sql server: 最短路径

---------------------------------------------------------------------

-- Road System  道路

---------------------------------------------------------------------

-- Listing 9-3: DDL & Sample Data for Cities, Roads

SET NOCOUNT ON;

USE tempdb;

GO

IF OBJECT_ID('dbo.Roads') IS NOT NULL

  DROP TABLE dbo.Roads;

GO

IF OBJECT_ID('dbo.Cities') IS NOT NULL

  DROP TABLE dbo.Cities;

GO

CREATE TABLE dbo.Cities

(

  cityid  CHAR(3)     NOT NULL PRIMARY KEY,

  city    VARCHAR(30) NOT NULL,

  region  VARCHAR(30) NULL,

  country VARCHAR(30) NOT NULL

);

INSERT INTO dbo.Cities(cityid, city, region, country)

  VALUES('ATL', 'Atlanta', 'GA', 'USA');

INSERT INTO dbo.Cities(cityid, city, region, country)

  VALUES('ORD', 'Chicago', 'IL', 'USA');

INSERT INTO dbo.Cities(cityid, city, region, country)

  VALUES('DEN', 'Denver', 'CO', 'USA');

INSERT INTO dbo.Cities(cityid, city, region, country)

  VALUES('IAH', 'Houston', 'TX', 'USA');

INSERT INTO dbo.Cities(cityid, city, region, country)

  VALUES('MCI', 'Kansas City', 'KS', 'USA');

INSERT INTO dbo.Cities(cityid, city, region, country)

  VALUES('LAX', 'Los Angeles', 'CA', 'USA');

INSERT INTO dbo.Cities(cityid, city, region, country)

  VALUES('MIA', 'Miami', 'FL', 'USA');

INSERT INTO dbo.Cities(cityid, city, region, country)

  VALUES('MSP', 'Minneapolis', 'MN', 'USA');

INSERT INTO dbo.Cities(cityid, city, region, country)

  VALUES('JFK', 'New York', 'NY', 'USA');

INSERT INTO dbo.Cities(cityid, city, region, country)

  VALUES('SEA', 'Seattle', 'WA', 'USA');

INSERT INTO dbo.Cities(cityid, city, region, country)

  VALUES('SFO', 'San Francisco', 'CA', 'USA');

INSERT INTO dbo.Cities(cityid, city, region, country)

  VALUES('ANC', 'Anchorage', 'AK', 'USA');

INSERT INTO dbo.Cities(cityid, city, region, country)

  VALUES('FAI', 'Fairbanks', 'AK', 'USA');

CREATE TABLE dbo.Roads

(

  city1       CHAR(3) NOT NULL REFERENCES dbo.Cities,

  city2       CHAR(3) NOT NULL REFERENCES dbo.Cities,

  distance INT     NOT NULL,

  PRIMARY KEY(city1, city2),

  CHECK(city1 < city2),

  CHECK(distance > 0)

);

INSERT INTO dbo.Roads(city1, city2, distance) VALUES('ANC', 'FAI', 359);

INSERT INTO dbo.Roads(city1, city2, distance) VALUES('ATL', 'ORD', 715);

INSERT INTO dbo.Roads(city1, city2, distance) VALUES('ATL', 'IAH', 800);

INSERT INTO dbo.Roads(city1, city2, distance) VALUES('ATL', 'MCI', 805);

INSERT INTO dbo.Roads(city1, city2, distance) VALUES('ATL', 'MIA', 665);

INSERT INTO dbo.Roads(city1, city2, distance) VALUES('ATL', 'JFK', 865);

INSERT INTO dbo.Roads(city1, city2, distance) VALUES('DEN', 'IAH', 1120);

INSERT INTO dbo.Roads(city1, city2, distance) VALUES('DEN', 'MCI', 600);

INSERT INTO dbo.Roads(city1, city2, distance) VALUES('DEN', 'LAX', 1025);

INSERT INTO dbo.Roads(city1, city2, distance) VALUES('DEN', 'MSP', 915);

INSERT INTO dbo.Roads(city1, city2, distance) VALUES('DEN', 'SEA', 1335);

INSERT INTO dbo.Roads(city1, city2, distance) VALUES('DEN', 'SFO', 1270);

