph seq
+    let tags = {
+      get_tag=tbl.mem;
+      set_tag=(fun v -> tbl.add v ());
+    } in
+    generic_tag ~tags ~bag ~graph seq
 
-let bfs_tag ~tags ~graph seq =
+  let bfs ?tbl ~graph seq =
-  traverse_tag ~tags ~bag:(mk_queue()) ~graph seq
+    generic ?tbl ~bag:(mk_queue ()) ~graph seq
 
-let dfs ?tbl ~graph seq =
+  let bfs_tag ~tags ~graph seq =
-  traverse ?tbl ~bag:mk_stack ~graph seq
+    generic_tag ~tags ~bag:(mk_queue()) ~graph seq
 
-let dfs_tag ~tags ~graph seq =
+  let dijkstra_tag ?(dist=fun _ -> 1) ~tags ~graph seq =
-  traverse_tag ~tags ~bag:(mk_stack()) ~graph seq
+    let tags' = {
-
+      get_tag=(fun (v,_) -> tags.get_tag v);
-let dijkstra ?(tbl=mk_table ?eq:None ?hash:None) ?(dist=fun _ -> 1) ~graph seq =
+      set_tag=(fun (v,_) -> tags.set_tag v);
-  (* a table [('v * int) -> 'a] built from a ['v -> 'a] table *)
-  let mk_tbl' size =
-    let vertex_tbl = tbl size in
-    { mem=(fun (v, _) -> vertex_tbl.mem v)
-    ; find=(fun (v, _) -> vertex_tbl.find v)
-    ; add=(fun (v, _) -> vertex_tbl.add v)
-    ; size=vertex_tbl.size
     }
-  and seq' = Seq.map (fun v -> v, 0) seq
+    and seq' = Seq.map (fun v -> v, 0) seq
-  and graph' = {
+    and graph' = {
-    children=(fun (v,d) -> Seq.map (fun e -> e, d) (graph.children v));
+      children=(fun (v,d) -> Seq.map (fun e -> e, d) (graph.children v));
-    origin=(fun (e, d) -> graph.origin e, d);
+      origin=(fun (e, d) -> graph.origin e, d);
-    dest=(fun (e, d) -> graph.dest e, d + dist e);
+      dest=(fun (e, d) -> graph.dest e, d + dist e);
-  } in
+    } in
-  let mk_bag () = mk_heap ~leq:(fun (_, d1) (_, d2) -> d1 <= d2) in
+    let bag = mk_heap ~leq:(fun (_, d1) (_, d2) -> d1 <= d2) in
-  traverse ~tbl:mk_tbl' ~bag:mk_bag ~graph:graph' seq'
+    generic_tag ~tags:tags' ~bag ~graph:graph' seq'
-
-let dijkstra_tag ?(dist=fun _ -> 1) ~tags ~graph seq = assert false (* TODO *)
-
 
