Designing a database of Recipes

The problem is similar to this (SO) question:
How to swap values of two rows in mysql without violating unique constraint?

Unfortunately, the answer is the same. Due to how MySQL checks UNIQUE (and primary and foreign key) constraints, i.e. row by row and not at the end of statements or at the end of transactions, swapping or rearranging values that are part of unique constraints, cannot be done easily.

I would go with your 1st suggestion:

1. Update each row's order with some large number (i.e. 1001, 1002, 1003) so that the original order is no longer conflicting, then update each row with the correct order values (1, 2, 3).

This way you can have the minimal (2) statements required to do the update and any other connection that reads the table between the 2 statements will still read a consistent state of values.

For the following assumed schema and example data

CREATE TABLE dbo.RecipeIngredients
    (
      RecipeId INT NOT NULL ,
      IngredientID INT NOT NULL ,
      Quantity INT NOT NULL ,
      UOM INT NOT NULL ,
      CONSTRAINT RecipeIngredients_PK 
          PRIMARY KEY ( RecipeId, IngredientID ) WITH (IGNORE_DUP_KEY = ON)
    ) ;

INSERT INTO dbo.RecipeIngredients
SELECT TOP (210000) ABS(CRYPT_GEN_RANDOM(8)/50000),
                     ABS(CRYPT_GEN_RANDOM(8) % 100),
                     ABS(CRYPT_GEN_RANDOM(8) % 10),
                     ABS(CRYPT_GEN_RANDOM(8) % 5)
FROM master..spt_values v1,                     
     master..spt_values v2


SELECT DISTINCT RecipeId, 'X' AS Name
INTO Recipes 
FROM  dbo.RecipeIngredients 

This populated 205,009 ingredient rows and 42,613 recipes. This will be slightly different each time due to the random element.

It assumes relatively few dupes (output after an example run was 217 duplicate recipe groups with two or three recipes per group). The most pathological case based on the figures in the OP would be 48,000 exact duplicates.

A script to set that up is

DROP TABLE dbo.RecipeIngredients,Recipes
GO

CREATE TABLE Recipes(
RecipeId INT IDENTITY,
Name VARCHAR(1))

INSERT INTO Recipes 
SELECT TOP 48000 'X'
FROM master..spt_values v1,                     
     master..spt_values v2

CREATE TABLE dbo.RecipeIngredients
    (
      RecipeId INT NOT NULL ,
      IngredientID INT NOT NULL ,
      Quantity INT NOT NULL ,
      UOM INT NOT NULL ,
      CONSTRAINT RecipeIngredients_PK 
          PRIMARY KEY ( RecipeId, IngredientID )) ;

INSERT INTO dbo.RecipeIngredients
SELECT RecipeId,IngredientID,Quantity,UOM
FROM Recipes
CROSS JOIN (SELECT 1,1,1 UNION ALL SELECT 2,2,2 UNION ALL  SELECT 3,3,3 UNION ALL SELECT 4,4,4) I(IngredientID,Quantity,UOM)

The following completed in less than a second on my machine for both cases.

CREATE TABLE #Concat
  (
     RecipeId     INT,
     concatenated VARCHAR(8000),
     PRIMARY KEY (concatenated, RecipeId)
  )

INSERT INTO #Concat
SELECT R.RecipeId,
       ISNULL(concatenated, '')
FROM   Recipes R
       CROSS APPLY (SELECT CAST(IngredientID AS VARCHAR(10)) + ',' + CAST(Quantity AS VARCHAR(10)) + ',' + CAST(UOM AS VARCHAR(10)) + ','
                    FROM   dbo.RecipeIngredients RI
                    WHERE  R.RecipeId = RecipeId
                    ORDER  BY IngredientID
                    FOR XML PATH('')) X (concatenated);

