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‎Permutations, Combinations, Sequences and Random Numbers/SQL Scripts/19 Random Walk Sequence.sql‎

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/*********************************************************************
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Scott Peters
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Random Walk
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https://advancedsqlpuzzles.com
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Last Updated: 07/25/2022
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This script is written in SQL Server's T-SQL
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---------------------------------------------------------------------
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The following solves a random walk for the following problem:
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You are the dinner host of a weekly gathering of 8 friends (including yourself).
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You want to determine who hosts the next dinner party using the following scheme:
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After dinner, the guests sit around a round table. You (the current host) flip a fair coin.
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If it comes up heads, you pass it to the person on your right, and if it comes up tails, you pass it to person on your left.
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The person who receives the coin repeats the procedure, flipping it and passing it right or left, depending on the outcome of the flip.
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This process keeps going until all but one dinner guest has held the coin.
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The last member who has not yet touched the coin is then declared the winner and must host the next dinner party.
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**********************************************************************/
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SET NOCOUNT ON;
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---------------------
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---------------------
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--Tables used in script
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DROP TABLE IF EXISTS #Numbers;
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DROP TABLE IF EXISTS #ParticipantsASC;
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DROP TABLE IF EXISTS #ParticipantsDESC;
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DROP TABLE IF EXISTS #Participants;
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DROP TABLE IF EXISTS #CoinFlipResults;
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DROP TABLE IF EXISTS #WinnerResults;
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DROP TABLE IF EXISTS #WinnerResultsHistory;
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GO
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---------------------
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---------------------
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--Create #WinnerResultsHistory table
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CREATE TABLE #WinnerResultsHistory
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(
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Iteration INTEGER IDENTITY(1,1) PRIMARY KEY,
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Participant INTEGER NOT NULL,
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CoinFlips INTEGER NOT NULL
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);
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GO
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------------------------
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------------------------
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------------------------
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--Create #Numbers table
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CREATE TABLE #Numbers
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(
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Number INTEGER IDENTITY(0,1) PRIMARY KEY, -- Begin at 0 and increate by 1
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InsertDate DATETIME NOT NULL
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);
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GO
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INSERT INTO #Numbers(InsertDate) VALUES (GETDATE());
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GO 300
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------------------------
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------------------------
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------------------------
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--Create #ParticipantsASC table
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CREATE TABLE #ParticipantsASC
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(
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CoinFlipSum INTEGER IDENTITY(0,1) PRIMARY KEY, -- Begin at 0 and increase by 1
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Participant INTEGER
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);
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GO
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--Create ###ParticipantsDESC table
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CREATE TABLE #ParticipantsDESC
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(
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CoinFlipSum INTEGER IDENTITY(-1,-1) PRIMARY KEY, -- Begin at -1 and increate by -1
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Participant INTEGER
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);
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GO
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--Create #Participants table
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CREATE TABLE #Participants
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(
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CoinFlipSum INTEGER NOT NULL,
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Participant INTEGER NOT NULL
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);
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GO
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------------------------
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------------------------
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------------------------
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--Create and populate the #Participants table
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--For simplicity, I create seperate sequences and tables
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DROP SEQUENCE IF EXISTS dbo.MySequenceASC;
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DROP SEQUENCE IF EXISTS dbo.MySequenceDESC;
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GO
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--Start with 0, increment by 1
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CREATE SEQUENCE dbo.MySequenceASC AS INTEGER
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START WITH 0
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INCREMENT BY 1
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MINVALUE 0
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MAXVALUE 7-----------------Set to number of participants!
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CYCLE;
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GO
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--Start with 7, increment by -1
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CREATE SEQUENCE dbo.MySequenceDESC AS INTEGER
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START WITH 7
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INCREMENT BY -1
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MINVALUE 0
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MAXVALUE 7-----------------Set to number of participants!
