💎SQL Reloaded: Power of Joins V (Semi-Joins and Anti-Joins)

An incursion in the world of joins is incomplete without approaching two other important techniques for writing queries: semi-joins and anti-joins, some of the techniques specific to them allowing to speed up queries and reduce queries’ complexity. An anti-join returns rows from the left table where no matches is found in the right table, while an semi-join returns returns rows from the left table if at least a match is found in the second table. 

The typical techniques for creating semi-joins and anti-joins are based on IN or EXISTS operators, respectively their negations the NOT EXISTS and NOT IN, both operators being available in SQL Server and Oracle. According to the above definitions also the EXCEPT and INTERSECT operators introduced in horizontal joins post could be used to create anti-joins, respectively semi-joins too, they being introduced by Microsoft starting with SQL Server 2005 in order to compare whole rows rather then a smaller set of attributes. Another operators that allows creating anti-joins and semi-joins and introduced with SQL Server 2005 is the CROSS APPLY and OUTER APPLY operators.

Because the  EXCEPT and INTERSECT operators were introduced in a previous post, this post is focused on the other mentioned operators, for exemplification of the techniques following to use again the Production.Product and Purchasing.PurchaseOrderDetail tables from AdventureWorks database.

IN operator allows to test whether a given (attribute) value is in a list of values, the respective list could be based also on the values returned by another query, called actually a subquery. The output is not influenced by the eventual duplicates in the list of values, though for the sake of simplicity and testability it makes sense to provide a list of distinct values.
 
EXISTS operator provides a similar functionality like the IN operator, however it checks only whether a record exists in what is called a correlated suquery (also known as repeated subquery, is a subquery making direct reference to one or more of the attributes of the main query). The subquery used with an IN operator could be easily translated to a correlated subquery by bringing the attribute used to create the list of values into the WHERE clause.

Let’s start with a simple problem to exemplify the use of a semi-join, for example to select only the products that have a PO (Purchase Order) placed, the query could be written as follows:
 

-- Products with PO placed (IN operator) 
SELECT ITM.ProductID  
, ITM.ProductNumber  
, ITM.StandardCost 
FROM Production.Product ITM  
WHERE ITM.ProductID IN (--list of Product IDs with PO placed 
    SELECT DISTINCT POD.ProductID  
     FROM Purchasing.PurchaseOrderDetail POD  
       JOIN Purchasing.PurchaseOrderHeader POH  
          ON POD.PurchaseOrderID = POH.PurchaseOrderID 
      WHERE POH.Status IN (2, 4) -- 2-Approved, 4-Complete  
     )  

The above query could be rewritten using the EXISTS operator, the correlated query being based on ProductID attribute found in both tables:
 

-- Products with PO placed (EXISTS operator) 
SELECT ITM.ProductID  
, ITM.ProductNumber  
, ITM.StandardCost 
FROM Production.Product ITM  
WHERE EXISTS (--list of Product IDs with PO placed 
     SELECT 1 
     FROM Purchasing.PurchaseOrderDetail POD  
       JOIN Purchasing.PurchaseOrderHeader POH  
          ON POD.PurchaseOrderID = POH.PurchaseOrderID 
     WHERE POH.Status IN (2, 4) -- 2-Approved, 4-Complete  
         AND POD.ProductID = ITM.ProductID -- correlated constraint 
)  

Notes:
1.    As usual special attention must be given to the handling of NULL values either by replacing them with a default value or by handing the NULL case in the WHERE clause.
2.   The Execution Plan for the above two queries is the same, SQL Server using a Hash Match (Left Semi Join) for both operators. I was trying to find information on whether there are any recommendations that advices on the use of one of the two operators in the detriment of the other, however I found nothing in this direction for SQL Server. R. Schrag offers a rule of dumb rooted in Oracle documentation and based on the selectivity of a query, a query being highly selective if it returns the least number of rows:

"If the main body of your query is highly selective, then an EXISTS clause might be more appropriate to semi-join to the target table. However, if the main body of your query is not so selective and the subquery (the target of the semi-join) is more selective, then an IN clause might be more appropriate." [1]

Both above solutions are ideal when no data are needed from the tables used in the subquery, however quite often such a need arises, for example to show the volume of PO placed, the last PO Date, and so on, in such cases an inner join could be used instead:
 

