在無向圖中查找連通子圖

問題：

給定一個由兩列「Identifier1」和「Identifier2」表示的無向圖，我們如何將彼此相關的識別碼進行分組並為它們分配唯一的群組ID？

解決方案：

這個問題可以透過將資料視為圖中的邊並遍歷所有邊來解決遞歸地。

遞歸演算法：

1. 建立一個包含兩列中所有唯一識別碼的表。
2. 建立一個包含兩列中所有邊（識別碼對）的表格方向。
3. 定義一個遞歸查詢，從每個標識符開始遍歷圖形，並建立遍歷標識符的路徑。
4. 以起始標識符（錨點標識符）將結果分組，以識別連接的元件。
5. 根據錨點識別碼為每個連接的元件分配唯一的群組 ID。

範例查詢 (SQL):

WITH
CTE_Idents AS (
    SELECT Ident1 AS Ident
    FROM @T

    UNION

    SELECT Ident2 AS Ident
    FROM @T
),
CTE_Pairs AS (
    SELECT Ident1, Ident2
    FROM @T
    WHERE Ident1 <> Ident2

    UNION

    SELECT Ident2 AS Ident1, Ident1 AS Ident2
    FROM @T
    WHERE Ident1 <> Ident2
),
CTE_Recursive AS (
    SELECT
        CAST(CTE_Idents.Ident AS varchar(8000)) AS AnchorIdent 
        , Ident1
        , Ident2
        , CAST(','   Ident1   ','   Ident2   ',' AS varchar(8000)) AS IdentPath
        , 1 AS Lvl
    FROM 
        CTE_Pairs
        INNER JOIN CTE_Idents ON CTE_Idents.Ident = CTE_Pairs.Ident1

    UNION ALL

    SELECT 
        CTE_Recursive.AnchorIdent 
        , CTE_Pairs.Ident1
        , CTE_Pairs.Ident2
        , CAST(CTE_Recursive.IdentPath   CTE_Pairs.Ident2   ',' AS varchar(8000)) AS IdentPath
        , CTE_Recursive.Lvl   1 AS Lvl
    FROM
        CTE_Pairs
        INNER JOIN CTE_Recursive ON CTE_Recursive.Ident2 = CTE_Pairs.Ident1
    WHERE
        CTE_Recursive.IdentPath NOT LIKE CAST('%,'   CTE_Pairs.Ident2   ',%' AS varchar(8000))
),
CTE_RecursionResult AS (
    SELECT AnchorIdent, Ident1, Ident2
    FROM CTE_Recursive
),
CTE_CleanResult AS (
    SELECT AnchorIdent, Ident1 AS Ident
    FROM CTE_RecursionResult

    UNION

    SELECT AnchorIdent, Ident2 AS Ident
    FROM CTE_RecursionResult
)
SELECT
    CTE_Idents.Ident
    ,CASE WHEN CA_Data.XML_Value IS NULL 
    THEN CTE_Idents.Ident ELSE CA_Data.XML_Value END AS GroupMembers
    ,DENSE_RANK() OVER(ORDER BY 
        CASE WHEN CA_Data.XML_Value IS NULL 
        THEN CTE_Idents.Ident ELSE CA_Data.XML_Value END
    ) AS GroupID
FROM
    CTE_Idents
    CROSS APPLY
    (
        SELECT CTE_CleanResult.Ident ','
        FROM CTE_CleanResult
        WHERE CTE_CleanResult.AnchorIdent = CTE_Idents.Ident
        ORDER BY CTE_CleanResult.Ident FOR XML PATH(''), TYPE
    ) AS CA_XML(XML_Value)
    CROSS APPLY
    (
        SELECT CA_XML.XML_Value.value('.', 'NVARCHAR(MAX)')
    ) AS CA_Data(XML_Value)
WHERE
    CTE_Idents.Ident IS NOT NULL
ORDER BY Ident;

重點：

• 遞歸CTE（公共表表達式）遍歷圖並建立連通分量。
• 最終的SELECT語句指派群組ID 並以所需格式產生輸出。
• 此解決方案經過最佳化，可避免冗餘計算並提供高效的結果。