INSERT INTO dbo.Roads(city1, city2, distance) VALUES('IAH', 'MCI', 795);

INSERT INTO dbo.Roads(city1, city2, distance) VALUES('IAH', 'LAX', 1550);

INSERT INTO dbo.Roads(city1, city2, distance) VALUES('IAH', 'MIA', 1190);

INSERT INTO dbo.Roads(city1, city2, distance) VALUES('JFK', 'ORD', 795);

INSERT INTO dbo.Roads(city1, city2, distance) VALUES('LAX', 'SFO', 385);

INSERT INTO dbo.Roads(city1, city2, distance) VALUES('MCI', 'ORD', 525);

INSERT INTO dbo.Roads(city1, city2, distance) VALUES('MCI', 'MSP', 440);

INSERT INTO dbo.Roads(city1, city2, distance) VALUES('MSP', 'ORD', 410);

INSERT INTO dbo.Roads(city1, city2, distance) VALUES('MSP', 'SEA', 2015);

INSERT INTO dbo.Roads(city1, city2, distance) VALUES('SEA', 'SFO', 815);

GO

SELECT * FROM dbo.Roads

GO

WITH Roads2  --每对城市生成行

AS

(

	SELECT city1 AS from_city,city2 AS to_city FROM dbo.Roads

	UNION ALL

	SELECT city2,city2 FROM dbo.Roads

),

RoadPaths AS

(

--返回第一级别的所有可到达的城市对

	SELECT from_city,to_city,

	CAST('.'+from_city+'.'+to_city+'.' AS VARCHAR(max)) AS path

	FROM Roads2

	UNION ALL

    SELECT F.from_city,T.to_city,--返回下一级别的可到达的城市对

	CAST(F.path+T.to_city+'.' AS VARCHAR(MAX)) --路径需要验明循环

	FROM RoadPaths AS F

	JOIN Roads2 AS T

	ON CASE WHEN F.path LIKE '%.'+T.to_city+'.%' --如果to_city出现在from_city的路径中，则检测到循环

		THEN 1 ELSE 0 END =0

	AND F.to_city =T.from_city

)

SELECT DISTINCT from_city,to_city FROM RoadPaths;--返回Roads 的传递包

GO

---------------------------------------------------------------------

-- Undirected Cyclic Graph

---------------------------------------------------------------------

-- Listing 9-38: Transitive Closure of Roads (Undirected Cyclic Graph) 传递闭包

WITH Roads2 -- Two rows for each pair (f-->t, t-->f)

AS

(

  SELECT city1 AS from_city, city2 AS to_city FROM dbo.Roads

  UNION ALL

  SELECT city2, city1 FROM dbo.Roads

),

RoadPaths AS

(

  -- Return all first-level reachability pairs

  SELECT from_city, to_city,

    -- path is needed to identify cycles

    CAST('.' + from_city + '.' + to_city + '.' AS VARCHAR(MAX)) AS path

  FROM Roads2

  UNION ALL

  -- Return next-level reachability pairs

  SELECT F.from_city, T.to_city,

    CAST(F.path + T.to_city + '.' AS VARCHAR(MAX))

  FROM RoadPaths AS F

    JOIN Roads2 AS T

      -- if to_city appears in from_city's path, cycle detected

      ON CASE WHEN F.path LIKE '%.' + T.to_city + '.%'

              THEN 1 ELSE 0 END = 0

      AND F.to_city = T.from_city

)

-- Return Transitive Closure of Roads

SELECT DISTINCT from_city, to_city

FROM RoadPaths;

GO

-- Listing 9-39: Creation Script for the fn_RoadsTC UDF

IF OBJECT_ID('dbo.fn_RoadsTC') IS NOT NULL

  DROP FUNCTION dbo.fn_RoadsTC;

GO

CREATE FUNCTION dbo.fn_RoadsTC() RETURNS @RoadsTC TABLE (

  from_city VARCHAR(3) NOT NULL,

  to_city   VARCHAR(3) NOT NULL,

  PRIMARY KEY (from_city, to_city)

)

AS

BEGIN

  DECLARE @added as INT;

  INSERT INTO @RoadsTC(from_city, to_city)