-- Products with PO placed (inner join) SELECT ITM.ProductID  
, ITM.ProductNumber  
, ITM.StandardCost 
, POD.TotalOrderQty 
, POD.LastOrderDate 
FROM Production.Product ITM  
JOIN (--aggregated PO details 
    SELECT POD.ProductID  
    , SUM(POD.OrderQty) TotalOrderQty 
    , Max(OrderDate) LastOrderDate 
     FROM Purchasing.PurchaseOrderDetail POD  
       JOIN Purchasing.PurchaseOrderHeader POH  
          ON POD.PurchaseOrderID = POH.PurchaseOrderID 
     WHERE POH.Status IN (2, 4) -- 2-Approved, 4-Complete  
     GROUP BY POD.ProductID 
    ) POD 
    ON POD.ProductID = ITM.ProductID 

For the same purpose could be used also a CROSS APPLY taking care to eliminate the Products for which no record is retrieved in the subquery, this approach is actually a mixture between an inner join and a correlated query:

 -- Products with PO placed (CROSS APPLY) 
SELECT ITM.ProductID  
, ITM.ProductNumber  
, ITM.StandardCost  
, POD.TotalOrderQty  
, POD.LastOrderDate  
FROM Production.Product ITM  
     CROSS APPLY (--aggregated PO details  
     SELECT SUM(POD.OrderQty) TotalOrderQty  
     , Max(OrderDate) LastOrderDate  
     FROM Purchasing.PurchaseOrderDetail POD  
           JOIN Purchasing.PurchaseOrderHeader POH  
              ON POD.PurchaseOrderID = POH.PurchaseOrderID  
     WHERE POH.Status IN (2, 4) -- 2-Approved, 4-Complete  
        AND POD.ProductID = ITM.ProductID  
    ) POD  
WHERE POD.TotalOrderQty IS NOT NULL

Notes:
1.   The IN and EXISTS query versions seems to provide better performance than the use of vertical joins, though from my experience is often needed to provide information also from the subqueries used with the respective operators, therefore the inner join provides more flexibility in the detriment of relatively poorer performance.
2.  Microsoft’s implementation for IN operator allows using only single list of values, in contrast with Oracle that allows working with lists of n-uples. This problem in theory could be solved using the IN operators with a correlated subquery. An example of such a problem is finding the last PO placed for each Product:

 -- Last PO placed per Product (IN + correlated query) 
SELECT POD.PurchaseOrderDetailID 
, POD.ProductID  
, POH.OrderDate 
, POD.OrderQty 
FROM Purchasing.PurchaseOrderDetail POD  
     JOIN Purchasing.PurchaseOrderHeader POH         ON POD.PurchaseOrderID = POH.PurchaseOrderID 
WHERE POH.Status IN (2, 4) -- 2-Approved, 4-Complete  
   AND POH.OrderDate IN (--Last PO Date per Product 
      SELECT Max(POH1.OrderDate) LastOrderDate 
      FROM Purchasing.PurchaseOrderDetail POD1 
          JOIN Purchasing.PurchaseOrderHeader POH1 
             ON POD1.PurchaseOrderID = POH1.PurchaseOrderID 
    WHERE POH1.Status IN (2, 4) -- 2-Approved, 4-Complete  
AND POD1.ProductID = POD.ProductID -- correlated constraint 
) 

This might not be the best approach to solve this problem though the query is intended only to show a technique. The query could be rewritten using an inner join or the EXISTS operator, but I will show only the later approach because it comes with an interesting technique – because the LastOrderDate and ProductID are used as pair of values in order to retrieve the last PO per Product, given the fact that LastOrderDate is an aggregate value, the correlated constraint needs to be added in HAVING clause:
 

-- Last PO placed per Product (correlated query) 
SELECT POD.PurchaseOrderDetailID 
, POD.ProductID  
, POH.OrderDate 
, POD.OrderQty 
FROM Purchasing.PurchaseOrderDetail POD  
     JOIN Purchasing.PurchaseOrderHeader POH 
        ON POD.PurchaseOrderID = POH.PurchaseOrderID 
WHERE POH.Status IN (2, 4) -- 2-Approved, 4-Complete  
     AND EXISTS(--Last PO Date per Product 
     SELECT 1 
     FROM Purchasing.PurchaseOrderDetail POD1 
          JOIN Purchasing.PurchaseOrderHeader POH1 
             ON POD1.PurchaseOrderID = POH1.PurchaseOrderID 
     WHERE POH1.Status IN (2, 4) -- 2-Approved, 4-Complete  
          AND POD1.ProductID = POD.ProductID -- correlated constraint 
     GROUP BY POD1.ProductID 
     HAVING Max(POH1.OrderDate) = POH.OrderDate 
     ) 

