Add RootsOfPartitionDS

There is already the IteratorOfRootsOfPartitionDS, but sometimes we just
want the roots as a list. This operation is essentially the same as
IteratorOfRootsOfPartitionDS but without the overhead of the iterator
code.

Author: james-d-mitchell

gap/union-find.gd

@@ -95,6 +95,13 @@ DeclareOperation("Unite",[IsPartitionDS and IsMutable, IsPosInt, IsPosInt]);
 #! @Returns an iterator
 DeclareOperation("RootsIteratorOfPartitionDS", [IsPartitionDS]);
 
+#! @Description
+#! Returns a list of the canonical representatives of the parts
+#! of the partition <A>unionfind</A>.
+#! @Arguments unionfind
+#! @Returns A list.
+DeclareOperation("RootsOfPartitionDS", [IsPartitionDS]);
+
 #! @Description
 #! Returns the number of parts of the partition <A>unionfind</A>.
 #! @Arguments unionfind

gap/union-find.gi

@@ -148,6 +148,26 @@ InstallMethod(RootsIteratorOfPartitionDS, [IsPartitionDSRep and IsPartitionDS],
     end));
 end);
 
+InstallMethod(RootsOfPartitionDS, [IsPartitionDSRep and IsPartitionDS],
+function(uf)
+  local pt, gp, data, n, result;
+    pt := 0;
+    gp := UF.getParent;
+    data := uf!.data;
+    n := SizeUnderlyingSetDS(uf);
+    result := [];
+    while pt <= n do
+      pt := pt + 1;
+      while pt <= n and gp(data[pt]) <> pt do
+        pt := pt + 1;
+      od;
+      if pt <= n then
+        Add(result, pt);
+      fi;
+    od;
+    return result;
+end);
+
 InstallMethod(PartsOfPartitionDS, [IsPartitionDS],
         function(u)
     local  p, i, r, x;

tst/uf.tst

@@ -57,6 +57,8 @@ gap> for x in i do Print(x,"\n"); od;
 8
 9
 10
+gap> RootsOfPartitionDS(u);
+[ 2, 4, 5, 6, 7, 8, 9, 10 ]
 gap> for x in i2 do Print(x,"\n"); od;
 4
 5
@@ -111,6 +113,8 @@ gap> Unite(u,9,12);
 gap> PartsOfPartitionDS(u);
 [ [ 1, 2, 3, 4 ], [ 5 ], [ 6 ], [ 7 ], [ 8 ], [ 9, 10, 11, 12 ], [ 13 ], 
   [ 14 ], [ 15 ], [ 16 ] ]
+gap> RootsOfPartitionDS(u);
+[ 2, 5, 6, 7, 8, 10, 13, 14, 15, 16 ]
 
 #
 gap> STOP_TEST( "uf.tst", 1);