+  let dijkstra ?(tbl=mk_table 128) ?dist ~graph seq =
+    let tags = {
+      get_tag=tbl.mem;
+      set_tag=(fun v -> tbl.add v ());
+    } in
+    dijkstra_tag ~tags ?dist ~graph seq
+
+  let dfs ?tbl ~graph seq =
+    generic ?tbl ~bag:(mk_stack ()) ~graph seq
+
+  let dfs_tag ~tags ~graph seq =
+    generic_tag ~tags ~bag:(mk_stack()) ~graph seq
+
+  module Event = struct
+    type edge_kind = [`Forward | `Back | `Cross ]
+
+    type 'e path = 'e list
+
+    (** A traversal is a sequence of such events *)
+    type ('v,'e) t =
+      [ `Enter of 'v * int * 'e path  (* unique index in traversal, path from start *)
+      | `Exit of 'v
+      | `Edge of 'e * edge_kind
+      ]
+
+    let get_vertex = function
+      | `Enter (v, _, _) -> Some (v, `Enter)
+      | `Exit v -> Some (v, `Exit)
+      | `Edge _ -> None
+
+    let get_enter = function
+      | `Enter (v, _, _) -> Some v
+      | `Exit _
+      | `Edge _ -> None
+
+    let get_exit = function
+      | `Exit v -> Some v
+      | `Enter _
+      | `Edge _ -> None
+
+    let get_edge = function
+      | `Edge (e, _) -> Some e
+      | `Enter _
+      | `Exit _ -> None
+
+    let get_edge_kind = function
+      | `Edge (e, k) -> Some (e, k)
+      | `Enter _
+      | `Exit _ -> None
+
+    (* is [v] the origin of some edge in [path]? *)
+    let rec list_mem_ ~eq ~graph v path = match path with
+      | [] -> false
+      | e :: path' ->
+        eq v (graph.origin e) || list_mem_ ~eq ~graph v path'
+
+    let dfs_tag ?(eq=(=)) ~tags ~graph seq =
+      let first = ref true in
+      fun k ->
+        if !first then first := false else raise Sequence_once;
+        let bag = mk_stack() in
+        let n = ref 0 in
+        Seq.iter
+          (fun v ->
+             (* start DFS from this vertex *)
+             bag.push (`Enter (v, []));
+             while not (bag.is_empty ()) do
+               match bag.pop () with
+               | `Enter (x, path) ->
+                 if not (tags.get_tag x) then (
+                   let num = !n in
+                   incr n;
+                   tags.set_tag x;
+                   k (`Enter (x, num, path));
+                   bag.push (`Exit x);
+                   Seq.iter
+                     (fun e -> bag.push (`Edge (e, e :: path)))
+                     (graph.children x);
+                 )
+               | `Exit x -> k (`Exit x)
+               | `Edge (e, path) ->
+                 let v = graph.dest e in
+                 let edge_kind =
+                   if tags.get_tag v
+                   then if list_mem_ ~eq ~graph v path
+                     then `Back
+                     else `Cross
+                   else `Forward
+                 in
+                 k (`Edge (e, edge_kind))
+             done
+          ) seq
+
+    let dfs ?(tbl=mk_table 128) ?eq ~graph seq =
+      let tags = {
+        set_tag=(fun v -> tbl.add v ());
+        get_tag=tbl.mem;
+      } in
+      dfs_tag ?eq ~tags ~graph seq
+  end
+end
+
+module Dot = struct
+  type attribute = [
+  | `Color of string
+  | `Shape of string
+  | `Weight of int
+  | `Style of string
+  | `Label of string
+  | `Other of string * string
+  ] (** Dot attribute *)
+
+  let pp_list pp_x out l =
+    Format.pp_print_string out "[";
+    List.iteri (fun i x ->
+        if i > 0 then Format.fprintf out ",@;";
+        pp_x out x
+      ) l;
+    Format.pp_print_string out "]"
+
+  (** Print an enum of Full.traverse_event *)
+  let pp_seq
+      ?(tbl=mk_table 128)
+      ?(attrs_v=fun _ -> [])
+      ?(attrs_e=fun _ -> [])
+      ?(name="graph")
+      ~graph out seq =
+    (* print an attribute *)
+    let pp_attr out attr = match attr with
+      | `Color c -> Format.fprintf out "color=%s" c
+      | `Shape s -> Format.fprintf out "shape=%s" s
+      | `Weight w -> Format.fprintf out "weight=%d" w
+      | `Style s -> Format.fprintf out "style=%s" s
+      | `Label l -> Format.fprintf out "label=\"%s\"" l
+      | `Other (name, value) -> Format.fprintf out "%s=\"%s\"" name value
+    (* map from vertices to integers *)
+    and get_id =
+      let count = ref 0 in
+      fun v ->
+        try tbl.find v
+        with Not_found ->
+          let n = !count in
+          incr count;
+          tbl.add v n;
+          n
+    in
+    (* the unique name of a vertex *)
+    let pp_vertex out v = Format.fprintf out "vertex_%d" (get_id v) in
+    (* print preamble *)
+    Format.fprintf out "@[<v2>digraph %s {@;" name;
+    (* traverse *)
+    let tags = {
+      get_tag=tbl.mem;
+      set_tag=(fun v -> ignore (get_id v)); (* allocate new ID *)
+    } in
+    let events = Traverse.Event.dfs_tag ~tags ~graph seq in
+    Seq.iter
+      (function
+        | `Enter (v, _n, _path) ->
+          let attrs = attrs_v v in
+          Format.fprintf out "  @[<h>%a %a;@]@." pp_vertex v (pp_list pp_attr) attrs
+        | `Exit _ -> ()
+        | `Edge (e, _) ->
+          let v1 = graph.origin e in
+          let v2 = graph.dest e in
+          let attrs = attrs_e e in
+          Format.fprintf out "  @[<h>%a -> %a %a;@]@."
+            pp_vertex v1 pp_vertex v2
+            (pp_list pp_attr)
+            attrs
+      ) events;
+    (* close *)
+    Format.fprintf out "}@]@;@?";
+    ()
+
+  let pp ?tbl ?attrs_v ?attrs_e ?name ~graph fmt v =
+    pp_seq ?tbl ?attrs_v ?attrs_e ?name ~graph fmt (Seq.return v)
+
+  let with_out filename f =
+    let oc = open_out filename in
+    try
+      let fmt = Format.formatter_of_out_channel oc in
+      let x = f fmt in
+      Format.pp_print_flush fmt ();
+      close_out oc;
+      x
+    with e ->
+      close_out oc;
+      raise e
+end
 