The NOT IN and NOT EXISTS versions of the operators simply negates the use of IN and EXISTS operators, showing thus the records for which a match is not found. The complementary problem of showing the Products with a PO placed is to show the Products without a PO placed, for this, as previously mentioned, being enough to add the NOT keyword in from of IN, respectively EXISTS in the first two queries from this post:

-- Products without PO placed (IN operator) 
SELECT ITM.ProductID  
, ITM.ProductNumber  
, ITM.StandardCost 
FROM Production.Product ITM  
WHERE ITM.ProductID NOT IN (--list of Product IDs with PO placed 
    SELECT DISTINCT POD.ProductID 
     FROM Purchasing.PurchaseOrderDetail POD 
       JOIN Purchasing.PurchaseOrderHeader POH 
          ON POD.PurchaseOrderID = POH.PurchaseOrderID 
      WHERE POH.Status IN (2, 4) -- 2-Approved, 4-Complete  
     )  

-- Products without PO placed (EXISTS operator) 
SELECT ITM.ProductID  
, ITM.ProductNumber  
, ITM.StandardCost 
FROM Production.Product ITM  
WHERE NOT EXISTS (--list of Product IDs with PO placed 
     SELECT 1 
     FROM Purchasing.PurchaseOrderDetail POD 
       JOIN Purchasing.PurchaseOrderHeader POH 
          ON POD.PurchaseOrderID = POH.PurchaseOrderID 
     WHERE POH.Status IN (2, 4) -- 2-Approved, 4-Complete  
         AND POD.ProductID = ITM.ProductID -- correlated constraint 
)  

An alternative to NOT IN and NOT EXISTS is the use of a LEFT JOIN transposing the project of A\B problem:
 

  -- Products without PO placed (left join) 
SELECT ITM.ProductID  
, ITM.ProductNumber  
, ITM.StandardCost FROM Production.Product ITM  
    LEFT JOIN (--aggregated PO details 
    SELECT POD.ProductID  
    FROM Purchasing.PurchaseOrderDetail POD 
       JOIN Purchasing.PurchaseOrderHeader POH 
          ON POD.PurchaseOrderID = POH.PurchaseOrderID 
     WHERE POH.Status IN (2, 4) -- 2-Approved, 4-Complete  
     GROUP BY POD.ProductID 
    ) POD 
    ON POD.ProductID = ITM.ProductID   
WHERE POD.ProductID IS NULL 

The CROSS APPLY could be used too, this time the WHERE clause from the main query being modified to show only the records without a match in CROSS APPLY, for this needing to be used a "disguised" aggregate too:
 

 -- Products without PO placed (CROSS APPLY) 
SELECT ITM.ProductID  
, ITM.ProductNumber  
, ITM.StandardCost  FROM Production.Product ITM  
    CROSS APPLY (-- PO details  
    SELECT Max(1) HasPOPlaced 
    FROM Purchasing.PurchaseOrderDetail POD  
          JOIN Purchasing.PurchaseOrderHeader POH  
             ON POD.PurchaseOrderID = POH.PurchaseOrderID  
    WHERE POH.Status IN (2, 4) -- 2-Approved, 4-Complete  
        AND POD.ProductID = ITM.ProductID  
    ) POD 
WHERE POD.HasPOPlaced IS NULL 

As can be seen there are multiple alternative ways of solving the same problem, none of the above described patters could be considered as best approach because in the end must be weighted between performance, flexibility, reusability and complexity.  In many cases the performance of a query is the most important factor, though the performance of any of the above techniques is relative because it needs to be considered factors like table structures and relations’ cardinality, server’s configuration and available resources, etc.

References:
[1] Schrag R. (2005). Speeding Up Queries with Semi-Joins and Anti-Joins: How Oracle Evaluates EXISTS, NOT EXISTS, IN, and NOT IN. [link]

💎SQL Reloaded: The Power of Joins IV (Multi-Joins Under Control)

       Few are the queries based only on the join between two tables, each additional table added to the query involving an additional join with one or more of the already considered tables. Such cases in which more than one join is involved in a query are referred as multi-joins or multiple joins, the joins could involve the same join operator or it can be a mixture of the horizontal or vertical joins. In this context can be discussed about join precedence, in other words the way in which a database engine processes the joins, on how to control the order in which the joins are processed, on how to use the joins in order to model a solution for a given problem or how the constraints are considered at macro level.