WITH C1
     AS (SELECT DISTINCT concatenated
         FROM   #Concat)
SELECT STUFF(Recipes, 1, 1, '')
FROM   C1
       CROSS APPLY (SELECT ',' + CAST(RecipeId AS VARCHAR(10))
                    FROM   #Concat C2
                    WHERE  C1.concatenated = C2.concatenated
                    ORDER  BY RecipeId
                    FOR XML PATH('')) R(Recipes)
WHERE  Recipes LIKE '%,%,%'

DROP TABLE #Concat 

One caveat

I assumed that the length of the concatenated string will not exceed 896 bytes. If it does this will raise an error at run time rather than silently failing. You will need to remove the primary key (and implicitly created index) from the #temp table. The maximum length of the concatenated string in my test setup was 125 characters.

If the concatenated string is too long to index then performance of the final XML PATH query consolidating the identical recipes could well be poor. Installing and using a custom CLR string aggregation would be one solution as that could do the concatenation with one pass of the data rather than a non indexed self join.

SELECT YourClrAggregate(RecipeId)
FROM #Concat
GROUP BY concatenated

I also tried

WITH Agg
     AS (SELECT RecipeId,
                MAX(IngredientID)          AS MaxIngredientID,
                MIN(IngredientID)          AS MinIngredientID,
                SUM(IngredientID)          AS SumIngredientID,
                COUNT(IngredientID)        AS CountIngredientID,
                CHECKSUM_AGG(IngredientID) AS ChkIngredientID,
                MAX(Quantity)              AS MaxQuantity,
                MIN(Quantity)              AS MinQuantity,
                SUM(Quantity)              AS SumQuantity,
                COUNT(Quantity)            AS CountQuantity,
                CHECKSUM_AGG(Quantity)     AS ChkQuantity,
                MAX(UOM)                   AS MaxUOM,
                MIN(UOM)                   AS MinUOM,
                SUM(UOM)                   AS SumUOM,
                COUNT(UOM)                 AS CountUOM,
                CHECKSUM_AGG(UOM)          AS ChkUOM
         FROM   dbo.RecipeIngredients
         GROUP  BY RecipeId)
SELECT  A1.RecipeId AS RecipeId1,
        A2.RecipeId AS RecipeId2
FROM   Agg A1
       JOIN Agg A2
         ON A1.MaxIngredientID = A2.MaxIngredientID
            AND A1.MinIngredientID = A2.MinIngredientID
            AND A1.SumIngredientID = A2.SumIngredientID
            AND A1.CountIngredientID = A2.CountIngredientID
            AND A1.ChkIngredientID = A2.ChkIngredientID
            AND A1.MaxQuantity = A2.MaxQuantity
            AND A1.MinQuantity = A2.MinQuantity
            AND A1.SumQuantity = A2.SumQuantity
            AND A1.CountQuantity = A2.CountQuantity
            AND A1.ChkQuantity = A2.ChkQuantity
            AND A1.MaxUOM = A2.MaxUOM
            AND A1.MinUOM = A2.MinUOM
            AND A1.SumUOM = A2.SumUOM
            AND A1.CountUOM = A2.CountUOM
            AND A1.ChkUOM = A2.ChkUOM
            AND A1.RecipeId <> A2.RecipeId
WHERE  NOT EXISTS (SELECT *
                   FROM   (SELECT *
                           FROM   RecipeIngredients
                           WHERE  RecipeId = A1.RecipeId) R1
                          FULL OUTER JOIN (SELECT *
                                           FROM   RecipeIngredients
                                           WHERE  RecipeId = A2.RecipeId) R2
                            ON R1.IngredientID = R2.IngredientID
                               AND R1.Quantity = R2.Quantity
                               AND R1.UOM = R2.UOM
                   WHERE  R1.RecipeId IS NULL
                           OR R2.RecipeId IS NULL) 

This works acceptably when there are relatively few duplicates (less than a second for the first example data) but performs badly in the pathological case as the initial aggregation returns exactly the same results for every RecipeID and so doesn't manage to cut down the number of comparisons at all.