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Permutations, Combinations, Sequences and Random Numbers/Recursion Examples/All Permutations Bit Mask Recursion.sql

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+/*----------------------------------------------------
+Scott Peters
+https://AdvancedSQLPuzzles.com
+
+Displays all permutations for the numbers 1 through n.
+
+*/----------------------------------------------------
+
+---------------------
+---------------------
+--Tables used
+DROP TABLE IF EXISTS #Numbers;
+GO
+
+---------------------
+---------------------
+--Declare and set variables
+DECLARE @vTotalNumbers BIGINT = 3;
+
+---------------------
+---------------------
+--Create a #Numbers table using recursion
+WITH cte_Recursion (Number) AS 
+(
+SELECT 1 AS Number
+UNION ALL
+SELECT  Number + 1
+FROM   cte_Recursion
+WHERE  Number < @vTotalNumbers
+)
+SELECT
+       Number
+INTO   #Numbers
+FROM   cte_Recursion
+OPTION (MAXRECURSION 0);
+
+---------------------
+---------------------
+WITH cte_Numbers AS
+(
+SELECT  CAST(Number AS VARCHAR(MAX)) AS Number
+FROM    #Numbers
+),
+cte_Bitmasks AS
+(
+SELECT
+        Number,
+        CAST(POWER(2, ROW_Number() OVER (ORDER BY Number) - 1) AS INT) AS Bitmask
+FROM    cte_Numbers
+),
+cte_Recursion AS
+(
+SELECT  Number AS Permutation,
+        Bitmask
+FROM    cte_Bitmasks
+UNION ALL
+SELECT  p.Permutation + ',' + b.Number,
+        p.Bitmask ^ b.Bitmask
+FROM    cte_Recursion p INNER JOIN
+        cte_Bitmasks b ON p.Bitmask ^ b.Bitmask > p.Bitmask
+)
+SELECT  ROW_NUMBER() OVER (ORDER BY GETDATE()) AS Id,
+        Permutation
+FROM    cte_Recursion
+WHERE   Bitmask = POWER(2, (SELECT COUNT(*) FROM cte_Numbers)) - 1;

Permutations, Combinations, Sequences and Random Numbers/Recursion Examples/All Permutations Recursion.sql

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+/*----------------------------------------------------
+Scott Peters
+https://AdvancedSQLPuzzles.com
+
+Displays all permutations for the numbers 1 through n.
+
+*/----------------------------------------------------
+
+---------------------
+---------------------
+DROP TABLE IF EXISTS #Numbers;
+GO
+
+---------------------
+---------------------
+DECLARE @vTotalNumbers INTEGER = 3;
+
+---------------------
+---------------------
+WITH cte_Numbers (Number)
+AS (
+    SELECT 1 AS Number
+    UNION ALL
+    SELECT  Number + 1
+    FROM   cte_Numbers
+    WHERE  Number < @vTotalNumbers
+)
+SELECT
+       Number
+INTO    #Numbers
+FROM   cte_Numbers
+OPTION (MAXRECURSION 0);
+
+---------------------
+---------------------
+WITH cte_Recursion (Permutation, Id, Depth)
+AS
+(
+SELECT  CAST(Number AS VARCHAR(MAX)),
+        CAST(CONCAT(Number,';') AS VARCHAR(MAX)),
+        1 AS Depth
+FROM    #Numbers
+UNION ALL
+SELECT  CONCAT(a.Permutation,',',b.Number),
+        CONCAT(a.Id,b.Number,';'),
+        a.Depth + 1
+FROM    cte_Recursion a,
+        #Numbers b
+WHERE   a.Depth < @vTotalNumbers AND
+        a.Id NOT LIKE CONCAT('%',b.Number,';%')
+)
+SELECT  Permutation
+FROM    cte_Recursion;

Permutations, Combinations, Sequences and Random Numbers/Recursion Examples/Associates Recursion.sql

