reverse collatz graph; also export Heap

lazyGraph.ml

@@ -348,7 +348,7 @@ let a_star graph
       let dist, v' = Heap.pop h in
       (* data for this vertex *)
       let cell = nodes.map_get v' in
-      if (not cell.cf_explored) || ignore v' then begin
+      if not (cell.cf_explored || ignore v') then begin
         (* 'explore' the node *)
         on_explore v';
         cell.cf_explored <- true;
@@ -573,6 +573,16 @@ let collatz_graph =
       else Node (i, i, Sequence.singleton ((), i * 3 + 1))
   in make force
 
+let collatz_graph_bis =
+  let force i =
+    let l =
+      [ true, if i mod 2 = 0 then i/2 else i*3+1
+      ; false, i * 2 ] @
+      if i mod 3 = 1 then [false, (i-1)/3] else []
+    in
+    Node (i, i, Sequence.of_list l)
+  in make force
+
 let heap_graph =
   let force i =
     Node (i, i, Sequence.of_list [(), 2*i; (), 2*i+1])

lazyGraph.mli

@@ -129,6 +129,14 @@ val bfs : ('id, 'v, 'e) t -> 'id -> ('id * 'v * int) Sequence.t
 val dfs : ('id, 'v, 'e) t -> 'id -> ('id * 'v * int) Sequence.t
   (** Lazy traversal in depth first *)
 
+module Heap : sig
+  type 'a t
+  val empty : cmp:('a -> 'a -> int) -> 'a t
+  val is_empty : _ t -> bool
+  val insert : 'a t -> 'a -> unit
+  val pop : 'a t -> 'a
+end
+
 val a_star : ('id, 'v, 'e) t ->
              ?on_explore:('id -> unit) ->
              ?ignore:('id -> bool) ->
@@ -229,6 +237,12 @@ end
 val divisors_graph : (int, int, unit) t
 
 val collatz_graph : (int, int, unit) t
+  (** If [n] is even, [n] points to [n/2], otherwise to [3n+1] *)
+
+val collatz_graph_bis : (int, int, bool) t
+  (** Same as {! collatz_graph}, but also with reverse edges (n -> n*2,
+      and n -> (n-1)/3 if n mod 3 = 1. Direct edges annotated with [true],
+      reverse edges with [false] *)
 
 val heap_graph : (int, int, unit) t
   (** maps an integer i to 2*i and 2*i+1 *)