 
 

src/data/CCGraph.mli

@@ -40,6 +40,7 @@ module Seq : sig
   val return : 'a -> 'a sequence
   val (>>=) : 'a t -> ('a -> 'b t) -> 'b t
   val map : ('a -> 'b) -> 'a t -> 'b t
+  val filter_map : ('a -> 'b option) -> 'a t -> 'b t
   val iter : ('a -> unit) -> 'a t -> unit
   val fold: ('b -> 'a -> 'b) -> 'b -> 'a t -> 'b
 end
@@ -53,10 +54,12 @@ type ('v, 'e) t = {
   dest: 'e -> 'v;
 }
 
-(** Mutable bitset for values of type ['v] *)
+type ('v, 'e) graph = ('v, 'e) t
+
+(** Mutable tags from values of type ['v] to tags of type [bool] *)
 type 'v tag_set = {
   get_tag: 'v -> bool;
-  set_tag: 'v -> unit; (** Set tag to [true] for the given element *)
+  set_tag: 'v -> unit; (** Set tag for the given element *)
 }
 
 (** Mutable table with keys ['k] and values ['a] *)
@@ -70,10 +73,13 @@ type ('k, 'a) table = {
 (** Mutable set *)
 type 'a set = ('a, unit) table
 
-(** Default implementation for {!table}: a {!Hashtbl.t} *)
 val mk_table: ?eq:('k -> 'k -> bool) -> ?hash:('k -> int) -> int -> ('k, 'a) table
+(** Default implementation for {!table}: a {!Hashtbl.t} *)
 
-(** {2 Traversals} *)
+val mk_map: ?cmp:('k -> 'k -> int) -> unit -> ('k, 'a) table
+(** Use a {!Map.S} underneath *)
+
+(** {2 Bags of vertices} *)
 
 (** Bag of elements of type ['a] *)
 type 'a bag = {
@@ -89,43 +95,129 @@ val mk_heap: leq:('a -> 'a -> bool) -> 'a bag
 (** [mk_heap ~leq] makes a priority queue where [leq x y = true] means that
     [x] is smaller than [y] and should be prioritary *)
 
-val traverse: ?tbl:(int -> 'v set) ->
+(** {2 Traversals} *)
-              bag:(unit -> 'v bag) ->
-              graph:('v, 'e) t ->
-              'v sequence -> 'v sequence
-(** Traversal of the given graph, starting from a sequence
-    of vertices, using the given bag to choose the next vertex to
-    explore. Each vertex is visited at most once. *)
 
-val traverse_tag: tags:'v tag_set ->
+module Traverse : sig
-                  bag:'v bag ->
+  val generic: ?tbl:'v set ->
-                  graph:('v, 'e) t ->
+                bag:'v bag ->
-                  'v sequence ->
-                  'v sequence_once
-(** One-shot traversal of the graph using a tag set and the given bag *)
-
-val bfs: ?tbl:(int -> 'v set) -> graph:('v, 'e) t -> 'v sequence -> 'v sequence
-
-val bfs_tag: tags:'v tag_set -> graph:('v, 'e) t -> 'v sequence -> 'v sequence_once
-
-val dfs: ?tbl:(int -> 'v set) -> graph:('v, 'e) t -> 'v sequence -> 'v sequence
-
-val dfs_tag: tags:'v tag_set -> graph:('v, 'e) t -> 'v sequence -> 'v sequence_once
-
-val dijkstra : ?tbl:(int -> 'v set) ->
-                ?dist:('e -> int) ->
                 graph:('v, 'e) t ->
                 'v sequence ->
-                ('v * int) sequence
+                'v sequence_once
-(** Dijkstra algorithm, traverses a graph in increasing distance order.
+  (** Traversal of the given graph, starting from a sequence
-    Yields each vertex paired with its distance to the set of initial vertices
+      of vertices, using the given bag to choose the next vertex to
-    (the smallest distance needed to reach the node from the initial vertices)
+      explore. Each vertex is visited at most once. *)
-    @param dist distance from origin of the edge to destination,
-      must be strictly positive. Default is 1 for every edge *)
 
