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