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CYCLE;
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GO
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INSERT INTO #ParticipantsASC (Participant)
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SELECT (NEXT VALUE FOR dbo.MySequenceASC) AS Participant;
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GO 300
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INSERT INTO #ParticipantsDESC (Participant)
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SELECT (NEXT VALUE FOR dbo.MySequenceDESC) AS Participant;
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GO 300
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INSERT INTO #Participants (CoinFlipSum, Participant)
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SELECT CoinFlipSum, Participant FROM #ParticipantsASC
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UNION ALL
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SELECT CoinFlipSum, Participant FROM #ParticipantsDESC;
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GO
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------------------------
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------------------------
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------------------------
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--Perform an evaluation of the #Participants and #Numbers table
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--Ensure you have enough records in the #Participants and #Numbers tables
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IF((SELECT COUNT(*) FROM #Participants) < (SELECT COUNT(*) FROM #Numbers))
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BEGIN
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PRINT('#Participants record count is less than #Numbers')
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RETURN;
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END;
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GO
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------------------------
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------------------------
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------------------------
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--Create table #CoinFlipResults
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CREATE TABLE #CoinFlipResults
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(
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StepNumber INTEGER PRIMARY KEY,
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WindowSum INTEGER
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);
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GO
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------------------------
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------------------------
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------------------------
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--Create table #WinnerResults
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CREATE TABLE #WinnerResults
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(
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Participant INTEGER PRIMARY KEY,
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StepNumberFirstTouched INTEGER
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);
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GO
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------------------------
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------------------------
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------------------------
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--Set the number of iterations
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DECLARE @Iterations INTEGER = 1000;
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------------------------
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------------------------
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------------------------
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--Perform the random walk
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WHILE @Iterations >= 1
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BEGIN
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SET @Iterations = @Iterations - 1;
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TRUNCATE TABLE #CoinFlipResults;
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TRUNCATE TABLE #WinnerResults;
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------------------------
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------------------------
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------------------------
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--Insert into #CoinFlipResults table
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;WITH cte_RandomNumber AS
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(
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SELECT Number AS StepNumber
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,ABS(CHECKSUM(NEWID()) % 2) + 1 AS RandomNumber
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FROM #Numbers
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WHERE Number > 0
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),
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cte_Pass AS
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(
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SELECT StepNumber
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,(CASE RandomNumber WHEN 1 THEN -1 WHEN 2 THEN 1 END) AS PassDetermination
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FROM cte_RandomNumber
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)
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INSERT INTO #CoinFlipResults
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SELECT StepNumber
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,SUM(PassDetermination) OVER (ORDER BY StepNumber) AS WindowSum
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FROM cte_Pass
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ORDER BY StepNumber;
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------------------------
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------------------------
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------------------------
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--Insert into #WinnerResults table
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WITH cte_ResultsView AS
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(
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SELECT A.*, '----' AS ID, B.*
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FROM #CoinFlipResults a LEFT OUTER JOIN
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#Participants b on a.WindowSum = b.CoinFlipSum
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)
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INSERT INTO #WinnerResults
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SELECT Participant,
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MIN(StepNumber) AS StepNumberFirstTouched
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FROM cte_ResultsView
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GROUP BY Participant
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ORDER BY 2 DESC;
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------------------------
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------------------------
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------------------------
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--Insert into #WinnerResultsHistory table
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INSERT INTO #WinnerResultsHistory (Participant, CoinFlips)
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SELECT
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(SELECT TOP 1 Participant FROM #WinnerResults WHERE Participant <> 0 ORDER BY StepNumberFirstTouched DESC),
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(SELECT TOP 1
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StepNumberFirstTouched
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FROM #WinnerResults
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WHERE StepNumberFirstTouched < (SELECT MAX(StepNumberFirstTouched) FROM #WinnerResults)
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ORDER BY StepNumberFirstTouched DESC);
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END--END LOOP
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GO
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------------------------
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------------------------
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------------------------
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--Display summary statistics of the results
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SELECT Participant,
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COUNT(*) AS Count,
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MIN(CoinFlips) AS Min,
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MAX(CoinFlips) AS Max,
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AVG(CoinFlips) AS Avg,
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MAX(CoinFlips) - MIN(CoinFlips) AS Range,
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STDEV(CoinFlips) AS StandardDeviation
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FROM #WinnerResultsHistory
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GROUP BY Participant
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UNION
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SELECT 99999 AS Participant,
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COUNT(*) AS Count,
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MIN(CoinFlips) AS Min,
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MAX(CoinFlips) AS Max,
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AVG(CoinFlips) AS Avg,
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MAX(CoinFlips) - MIN(CoinFlips) AS Range,
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STDEV(CoinFlips) AS StandardDeviation
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FROM #WinnerResultsHistory;
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GO

‎Permutations, Combinations, Sequences and Random Numbers/SQL Scripts/20 Markov Chain Recursion.sql‎

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/*----------------------------------------------------
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Scott Peters
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Markov Chains
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https://AdvancedSQLPuzzles.com
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This script is written in SQL Server's T-SQL
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---------------------------------------------------------------------
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Below will solve for the following:
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In Probability Land, on a sunny day there is an equal probability of the next day being sunny or rainy.