      The order in which a database engine processes the joins is highly dependent on queries, tables and servers’ characteristics, and it’s quite a comprehensive topic that deserves an ample discussion that could span several posts. Keeping it simple, once the execution plan is determined, the engine starts with the first join, the result being joined with the next table, and so on. The question is how could we make the database engine to apply a certain processing order and how could we facilitate the whole process. Given the fact that in order to solve a problem often we have only 1 or 2 solutions that together with the nature of the relationship between tables involve dictates the nature (types) and the order of the joins, I can’t they there is much flexibility from this point of view. In the end it resumes in knowing the rules that govern the joins, for example in case of commutative join operators it doesn’t really matter how the joins are written, however special attention must be given to non-commutative operations (e.g. left/right outer joins) and the implications of mixing outer with inner joins.

    One approach is to start with the table having the lowest level of detail or the row-preserving table, and first add successively the child tables with the lower cardinality (number of records) and then the other tables in increasing level of detail. On the other side it depends also on the problems needed to be solved. Taking for example the Production.Product, Purchasing.PurchaseOrderDetail and Purchasing.PurchaseOrderHeader tables from AdventureWorks database a query showing the lowest level of details would start with the PO (Purchase Order) Details, and considering that for each PO Detail should exist a PO Header and a Product, could be used an inner join in order to add the PO Header and Product information:

-- PO Details 
SELECT POD.PurchaseOrderDetailID  
, POD.PurchaseOrderID 
, ITM.ProductID  
, ITM.ProductNumber  
, ITM.StandardCost 
, POD.UnitPrice 
, POD.OrderQty 
FROM Purchasing.PurchaseOrderDetail POD  
    JOIN Production.Product ITM 
      ON POD.ProductID = ITM.ProductID 
   JOIN Purchasing.PurchaseOrderHeader POH 
     ON POD.PurchaseOrderID = POH.PurchaseOrderID 
--WHERE POH.Status IN (2, 4) -- 2-Approved, 4-Complete 

  Another view within the same data could be based on a requirement to have the Products as row-preserving table, and because there could be Products without a PO placed, this requires to have a left join between the Products and PO Details. In theory because there should be a PO Header for each PO Detail, an inner join would be enough, however an inner join will restrain the scope of the query only to the PO Details eliminating thus the Products without a PO Placed, so a left join must be used between PO Details and PO Headers:

-- Products with PO Details 
SELECT POD.PurchaseOrderDetailID  
, POD.PurchaseOrderID 
, ITM.ProductID  
, ITM.ProductNumber  
, ITM.StandardCost 
, POD.UnitPrice 
, POD.OrderQty 
FROM Production.Product ITM  
    LEFT JOIN Purchasing.PurchaseOrderDetail POD                
       ON ITM.ProductID = POD.ProductID  
     LEFT JOIN Purchasing.PurchaseOrderHeader POH           
      ON POD.PurchaseOrderID = POH.PurchaseOrderID 
--WHERE POH.Status IN (2, 4) -- 2-Approved, 4-Complete 
-- OR POD.ProductID IS NULL 

     In case a constraint needs to be added based on the attributes from the null-preserving table (e.g. the commented constraint based on the PO Status), then the overall constraint should be modified in order to reflect the need to show the Products without a PO placed, this being the purpose of the second commented constraint.  
    Each table referenced by the PO Details or PO Headers and the tables further referenced by the respective tables, when added to the above query require a left join in order to keep the level of detail of the query. On the other side the left joins are performing poorer than the inner joins, so inner joins should be used whenever is possible. A technique to reduce the number of left joins in a query and accommodate the non-join constraints based on the null-preserving tables is to include such tables in a view or inline view. Here’s the modified above query using an inline view for PO Details:

-- Products with PO Details (inline view) 
SELECT POD.PurchaseOrderDetailID , POD.PurchaseOrderID 
, ITM.ProductID  
, ITM.ProductNumber  
, ITM.StandardCost 
, POD.UnitPrice 
, POD.OrderQty 
FROM Production.Product ITM  
    LEFT JOIN ( -- PO Details 
    SELECT POD.PurchaseOrderDetailID  
    , POD.PurchaseOrderID 
    , POD.ProductID     , POD.UnitPrice 
     , POD.OrderQty 
     FROM Purchasing.PurchaseOrderDetail POD  
        JOIN Purchasing.PurchaseOrderHeader POH  
           ON POD.PurchaseOrderID = POH.PurchaseOrderID 
       --WHERE POH.Status IN (2, 4) -- 2-Approved, 4-Complete  
     ) POD  
     ON ITM.ProductID = POD.ProductID 