    SELECT city1, city2 FROM dbo.Roads;

  SET @added = @@rowcount;

  INSERT INTO @RoadsTC

    SELECT city2, city1 FROM dbo.Roads

  SET @added = @added + @@rowcount;

  WHILE @added > 0 BEGIN

    INSERT INTO @RoadsTC

      SELECT DISTINCT TC.from_city, R.city2

      FROM @RoadsTC AS TC

        JOIN dbo.Roads AS R

          ON R.city1 = TC.to_city

      WHERE NOT EXISTS

        (SELECT * FROM @RoadsTC AS TC2

         WHERE TC2.from_city = TC.from_city

           AND TC2.to_city = R.city2)

        AND TC.from_city <> R.city2;

    SET @added = @@rowcount;

    INSERT INTO @RoadsTC

      SELECT DISTINCT TC.from_city, R.city1

      FROM @RoadsTC AS TC

        JOIN dbo.Roads AS R

          ON R.city2 = TC.to_city

      WHERE NOT EXISTS

        (SELECT * FROM @RoadsTC AS TC2

         WHERE TC2.from_city = TC.from_city

           AND TC2.to_city = R.city1)

        AND TC.from_city <> R.city1;

    SET @added = @added + @@rowcount;

  END

  RETURN;

END

GO

-- Use the fn_RoadsTC UDF  --传递闭包函数

SELECT * FROM dbo.fn_RoadsTC();

GO

-- Listing 9-40: All paths and distances in Roads (15262 rows）返回所有路径和距离

WITH Roads2

AS

(

  SELECT city1 AS from_city, city2 AS to_city, distance FROM dbo.Roads

  UNION ALL

  SELECT city2, city1, distance FROM dbo.Roads

),

RoadPaths AS

(

  SELECT from_city, to_city, distance,

    CAST('.' + from_city + '.' + to_city + '.' AS VARCHAR(MAX)) AS path

  FROM Roads2

  UNION ALL

  SELECT F.from_city, T.to_city, F.distance + T.distance,

    CAST(F.path + T.to_city + '.' AS VARCHAR(MAX))

  FROM RoadPaths AS F

    JOIN Roads2 AS T

      ON CASE WHEN F.path LIKE '%.' + T.to_city + '.%'

              THEN 1 ELSE 0 END = 0

      AND F.to_city = T.from_city

)

-- Return all paths and distances

SELECT * FROM RoadPaths;

GO

-- Listing 9-41: Shortest paths in Roads 返回最短路径

WITH Roads2

AS

(

  SELECT city1 AS from_city, city2 AS to_city, distance FROM dbo.Roads

  UNION ALL

  SELECT city2, city1, distance FROM dbo.Roads

),

RoadPaths AS

(

  SELECT from_city, to_city, distance,

    CAST('.' + from_city + '.' + to_city + '.' AS VARCHAR(MAX)) AS path

  FROM Roads2

  UNION ALL

  SELECT F.from_city, T.to_city, F.distance + T.distance,

    CAST(F.path + T.to_city + '.' AS VARCHAR(MAX))

  FROM RoadPaths AS F

    JOIN Roads2 AS T

      ON CASE WHEN F.path LIKE '%.' + T.to_city + '.%'

              THEN 1 ELSE 0 END = 0

      AND F.to_city = T.from_city

),

RoadsMinDist -- Min distance for each pair in TC 每对城市的最短距离

AS

(

  SELECT from_city, to_city, MIN(distance) AS mindist

  FROM RoadPaths

  GROUP BY from_city, to_city

)

-- Return shortest paths and distances 返回最短路径和距离

SELECT RP.*

FROM RoadsMinDist AS RMD

  JOIN RoadPaths AS RP

    ON RMD.from_city = RP.from_city

    AND RMD.to_city = RP.to_city

    AND RMD.mindist = RP.distance;

GO

-- Listing 9-42: Load Shortest Road Paths Into a Table 把最短路径保存到表

WITH Roads2

AS

(

  SELECT city1 AS from_city, city2 AS to_city, distance FROM dbo.Roads

  UNION ALL

  SELECT city2, city1, distance FROM dbo.Roads

),

RoadPaths AS

(

  SELECT from_city, to_city, distance,

    CAST('.' + from_city + '.' + to_city + '.' AS VARCHAR(MAX)) AS path

  FROM Roads2

  UNION ALL

  SELECT F.from_city, T.to_city, F.distance + T.distance,

    CAST(F.path + T.to_city + '.' AS VARCHAR(MAX))