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+/*----------------------------------------------------
+Scott Peters
+https://AdvancedSQLPuzzles.com
+
+Groups hierarchies together.
+
+*/----------------------------------------------------
+
+---------------------
+---------------------
+DROP TABLE IF EXISTS #Associates;
+GO
+
+---------------------
+---------------------
+CREATE TABLE #Associates
+(
+Associate1 VARCHAR(100),
+Associate2 VARCHAR(100),
+PRIMARY KEY (Associate1, Associate2)
+);
+GO
+
+---------------------
+---------------------
+INSERT INTO #Associates (Associate1, Associate2) VALUES
+('Anne','Betty'),
+('Anne','Charles'),
+('Betty','Dan'),
+('Charles','Emma'),
+('Francis','George'),
+('George','Harriet');
+GO
+
+---------------------
+---------------------
+WITH cte_Recursion AS
+(
+SELECT  Associate1,
+        Associate2,
+        1 AS Depth
+FROM    #Associates
+UNION ALL
+SELECT  a.Associate1,
+        b.Associate2,
+        Depth + 1 AS Depth
+FROM    #Associates a INNER JOIN
+        cte_Recursion b ON a.Associate2 = b.Associate1
+)
+SELECT  *
+FROM    cte_Recursion
+UNION ALL
+SELECT  Associate1,
+        Associate1,
+        0 AS Depth
+FROM    #Associates;
+GO

Permutations, Combinations, Sequences and Random Numbers/Recursion Examples/Double the Number Recursion.sql

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+/*----------------------------------------------------
+Scott Peters
+https://AdvancedSQLPuzzles.com
+
+Begining at 1, this recursive statement will double 
+the number for each record... 1, 2, 4, 8. 16, 32.....
+
+*/----------------------------------------------------
+
+---------------------
+---------------------
+DROP TABLE IF EXISTS #Numbers;
+GO
+
+---------------------
+---------------------
+CREATE TABLE #Numbers
+(
+Number INTEGER NOT NULL PRIMARY KEY
+);
+
+INSERT INTO #Numbers VALUES (1),(2),(3),(4),(5);
+GO
+
+---------------------
+---------------------
+;WITH cte_Numbers AS
+(
+SELECT  *
+FROM    #Numbers
+),
+cte_Recursion AS
+(
+SELECT  Number,
+        CASE WHEN Number = 1 THEN 1 ELSE Number * 2 END AS RunningSum
+FROM    #Numbers
+WHERE Number = 1
+UNION ALL
+SELECT  
+        t.Number,
+		(RunningSum * 2) AS RunningSum
+FROM    cte_Recursion cte
+        INNER JOIN
+        cte_Numbers t ON t.Number = (cte.Number + 1)
+)
+SELECT   *
+FROM     cte_Recursion
+ORDER BY Number;

Permutations, Combinations, Sequences and Random Numbers/Recursion Examples/Factorials Recursion.sql

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+/*----------------------------------------------------
+Scott Peters
+https://AdvancedSQLPuzzles.com
+
+Calcualtes factorials
+
+*/----------------------------------------------------
+
+---------------------
+---------------------
+DECLARE @vTotalNumbers INTEGER = 10;
+
+---------------------
+---------------------
+WITH cte_Recursion (Number, Factorial) AS
+(
+SELECT 1,
+       1
+UNION ALL
+SELECT  Number + 1 AS Number,
+       (Number + 1) * Factorial AS Factorial
+FROM   cte_Recursion
+WHERE  Number < @vTotalNumbers
+)
+SELECT Number,
+       Factorial
+FROM   cte_Recursion
+OPTION (MAXRECURSION 0);--A value of 0 means no limit to the recursion level;
+

Permutations, Combinations, Sequences and Random Numbers/Recursion Examples/Fibonacci Sequence Recursion.sql