-val dijkstra_tag : ?dist:('e -> int) ->
+  val generic_tag: tags:'v tag_set ->
-                    tags:'v tag_set ->
+                   bag:'v bag ->
-                    graph:('v, 'e) t ->
+                   graph:('v, 'e) t ->
-                    'v sequence ->
+                   'v sequence ->
-                    ('v * int) sequence_once
+                   'v sequence_once
+  (** One-shot traversal of the graph using a tag set and the given bag *)
 
+  val dfs: ?tbl:'v set ->
+           graph:('v, 'e) t ->
+           'v sequence ->
+           'v sequence_once
+
+  val dfs_tag: tags:'v tag_set ->
+               graph:('v, 'e) t ->
+               'v sequence ->
+               'v sequence_once
+
+  val bfs: ?tbl:'v set ->
+           graph:('v, 'e) t ->
+           'v sequence ->
+           'v sequence_once
+
+  val bfs_tag: tags:'v tag_set ->
+               graph:('v, 'e) t ->
+               'v sequence ->
+               'v sequence_once
+
+  val dijkstra : ?tbl:'v set ->
+                  ?dist:('e -> int) ->
+                  graph:('v, 'e) t ->
+                  'v sequence ->
+                  ('v * int) sequence_once
+  (** Dijkstra algorithm, traverses a graph in increasing distance order.
+      Yields each vertex paired with its distance to the set of initial vertices
+      (the smallest distance needed to reach the node from the initial vertices)
+      @param dist distance from origin of the edge to destination,
+        must be strictly positive. Default is 1 for every edge *)
+
+  val dijkstra_tag : ?dist:('e -> int) ->
+                      tags:'v tag_set ->
+                      graph:('v, 'e) t ->
+                      'v sequence ->
+                      ('v * int) sequence_once
+
+  (** {2 More detailed interface} *)
+  module Event : sig
+    type edge_kind = [`Forward | `Back | `Cross ]
+
+    type 'e path = 'e list
+
+    (** A traversal is a sequence of such events *)
+    type ('v,'e) t =
+      [ `Enter of 'v * int * 'e path  (* unique index in traversal, path from start *)
+      | `Exit of 'v
+      | `Edge of 'e * edge_kind
+      ]
+
+    val get_vertex : ('v, 'e) t -> ('v * [`Enter | `Exit]) option
+    val get_enter : ('v, 'e) t -> 'v option
+    val get_exit : ('v, 'e) t -> 'v option
+    val get_edge : ('v, 'e) t -> 'e option
+    val get_edge_kind : ('v, 'e) t -> ('e * edge_kind) option
+
+    val dfs: ?tbl:'v set ->
+             ?eq:('v -> 'v -> bool) ->
+             graph:('v, 'e) graph ->
+             'v sequence ->
+             ('v,'e) t sequence_once
+    (** Full version of DFS.
+        @param eq equality predicate on vertices *)
+
+    val dfs_tag: ?eq:('v -> 'v -> bool) ->
+                 tags:'v tag_set ->
+                 graph:('v, 'e) graph ->
+                 'v sequence ->
+                 ('v,'e) t sequence_once
+    (** Full version of DFS using integer tags
+        @param eq equality predicate on vertices *)
+  end
+end
+
+
+(** {2 Pretty printing in the DOT (graphviz) format} *)
+module Dot : sig
+  type attribute = [
+  | `Color of string
+  | `Shape of string
+  | `Weight of int
+  | `Style of string
+  | `Label of string
+  | `Other of string * string
+  ] (** Dot attribute *)
+
+  val pp : ?tbl:('v,int) table ->
+           ?attrs_v:('v -> attribute list) ->
+           ?attrs_e:('e -> attribute list) ->
+           ?name:string ->
+           graph:('v,'e) t ->
+           Format.formatter ->
+           'v ->
+           unit
+
+  val pp_seq : ?tbl:('v,int) table ->
+               ?attrs_v:('v -> attribute list) ->
+               ?attrs_e:('e -> attribute list) ->
+               ?name:string ->
+               graph:('v,'e) t ->
+               Format.formatter ->
+               'v sequence ->
+               unit
+
+  val with_out : string -> (Format.formatter -> 'a) -> 'a
+  (** Shortcut to open a file and write to it *)
+end