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sql - 使用递归公用表表达式检测 SQL 图中的循环

问题描述

给定具有循环的有向图，如何仅使用标准 SQL 检测和列出循环？输入 = 图边和一个根节点，我们从中计算传递闭包。输出 = 循环中的节点列表。

标签： sqlsql-serverrecursion

解决方案

CREATE TABLE #myEdge (
    ID INT IDENTITY(1,1) PRIMARY KEY,
    NodeIDFrom INT,
    NodeIDTo INT
)

INSERT INTO #myEdge(NodeIDFrom, NodeIDTo) VALUES (4, 5),(5, 6),(6, 4);

DECLARE @rootNode AS integer = 4;

--compute the transitive closure from this root. column Niveau holds the recursion nesting level.

WITH cte_transitive_closure(rootNode, NodeFrom, NodeTo, Niveau)
AS (
    SELECT @rootNode, NULL, @rootNode, 0

    UNION ALL

    SELECT rootNode, e.NodeIDFrom, e.NodeIDTo, Niveau+1
    FROM cte_transitive_closure AS cte
    JOIN #myEdge AS e ON cte.NodeTo=e.NodeIdFrom
    WHERE Niveau < 99
)
SELECT *
INTO #transitive_closure
FROM cte_transitive_closure;

SELECT * FROM #transitive_closure;

--starting from root as a reached target, move back in the trace until the root is hit again.

WITH cte_cycle(NodeFrom, NodeTo, Cycle)
AS (
    SELECT @rootNode,NULL,0

    UNION ALL

    SELECT t.NodeFrom, t.NodeTo, 0
    FROM cte_cycle AS cte
    JOIN #transitive_closure AS t ON cte.NodeFrom = t.NodeTo
    WHERE t.NodeFrom != @rootNode AND Cycle=0

    UNION ALL

    SELECT t.NodeFrom, t.NodeTo, 1
    FROM cte_cycle AS cte
    JOIN #transitive_closure AS t ON cte.NodeFrom = t.NodeTo
    WHERE t.NodeFrom = @rootNode AND Cycle=0
)
SELECT DISTINCT * FROM cte_cycle;


result set:

NodeFrom    -> NodeTo   (Cycle)

4   -> NULL (0)

4   -> 5    (1)

5   -> 6    (0)

6   -> 4    (0)

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