     A few years back I found an interesting article of Itzik Ben-Gan on undocumented join features existing in SQL Server, in the respective article he was showing how parentheses and join constraints’ order could be used to control the order in which joined are processed. Parentheses could be used to group the tables and the join between them, allowing thus to perform an inner join between PO Details and PO Headers, the results following to represent the null-preserving table joined with Products table:

-- Products with PO Details (parentheses grouping) 
SELECT POD.PurchaseOrderDetailID  
, POD.PurchaseOrderID 
, ITM.ProductID  
, ITM.ProductNumber  
, ITM.StandardCost 
, POD.UnitPrice 
, POD.OrderQty 
FROM Production.Product ITM  
     LEFT JOIN ( 
           Purchasing.PurchaseOrderDetail POD  
           JOIN Purchasing.PurchaseOrderHeader POH  
               ON POD.PurchaseOrderID = POH.PurchaseOrderID 
        --AND POH.Status IN (2, 4)-- 2-Approved, 4-Complete 
       )  
     ON ITM.ProductID = POD.ProductID 

     The second undocumented method is based on tables and join constraints’ order, being possible to list the table in the reverse order in which they need to be processed and thus accommodate the right type of join in between, the join constraints following the same reverse logic. Thus the PO Headers could be placed the last in the list together with the PO Details and use a inner join between them, the result between them being joined to Products using a left join.

-- Products with PO Details (condition order) 
SELECT POD.PurchaseOrderDetailID  
, POD.PurchaseOrderID 
, ITM.ProductID  
, ITM.ProductNumber  
, ITM.StandardCost 
, POD.UnitPrice 
, POD.OrderQty 
FROM Production.Product ITM  
     LEFT JOIN Purchasing.PurchaseOrderDetail POD 
        LEFT JOIN Purchasing.PurchaseOrderHeader POH 
           ON POD.PurchaseOrderID = POH.PurchaseOrderID 
         ON ITM.ProductID = POD.ProductID  
--WHERE POH.Status IN (2, 4) -- 2-Approved, 4-Complete 
-- OR POD.ProductID IS NULL 

💎SQL Reloaded: The Power of Joins III (Vertical Joins)

Introduction 

 
      A vertical join allows the possibility of retrieving data from multiple datasets by combining the attributes from one or more datasets on the same row, being possible to include complex expressions using any combination of attributes. The join within a vertical join is based only on the attributes specified in the join constraint(s), typically each constraint taking the form of an identity, in this case the data types must match, though also complex expressions evaluated to a value of true/false could be used.

      Within SQL Server 2000 were possible two syntaxes for vertical joins – the ANSI and non-ANSI syntaxes, however in later versions the non-ANSI syntax could be enabled only by changing database’s compatibility level to 80, Microsoft recommends using only the ANSI standard because the non-ANSI syntax could be dropped in future versions. In ANSI syntax are used the LEFT OTER JOIN, RIGHT OUTER JOIN, INNER JOIN and FULL OUTER JOIN operators in the FROM clause while in non-ANSI syntax the join constraints appear in WHERE clause, being used the *= and =* operators for LEFT OUTER JOIN, respectively RIGHT OUTER JOIN, and = for an INNER JOIN, the FULL OUTER JOIN not being supported in non-ANSI. Starting with SQL Server 2005 were introduced also the CROSS APPLY and OUTER APPLY operators that could be used to model cross joins. 

-- Joins ANSI syntax 
SELECT A.Attribute1 
[, A.Attribute] 
[, B.Attribute] 
FROM TABLE1 A 
    [LEFT|RIGHT|FULL] [INNER|OUTER] TABLE2 B 
        ON <join_constraints> 
[WHERE <constraints>] 

-- Joins non-ANSI syntax 
SELECT A.Attribute1 
[, A.Attribute] 
[, B.Attribute] 
FROM TABLE1 A 
,TABLE2 B 
[WHERE<join_constraints>] 
[AND|OR <join_constraints>] 

Notes:
1.   In case of horizontal joins the Set Theory applies mainly to the join constraints, an element in the dataset being the n-uple formed by the attributes participating in the join constraints. Many times it’s natural to use the foreign key-primary key attribute pairs though tables’ design and the logic to be modeled don’t always allow this luxury, therefore when choosing the attributes participating in the join is targeted to find the smallest n-uple with unique values across the whole dataset. From a performance standpoint is preferred to use the attributes that are part of an index, actually in many cases an index arrives to be created for the attributes used often in joins in order to increase queries’ performance. If the n-uple used in the join doesn’t have unique values, in other words exists two records in the dataset on which the n-uple takes the same values for each attribute of the n-uple, then duplicates are induced in the join. 

