Recursive CTE to find all ancestors OF ALL ITEMS

Question

I have a simple hierarchy and need to be able to generate a single table that matches EACH item in the table with ALL of its ancestors. (Caps to emphasize that this is not a duplicate question!)

So here's a table:

Select Item='A', Parent=null into Items union
Select Item='B', Parent='A'  union
Select Item='C', Parent='A'  union
Select Item='D', Parent='B'  union
Select Item='E', Parent='B'  union
Select Item='F', Parent='C'  union
Select Item='G', Parent='C'  union
Select Item='H', Parent='D'  
Go

... which represents this hierarchy:

       A
     /   \
    B     C
   / \   / \
   D E   F G
  /
  H

So B has one ancestor (A), and H has 3 ancestors (D,B,A). This is the desired output:

 Item | Ancestor
 B    | A
 C    | A
 D    | A
 D    | B
 E    | A
 E    | B
 F    | A
 F    | C
 G    | A
 G    | C
 H    | A
 H    | B
 H    | D

Using a recursive CTE, I'm able to find all descendants for any ONE item...

Create Function ItemDescendants(@Item char) Returns @result Table(Item char) As Begin
    ; With AllDescendants as (
        Select
            Item,
            Parent
        From Items i
        Where Item=@Item
        UNION ALL
        Select
            i.Item,
            i.Parent
        from Items i
        Join AllDescendants a on i.Parent=a.Item
    )
    Insert into @result (Item)
    Select Item from AllDescendants
    Where Item<>@Item;
    Return;
End
Go

... but then to get the full expanded list, I have to resort to a cursor (yuk!):

Select Item, Parent into #t From Items

Declare @Item char
Declare c Cursor for (Select Item from Items)
Open c
Fetch c into @Item
While (@@Fetch_Status=0) Begin
    Insert into #t (Item, Ancestor) Select Item, @Item from dbo.ItemDescendants(@Item) 
    Fetch c into @Item
End
Close c
Deallocate c

Select Distinct
    Item,
    Ancestor
From #t
Where Parent is not null
Order by Item,Parent

Drop Table #t

This works, but I would be so much happier if I could do it with a single elegant query. Seems like it should be possible - any ideas?

Answer 1

Assuming I understand you right, it should be as simple as recursing backwards from the leaf nodes (which is easy since the table Items is storing only the leaf nodes):

;with AncestryTree as (
  select Item, Parent
  from Items
  where Parent is not null
  union all
  select Items.Item, t.Parent  
  from AncestryTree t 
  join Items on t.Item = Items.Parent
 )
select * from AncestryTree
order by Item, Parent

SQL Fiddle demo