How to properly label branches of a tree in a depth first search

Question

I have a tree with a structure like this:

     __2__3__4
    /   \\__5__6
0__1___7/__8__9
   \\\\
    \\\\__10__11__12
     \\__  __  __
        13  14  15
         


        

Answer 1

Okay, I'll try to refrain from tweaking this answer again. It's just been so fun learning about the sort order of VarBinary, finding the POWER function, CTEs beating on one another, ... .

Are you looking for anything like:

declare @Nodes as Table ( NodeId Int Identity(0,1), Name VarChar(10) )
declare @Relations as Table ( ParentNodeId Int, ChildNodeId Int, SiblingOrder Int )
insert into @Nodes ( Name ) values
--  ( '0' ), ( '1' ), ( '2' ), ( '3' ), ( '4' ), ( '5' ), ( '6' ), ( '7' ), ( '8' ),
--  ( '9' ), ( '10' ), ( '11' ), ( '12' ), ( '13' ), ( '14' ), ( '15' )
  ( 'zero' ), ( 'one' ), ( 'two' ), ( 'three' ), ( 'four' ), ( 'five' ), ( 'six' ), ( 'seven' ), ( 'eight' ),
  ( 'nine' ), ( 'ten' ), ( 'eleven' ), ( 'twelve' ), ( 'thirteen' ), ( 'fourteen' ), ( 'fifteen' )

insert into @Relations ( ParentNodeId, ChildNodeId, SiblingOrder ) values
  ( 0, 1, 0 ),
  ( 1, 2, 0 ), ( 1, 7, 1 ), ( 1, 10, 2 ), ( 1, 13, 3 ),
  ( 2, 3, 0 ), ( 2, 5, 1 ),
  ( 3, 4, 0 ),
  ( 5, 6, 0 ),
  ( 7, 5, 0 ), ( 7, 8, 1 ),
  ( 8, 9, 0 ),
  ( 10, 11, 0 ),
  ( 11, 12, 0 ),
  ( 13, 14, 0 ),
  ( 14, 15, 0 )

declare @MaxSiblings as BigInt = 100
; with
DiGraph ( NodeId, Name, Depth, ParentNodeId, Path, ForkIndex, DepthFirstOrder )
as (
  -- Start with the root node(s).
  select NodeId, Name, 0, Cast( NULL as Int ), Cast( Name as VarChar(1024) ),
    Cast( 0 as BigInt ), Cast( Right( '00' + Cast( 0 as VarChar(2) ), 2 ) as VarChar(128) )
    from @Nodes
    where not exists ( select 42 from @Relations where ChildNodeId = NodeId )
  union all
  -- Add children one generation at a time.
  select R.ChildNodeId, N.Name, DG.Depth + 1, R.ParentNodeId, Cast( DG.Path + ' > ' + N.Name as VarChar(1024) ),
    DG.ForkIndex + R.SiblingOrder * Power( @MaxSiblings, DG.Depth - 1 ),
    Cast( DG.DepthFirstOrder + Right( '00' + Cast( R.SiblingOrder as VarChar(2) ), 2 ) as VarChar(128) )
    from @Relations as R inner join
      DiGraph as DG on DG.NodeId = R.ParentNodeId inner join
      @Nodes as N on N.NodeId = R.ChildNodeId inner join
      @Nodes as Parent on Parent.NodeId = R.ParentNodeId
  ),

DiGraphSorted ( NodeId, Name, Depth, ParentNodeId, Path, ForkIndex, DepthFirstOrder, RowNumber )
as ( select *, Row_Number() over ( order by DepthFirstOrder ) as 'RowNumber' from DiGraph )

select ParentNodeId, NodeId, Depth, Path,
  ( select Count(*) from DiGraphSorted as L
    left outer join DiGraphSorted as R on R.RowNumber = L.RowNumber - 1 where
    R.RowNumber < DG.RowNumber and L.ForkIndex <> R.ForkIndex ) as 'ForkNumber' -- , '', *
  from DiGraphSorted as DG
  order by RowNumber