  FROM RoadPaths AS F

    JOIN Roads2 AS T

      ON CASE WHEN F.path LIKE '%.' + T.to_city + '.%'

              THEN 1 ELSE 0 END = 0

      AND F.to_city = T.from_city

),

RoadsMinDist

AS

(

  SELECT from_city, to_city, MIN(distance) AS mindist

  FROM RoadPaths

  GROUP BY from_city, to_city

)

SELECT RP.*

INTO dbo.RoadPaths

FROM RoadsMinDist AS RMD

  JOIN RoadPaths AS RP

    ON RMD.from_city = RP.from_city

    AND RMD.to_city = RP.to_city

    AND RMD.mindist = RP.distance;

CREATE UNIQUE CLUSTERED INDEX idx_uc_from_city_to_city

  ON dbo.RoadPaths(from_city, to_city);

GO

-- Return shortest path between Los Angeles and New York 测试查询最短路径

SELECT * FROM dbo.RoadPaths

WHERE from_city = 'LAX' AND to_city = 'JFK';

GO

-- Listing 9-43: Creation Script for the fn_RoadsTC UDF

IF OBJECT_ID('dbo.fn_RoadsTC') IS NOT NULL

  DROP FUNCTION dbo.fn_RoadsTC;

GO

CREATE FUNCTION dbo.fn_RoadsTC() RETURNS @RoadsTC TABLE

(

  uniquifier INT          NOT NULL IDENTITY,

  from_city  VARCHAR(3)   NOT NULL,

  to_city    VARCHAR(3)   NOT NULL,

  distance   INT          NOT NULL,

  route      VARCHAR(MAX) NOT NULL,

  PRIMARY KEY (from_city, to_city, uniquifier)

)

AS

BEGIN

  DECLARE @added AS INT;

  INSERT INTO @RoadsTC

    SELECT city1 AS from_city, city2 AS to_city, distance,

      '.' + city1 + '.' + city2 + '.'

    FROM dbo.Roads;

  SET @added = @@rowcount;

  INSERT INTO @RoadsTC

    SELECT city2, city1, distance, '.' + city2 + '.' + city1 + '.'

    FROM dbo.Roads;

  SET @added = @added + @@rowcount;

  WHILE @added > 0 BEGIN

    INSERT INTO @RoadsTC

      SELECT DISTINCT TC.from_city, R.city2,

        TC.distance + R.distance, TC.route + city2 + '.'

      FROM @RoadsTC AS TC

        JOIN dbo.Roads AS R

          ON R.city1 = TC.to_city

      WHERE NOT EXISTS

        (SELECT * FROM @RoadsTC AS TC2

         WHERE TC2.from_city = TC.from_city

           AND TC2.to_city = R.city2

           AND TC2.distance <= TC.distance + R.distance)

        AND TC.from_city <> R.city2;

    SET @added = @@rowcount;

    INSERT INTO @RoadsTC

      SELECT DISTINCT TC.from_city, R.city1,

        TC.distance + R.distance, TC.route + city1 + '.'

      FROM @RoadsTC AS TC

        JOIN dbo.Roads AS R

          ON R.city2 = TC.to_city

      WHERE NOT EXISTS

        (SELECT * FROM @RoadsTC AS TC2

         WHERE TC2.from_city = TC.from_city

           AND TC2.to_city = R.city1

           AND TC2.distance <= TC.distance + R.distance)

        AND TC.from_city <> R.city1;

    SET @added = @added + @@rowcount;

  END

  RETURN;

END

GO

-- Return shortest paths and distances

SELECT from_city, to_city, distance, route

FROM (SELECT from_city, to_city, distance, route,

        RANK() OVER (PARTITION BY from_city, to_city

                     ORDER BY distance) AS rk

      FROM dbo.fn_RoadsTC()) AS RTC

WHERE rk = 1;

GO

-- Cleanup

DROP TABLE dbo.RoadPaths;

GO

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