如何在深度优先搜索中正确标记树的分支

Question

我有一个像这样结构的树:

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

节点1有四个子节点(2,7,10,13),节点2和节点7各有两个子节点(作为子节点共享节点5).我要做的是创建一个CTE,它提供包含父节点,节点,远离根的距离以及包含在其中的分支(或分支)的记录.

IF (OBJECT_ID('tempdb..#Discovered') IS NOT NULL)
BEGIN
    DROP TABLE #Discovered
END

CREATE TABLE #Discovered
(
    ID int PRIMARY KEY NOT NULL,
    Predecessor int NULL,
    OrderDiscovered int
);

INSERT INTO #Discovered (ID, Predecessor, OrderDiscovered)
VALUES (@nodeId, NULL, 0);

    --loop through node connections table in a breadth first manner
WHILE @@ROWCOUNT > 0
BEGIN
    INSERT INTO #Discovered (ID, Predecessor, OrderDiscovered)
    SELECT c.node2_id
               ,MIN(c.node1_id)
               ,MIN(d.OrderDiscovered) + 1

    FROM #Discovered d JOIN node_connections c ON d.ID = c.node1_id
    WHERE c.node2_id NOT IN (SELECT ID FROM #Discovered)
    GROUP BY c.node2_id
END;

SELECT * FROM #Discovered;

WITH BacktraceCTE(Id, Predecessor, OrderDiscovered, Path, fork)

 AS 

 (  

     SELECT d.ID, d.Predecessor, d.OrderDiscovered, CAST(d.ID AS varchar(MAX)), 0

     FROM #Discovered d

     WHERE d.Id = @itemId


     UNION ALL             

     -- Recursive member, select all the nodes which have the previous

     SELECT d.ID, d.Predecessor, d.OrderDiscovered,  

         CAST(cte.Path + '->' + CAST(d.ID as varchar(10)) as varchar(MAX)),
         fork + CONVERT ( Integer, ROW_NUMBER() OVER (ORDER BY d.ID)) - 1

     FROM #Discovered d JOIN BacktraceCTE cte ON d.Predecessor = cte.ID

 )          

 SELECT  Predecessor as node1_id, OrderDiscovered as hop, fork, ID as node2_id, Path FROM BacktraceCTE  
 ORDER BY fork, OrderDiscovered;

问题在于如何计算fork.每次CTE返回到先前的级别时,它只有可用的行号以及该级别的叉号.我想要实现的是记录,其中每个hop和fork组合都是唯一的.

但是,使用上面的代码,我将得到结果,表示节点2到5最终是跳3分叉1和节点7到5也最终是跳3分叉1.

这是树再次标记的分支,它们应该如何显示:

     __2__3__4      :0
    /   \__5__6     :1,2
0__1___7/__8__9     :3
   \\
    \\__10__11__12  :4
     \__  __  __
        13  14  15  :5

正如你所看到的for forks 1和2我认为最好的方法是对分支进行两次计数,给它自己的标识符,从而保留hop和fork组合的唯一性.

请帮我弄清楚我需要做些什么才能实现这一目标.我觉得这应该是CTE的可能,但也许我错了,如果我是,我很想知道解决这个问题的更好方法是什么.

编辑 结果集如下所示:

前身,ID,订单发现,路径,叉

• null,0,0,0,0

• 0,1,1,0-> 1,0

• 1,2,2,0-> 1-> 2,0

• 2,3,3,0-> 1-> 2-> 3,0

• 3,4,4,0-> 1-> 2-> 3-> 4,0

• 2,5,3,0-> 1-> 2-> 5,1

• 5,6,4,0-> 1-> 2-> 5-> 6,1

• 1,7,2,0-> 1-> 7,2

• 7,5,3,0-> 1-> 7-> 5,2

• 5,6,4,0-> 1-> 7-> 5-> 6,2

• 7,8,3,0-> 1-> 7-> 8,3

• 8,9,4,0-> 1-> 7-> 8-> 9,3

• 1,10,2,0-> 1-> 10,4

• 10,11,3,0-> 1-> 10-> 11,4

• 11,12,4,0-> 1-> 10-> 11-> 12,4

• 1,13,2,0-> 1-> 13,5

• 13,14,3,0-> 1-> 13-> 14,5

• 14,15,4,0-> 1-> 13-> 14-> 15,5

Answer 1

好吧，我会尽量避免再次调整这个答案。了解 VarBinary 的排序顺序、找到 POWER 函数、CTE 相互竞争……真是太有趣了。

您是否正在寻找类似的东西：

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