2.    The records whose attributes participating in the join constraint have NULL values are ignored, so it might be needed to consider replacing the NULL values with a default value, though must be paid attention also to the possibility of introducing duplicates. 

3.    Oracle supports the SQL ANSI syntax together with a slightly different form of non-ANSI syntax.  Especially when considering the portability of code it makes sense to use  the SQL ANSI syntax in any RDBMS that supports it; I mention this aspect because many Oracle developers are still using the non-ANSI syntax. 

4.    In case an attribute is found in more than one table then it’s needed to use aliases for the tables in which the attribute is found or prefix the attribute with the table and schema name (e.g. Production.Product.Name). Actually from performance reasons it’s advisable to always use aliases, thus the database engine identifying easier the source table for each attribute. 

5.     In theory in the SELECT statement could include all the attributes from the tables participating in the join, though it’s recommendable to use only the attributes needed (when possible should be also avoided SELECT * constructs). For output’s readability it makes sense to group together the attributes coming from the same table or arrange them in a patterns that could be easily understood by the users. 

6.     The cross, inner and full outer joins are the only commutative operations, in other words the same results are obtained if the tables are inversed. It can be discussed also about associativity, the ability of changing the table join processing precedence without affecting the result, [1] for example discussing in detail this topic.

      For demonstrating the application of vertical joins I will use the Production.Product, Purchasing.PurchaseOrderDetail POD and HumanResources.Employee tables from AdventureWorks database.

The Inner Join 

 
    The INNER JOIN operators, shortened sometimes as JOIN, allows retrieving the rows matched from both tables based on the join constraints, thus if for one record isn’t found a match in the other table then the record will not appear in the result dataset. 

  

-- Inner Join ANSI syntax 
SELECT ITM.ProductID 
, POD.PurchaseOrderID 
FROM Production.Product ITM 
    JOIN Purchasing.PurchaseOrderDetail POD  
       ON ITM.ProductID = POD.ProductID 
WHERE ITM.MakeFlag = 0 

-- Inner Join non-ANSI syntax 
SELECT ITM.ProductID 
, POD.PurchaseOrderID 
FROM Production.Product ITM 
Purchasing.PurchaseOrderDetail POD 
WHERE ITM.ProductID=POD.ProductID 
    AND ITM.MakeFlag = 0 

Note:
      The inner join could be considered the projection of the intersection operation from Set Theory applied to the attributes participating in the join constraints.

      In order to exemplify what’s happening in the background I will use a smaller subset from each of the two tables used as input, and the final result for the inner join: 

 

   As can be seen from the above image, the 8th, 9th and 10th records from Purchase Orders sample table corresponding to PurchaseOrderID = 7 are not appearing in the result dataset because the corresponding Product IDs (317, 318 and 319) for the respective lines are not found in the Products sample table. Also the second line from Products sample table corresponding to ProductID = 2 is not appearing in the result dataset because there is no Purchase Order placed for the respective Product.

Note:
      The below query summarizes the sample tables used above and the output of the inner join, inline views being used for each of the tables in order to simplify the use of the example with all types of join, thus only the join type needs to be changed for exemplification: 

  

SELECT IsNull(ITM.ProductID, POD.ProductID) ProductID 
, POD.PurchaseOrderID 
, ITM.ProductNumber 
, ITM.StandardCost 
, POD.UnitPrice 
, POD.OrderQty 
FROM ( -- sample Products 
     SELECT ProductID 
     , ProductNumber 
     , StandardCost 
      FROM Production.Product 
      WHERE ProductID IN (1, 2, 359, 360, 530, 4, 512, 513) 
      AND MakeFlag = 0) ITM 
      JOIN (-- sample Purchase Orders 
          SELECT ProductID 
         , PurchaseOrderID 
         , UnitPrice 
         , OrderQty 
         FROM Purchasing.PurchaseOrderDetail 
         WHERE PurchaseOrderID IN (1,2,3,4,5,6,7)) POD 
     ON ITM.ProductID = POD.ProductID 
ORDER BY 2 

The Left Outer Join 

 
    The LEFT OUTER JOIN, shortened sometimes as LEFT JOIN, allows retrieving all the rows from the left table and only the matched records from the right table based on the join constraints.