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On a rainy day, there is a 70% chance it will rain the next day, and a 30% chance it will be sunny the next day.
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On average, how many rainy days are there in Probability Land?
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*/----------------------------------------------------
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-------------------------------
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-------------------------------
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--Tables used in script
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DROP TABLE IF EXISTS #Probabilities;
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DROP TABLE IF EXISTS #Numbers;
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DROP TABLE IF EXISTS #RandomNumbers;
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DROP TABLE IF EXISTS #ProbabilitesFinal;
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GO
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-------------------------------
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-------------------------------
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--Create and populate table #Probabilities
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CREATE TABLE #Probabilities
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(
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CurrentState INTEGER NOT NULL,
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FutureState INTEGER NOT NULL,
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Probability INTEGER NOT NULL,
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);
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GO
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--1 is Rainy, 2 is Sunny
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INSERT INTO #Probabilities (CurrentState, FutureState, Probability) VALUES
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(1,1,1),(1,1,2),(1,1,3),(1,1,4),(1,1,5),(1,1,6),(1,1,7),(1,2,8),(1,2,9),(1,2,10),
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(2,2,1),(2,2,2),(2,2,3),(2,2,4),(2,2,5),(2,1,6),(2,1,7),(2,1,8),(2,1,9),(2,1,10);
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GO
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-------------------------------
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-------------------------------
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--Declare and set the variables
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--This equates to the number of days to simulate
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DECLARE @vTotalNumbers INTEGER = 10000;
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-------------------------------
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-------------------------------
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--Insert into #Numbers table using recursion
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WITH cte_Recursion (Number)
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AS (
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SELECT 1 AS Number
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UNION ALL
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SELECT Number + 1
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FROM cte_Recursion
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WHERE Number < @vTotalNumbers
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)
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SELECT Number AS StepNumber
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INTO #Numbers
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FROM cte_Recursion
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OPTION (MAXRECURSION 0);
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-------------------------------
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-------------------------------
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--Insert into #RandomNumbers table
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SELECT StepNumber,
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CAST(NULL AS INTEGER) AS CurrentState,
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ABS(CHECKSUM(NEWID()) % 10) + 1 AS Probability
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INTO #RandomNumbers
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FROM #Numbers;
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GO
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--Seed the first record in the #RandomNumbers table
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--I'm arbitrarily setting this to 1 (Rain).
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UPDATE #RandomNumbers
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SET CurrentState = 1
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WHERE StepNumber = 1;
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GO
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-------------------------------
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-------------------------------
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--Insert into #ProbabilitesFinal using recursion
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WITH cte_Recursion AS
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(
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SELECT StepNumber
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,Probability
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,CurrentState
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FROM #RandomNumbers a WHERE StepNumber = 1
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UNION ALL
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SELECT n.StepNumber
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,n.Probability
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,CAST(p.FutureState AS INTEGER) AS CurrentState
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FROM cte_Recursion cte
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INNER JOIN
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#RandomNumbers n ON (cte.StepNumber + 1) = n.StepNumber
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INNER JOIN
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#Probabilities p ON cte.Probability = p.Probability AND cte.CurrentState = p.CurrentState
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)
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SELECT StepNumber
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,CurrentState
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,(CASE CurrentState WHEN 1 THEN 'Rainy' WHEN 2 THEN 'Sunny' END) AS [Description]
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,Probability
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INTO #ProbabilitesFinal
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FROM cte_Recursion
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ORDER BY StepNumber
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OPTION (MAXRECURSION 0);
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GO
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-------------------------------
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-------------------------------
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--Display a summary of counts
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SELECT [Description],
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COUNT(*) AS [Count]
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FROM #ProbabilitesFinal
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GROUP BY [Description]
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ORDER BY 1;
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GO

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