--- a/progs/cube.scala	Sun Jan 15 10:58:13 2023 +0000
+++ b/progs/cube.scala	Sat Mar 11 22:01:53 2023 +0000
@@ -1,7 +1,7 @@
 // 2 x 2 x 2 Rubik's Cube
 //========================
 
-// more memory for the JVM
+// for more memory for the JVM, call
 //
 // JAVA_OPTS="-Xmx2g" scala
 
@@ -94,7 +94,7 @@
          Face(c.f1.c11, c.f1.c12, c.f6.c21, c.f6.c22))         
 
 
-// simple bf-search without solution, just true
+// simple bf-search without generating a solution, just true
 
 def actions(c: Cube) : List[Cube] = 
   List(up(c), clock(c), right(c)) 
@@ -108,7 +108,8 @@
 
 search(List(init), 0)
 
-// Set version
+
+// set version
 def actions_set(c: Cube) : Set[Cube] =
   Set(up(c), clock(c), right(c))
 
@@ -122,7 +123,7 @@
 search_set(Set(init), 0)
 
 
-// For generating list of actions
+// for generating list of actions
 abstract class Action
 case object Up extends Action
 case object Right extends Action
@@ -130,7 +131,7 @@
 
 type Actions = List[Action]
 
-// List version generating a list of actions
+// list version generating a list of actions
 def actions_list(c: Cube, act: Actions) : List[(Cube, Actions)] = 
   List((up(c), Up::act), 
        (clock(c), Clock::act), 
@@ -147,7 +148,7 @@
 search_list(List((init, Nil)), 0)._2.reverse.mkString("\n") 
 
 
-// Map version generating a list of actions
+// map version generating a list of actions
 def actions_map(c: Cube, as: Actions) : Map[Cube, Actions] = 
   Map(up(c) -> (Up::as), 
       clock(c) -> (Clock::as), 
@@ -166,7 +167,7 @@
 
 
 
-// Bidirectional breadth-first search
+// bidirectional breadth-first search
 def bsearch(cs: Map[Cube, Actions], 
             bs: Map[Cube, Actions], d: Int) : Actions = { 
   println(s"Depth: $d    Cands: ${cs.keySet.size}/${bs.keySet.size}") 
@@ -180,6 +181,20 @@
 
 
 
+// bidirectional breadth-first search
+def bsearch(cs: Map[Cube, Actions], 
+            bs: Map[Cube, Actions], d: Int) : Actions = { 
+  println(s"Depth: $d    Cands: ${cs.keySet.size}/${bs.keySet.size}") 
+  val res = cs.keySet intersect bs.keySet 
+  if (!res.isEmpty) (cs(res.head).reverse ::: bs(res.head))
+  else bsearch(cs.flatMap{ (c, as) => actions_map(c, as) }, 
+               bs.flatMap{ (c, as) => actions_map(c, as) }, d + 1)
+}  
+
+bsearch(Map(init ->  Nil), Map(solved -> Nil), 0).mkString("\n")
+
+
+