-- Left Join ANSI syntax 
SELECT ITM.ProductID 
, POD.PurchaseOrderID 
FROM Production.Product ITM 
      LEFT JOIN Purchasing.PurchaseOrderDetail POD 
         ON ITM.ProductID = POD.ProductID 
WHERE ITM.MakeFlag = 0 

-- Left Join non-ANSI syntax 
SELECTITM.ProductID 
, POD.PurchaseOrderID 
FROM Production.Product ITM 
, Purchasing.PurchaseOrderDetail POD 
WHERE ITM.ProductID*=POD.ProductID 
    AND ITM.MakeFlag = 0   

      In order to exemplify what’s happening in the background I will use a smaller subset from each of the two tables used as input, and the final result for the left outer join:   

 

    Because the Products sample table is used as row-preserving table it will be shown all the records it holds together with the matched records from the Purchase Orders sample table, thus the Purchase Orders sample table corresponding to PurchaseOrderID = 7 are not appearing in the result dataset because the corresponding Product IDs (317, 318 and 319) for the respective lines are not found in the Products sample table. 

     If the tables are inversed then the Purchase Orders table becomes the row-preserving table and thus all the records from it are shown, including the records for which no Product is found in the Products sample table.

Notes:
1.   The left join has no direct correspondent operation from Set Theory but it’s the projection of AU(A∩B) formula, which equals to (A\B)U(A∩B). The left join could be used also to determine the projection of A\B by adding in the WHERE clause the constraint that allows retrieving only the records for which no match was found to the right table: 

-- LEFT Join ANSI syntax for A\B 
SELECT ITM.ProductID 
, POD.PurchaseOrderID 
FROM Production.Product ITM 
    LEFT JOIN Purchasing.PurchaseOrderDetail POD 
      ON ITM.ProductID = POD.ProductID 
WHERE POD.ProductID IS NULL 

2.    Special attention must be given to the way the join and non-join constraints are added to the WHERE clause, because if the constraint is based solely on the null-supplying table and included in the WHERE clause without handling the Null case then an inner join could have been written instead because the rows for the attributes participating in constraints are ignored. In order to preserve left join’s character the constraint should be brought into the join constraint as below: 

-- Right Join ANSI syntax modified 
SELECT ITM.ProductID 
, POD.PurchaseOrderID 
FROM Purchasing.PurchaseOrderDetail POD 
     LEFT JOIN Production.Product ITM 
        ON ITM.ProductID = POD.ProductID 
AND ITM.MakeFlag = 0 

 
      Because unlike in Oracle the both terms of an non-ANSI left join operator must contain columns (attributes), then the IsNull function could be used in order to handle the NULL values:   

SELECT ITM.ProductID 
, POD.PurchaseOrderID 
FROMPurchasing.PurchaseOrderDetail POD 
, Production.Product ITM 
WHERE POD.ProductID *= ITM.ProductID 
AND IsNull(ITM.MakeFlag, 0) = 0   

      The same method could be used also to keep non-join constraints in the WHERE clause when using the ANSI syntax for outer joins. 

3.    There are cases in which is needed to replace with default values the NULL values from the not matched records from the Null-preserving table.

The Right Outer Join 

    The RIGHT OUTER JOIN, shortened sometimes as RIGHT JOIN, allows retrieving all the rows from the right table and only the matched records from the right table based on the join constraints. A left join could be rewritten as a right join, just by inversing the tables, in fact the above examples given for left joins are rewritten using a right join:   

-- Right Join ANSI syntax 
SELECT ITM.ProductID 
, POD.PurchaseOrderID 
FROM Purchasing.PurchaseOrderDetail POD 
     RIGHT JOIN Production.Product ITM 
          ON ITM.ProductID = POD.ProductID 
WHERE ITM.MakeFlag = 0 

-- Right Join ANSI syntax modified 
SELECT ITM.ProductID 
, POD.PurchaseOrderID 
FROM Purchasing.PurchaseOrderDetail POD 
    RIGHT JOIN Production.Product ITM 
         ON ITM.ProductID = POD.ProductID 
AND ITM.MakeFlag = 0  

   In order to exemplify what’s happening in the background I will use a smaller subset from each of the two tables used as input, and the final result for the right outer join:

     As opposed to the general syntax examples given above for the left outer join in which the Products sample table is used as row-preserving table, in the above image the Purchase Orders sample table is used as row-preserving table, thus are shown all the records it holds and only the matched Products.

The Full Outer Join   

    The FULL OUTER JOIN, shortened sometimes as FULL JOIN, allows retrieving the rows matched from both tables based on the join together with the not matched records from both tables.

-- Full Outer Join ANSI syntax 
SELECT ITM.ProductID 
, POD.PurchaseOrderID 
FROM Production.Product ITM 
    FULL JOIN Purchasing.PurchaseOrderDetail POD 
       ON ITM.ProductID = POD.ProductID  

   In order to exemplify what’s happening in the background I will use a smaller subset from each of the two tables used as input, and the final result for the full outer join:

  As can be seen from the above image are considered all the rows from both tables, including the Purchase Orders for which no match was found in the Products sample table and the Products for which no Purchase Order is found in the corresponding sample table.  