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+/*----------------------------------------------------
+Scott Peters
+https://AdvancedSQLPuzzles.com
+
+Calculates Fibonacci numbers
+
+*/----------------------------------------------------
+
+WITH cte_Recursion (PrevNumber, Number) AS
+(
+SELECT  0, 1
+UNION ALL
+SELECT  Number, PrevNumber + Number
+FROM    cte_Recursion
+WHERE   Number < 1000000000
+)
+SELECT PrevNumber AS Fibonacci
+FROM   cte_Recursion
+OPTION (MAXRECURSION 0);

Permutations, Combinations, Sequences and Random Numbers/Recursion Examples/Floor and Ceiling Caps Recursion.sql

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+/*----------------------------------------------------
+Scott Peters
+https://AdvancedSQLPuzzles.com
+
+Displays a running total where the sum cannot go higher than 10 or lower than 0.
+
+*/----------------------------------------------------
+
+
+DROP TABLE IF EXISTS #Numbers;
+GO
+
+CREATE TABLE #Numbers
+(
+Id         INTEGER,
+StepNumber INTEGER,
+[Count]    INTEGER
+);
+GO
+
+INSERT INTO #Numbers VALUES
+ (1,1,1) 
+,(1,2,-2)
+,(1,3,-1)
+,(1,4,12)
+,(1,5,-2)
+,(2,1,7)
+,(2,2,-3);
+GO
+
+WITH cte_Numbers AS
+(
+SELECT  *
+FROM    #Numbers
+),
+cte_Recursion AS
+(
+SELECT  Id,
+        [Count],
+		[Count] as RunningSum,
+        CASE WHEN [Count] < 0 THEN 0
+             WHEN [Count] > 10 THEN 10
+             ELSE [Count]
+        END AS RunningSumFloorCap,
+        StepNumber
+FROM    #Numbers
+WHERE StepNumber = 1
+UNION ALL
+SELECT  cte.ID,
+        t.[Count],
+		t.[Count] + cte.[Count],
+        (CASE WHEN t.[Count] + cte.RunningSumFloorCap < 0 THEN 0
+              WHEN t.[Count] + cte.RunningSumFloorCap > 10 THEN 10
+              ELSE t.[Count] + cte.RunningSumFloorCap
+        END) AS RunningSumFloorCap,
+        t.StepNumber
+FROM    cte_Recursion cte
+        INNER JOIN
+        cte_Numbers t ON t.StepNumber = (cte.StepNumber + 1) AND t.ID = cte.ID
+)
+SELECT   *
+FROM     cte_Recursion
+ORDER BY ID,
+         StepNumber;

Permutations, Combinations, Sequences and Random Numbers/Recursion Examples/Group Concatenation Recursion.sql

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+/*----------------------------------------------------
+Scott Peters
+https://AdvancedSQLPuzzles.com
+
+Same as the STRING_AGG funtion.
+Concatenates the values of string expressions and places separator values between them.
+
+*/----------------------------------------------------
+
+-------------------------------
+-------------------------------
+DROP TABLE IF EXISTS #Example;
+GO
+
+-------------------------------
+-------------------------------
+CREATE TABLE #Example
+(
+SequenceNumber  INTEGER PRIMARY KEY,
+String          VARCHAR(100)
+);
+GO
+
+INSERT INTO #Example VALUES
+(1,'Hello'),
+(2,'World!');
+GO
+
+-------------------------------
+-------------------------------
+WITH
+cte_Recursion(String2,Depth) AS
+(
+SELECT  CAST('' AS NVARCHAR(MAX)),
+        CAST(MAX(SequenceNumber) AS INTEGER)
+FROM    #Example
+UNION ALL
+SELECT  e.String + ' ' + r.String2, r.Depth - 1
+FROM    cte_Recursion r INNER JOIN
+        #Example e ON r.Depth = e.SequenceNumber
+)
+SELECT  String2
+FROM    cte_Recursion
+WHERE   Depth = 0;