Implement standartization

tests/gap.g

@@ -1,3 +1,6 @@
+LoadPackage("Digraphs");
+LoadPackage("Semigroups");
+
 AsWordGraph := function(C)
   local lookup, S, A, out, next, pos, class, a;
 
@@ -19,33 +22,42 @@ AsWordGraph := function(C)
   return Digraph(out);
 end;
 
-StandardizeWordGraph := function(D)
-  local s, t, N, n, result, x, r;
+StandardizeWordGraph := function(D, root)
+  local i, alph, letter, que, seen, node, child, next_node, perm;
 
   # TODO arg checks
   if IsNullDigraph(D) then
     return D;
   fi;
-  s := 0;
-  t := 0;
-  N := OutNeighbours(D);
-  n := Length(N[1]);
-  result := DigraphMutableCopy(D);
 
-  while s <= t do
-    for x in [1 .. n] do
-      r := N[s + 1][x];
-      if r > t then 
-        t := t + 1;
-        if r > t then
-          OnDigraphs(result, (t + 1, r));
-          N := OutNeighbours(result);
-        fi;
+  i := 1;
+  que := [root];
+  seen := BlistList([1 .. DigraphNrVertices(D)], [root]);
+  next_node := OutNeighbours(D);
+  alph := Length(next_node[root]);
+
+  while i <= Length(que) do
+    node := que[i];
+    for letter in [1 .. alph] do
+      child := next_node[node][letter];
+      if not seen[child] then
+        Append(que, child);
+        seen[child] := true;
       fi;
     od;
-    s := s + 1;
+    i := i + 1;
   od;
-  return result;
+
+  if Length(que) <> DigraphNrVertices(D) then
+    # Not all nodes reachable from root!
+    return fail;
+  fi;
+
+  perm := List([1 .. Length(que)], x -> 0);
+  for i in [1 .. Length(que)] do
+    perm[que[i]] := i;
+  od;
+  return OnDigraphs(D, perm);
 end;
 
 ToWordGraphs := function(Cs)