Note:
1.      As in the left outer join’s case, special attention must be given to the non-join constraints added in the WHERE clause because they could reduce the range of applicability of the full outer join to a left/right outer join or to an inner join. Eventually, if really needed to add non-join constraints, instead of the base table it could be used an inline view as input for the full outer join.   

2.      In SQL Server there is no non-ANSI operator equivalent to the ANSI full outer join operator, though the same functionality could be obtained by using the union between the result of a left outer join and the one of a right outer join:

-- Full Outer Join non-ANSI syntax equivalent 
SELECT ITM.ProductID 
, POD.PurchaseOrderID 
FROM Production.Product ITM 
, Purchasing.PurchaseOrderDetail POD 
WHERE ITM.ProductID *= POD.ProductID 
UNION 
SELECT 
ITM.ProductID 
, POD.PurchaseOrderID 
FROM Production.Product ITM 
, Purchasing.PurchaseOrderDetail POD 
WHERE ITM.ProductID =* POD.ProductID 

    In some cases could be useful to rewrite the above query using the ANSI syntax, but this time it makes sense to use the UNION ALL operator instead and limit the second dataset only to the Products for which no Purchase Order was placed:   

-- Full Outer Join ANSI syntax equivalent using Left & Right Outer Joins 
SELECT ITM.ProductID 
, POD.PurchaseOrderID 
FROM Production.Product ITM 
     LEFT JOIN Purchasing.PurchaseOrderDetail POD  
         ON ITM.ProductID = POD.ProductID 
UNIONALL 
SELECT ITM.ProductID 
, POD.PurchaseOrderID 
FROM Production.Product ITM 
      RIGHT JOIN Purchasing.PurchaseOrderDetail POD  
            ON ITM.ProductID = POD.ProductID 
WHERE ITM.ProductID IS NULL 

The Cross Join 

    The CROSS JOIN resumes at listing the joined tables without specifying the join constraint and it returns the carthezian product between the two tables, a row from the first table being matched to each row from the second table, thus if the first table has m rows and the second n rows, the final query will return m*n rows. If in non-ANSI syntax it’s pretty simple to create a cross join, using ANSI syntax the same could be obtained using a full outer join with a join constraint that always equates to true independently of the tables’ attributes values (e.g. 1=1) or, starting with SQL Server 2005,  when was first introduced, could be used the cross apply operator.   

-- Cross Join ANSI syntax (CROSS APPLY) 
SELECT ITM.ProductID 
, POD.PurchaseOrderID 
FROM Production.Product ITM 
     CROSS APPLY Purchasing.PurchaseOrderDetail POD 

-- Cross Join ANSI syntax (FULL OUTER JOIN) 
SELECT ITM.ProductID 
, POD.PurchaseOrderID 
FROM Production.Product ITM 
    FULL OUTER JOIN Purchasing.PurchaseOrderDetail POD 
      ON 1=1 

-- Cross Join non-ANSI syntax 
SELECT ITM.ProductID 
, POD.PurchaseOrderID 
FROM Production.Product ITM 
, Purchasing.PurchaseOrderDetail POD 

The Self Join   

     The self join is a special type of vertical join in which the left and right tables in a join represent the same table, and it could take the form of any of the above mentioned types of joins. This typically implies the existence of a self-reference attribute that references the primary key of another record, such structures being useful in modeling hierarchies (e.g. Bill of Materials, Human Resources hierarchies). For example HumanResources.Employee table stores together with the current Employee also ManagerID which stores the EmployeeID of Employee’s Manager, that stores at its turn the reference to Manager’s Manager, thus a whole structure of an organization could be built with self joins. The simplified queries for getting the Manager of Employee’s Manager could be written with a left join, this mainly because there might be Employees who don’t have a manager:   

-- Self Join ANSI Syntax (LEFT JOIN) 
SELECT EMP.EmployeeID 
, EMP.ManagerID 
, MNG.ManagerID ManagersManagerID 
FROM HumanResources.Employee EMP 
    LEFT JOIN HumanResources.Employee MNG 
       ON EMP.ManagerID = MNG.EmployeeID 

-- Self Join non-ANSI Syntax (LEFT JOIN) 
SELECT EMP.EmployeeID 
, EMP.ManagerID 
, MNG.ManagerID ManagersManagerID 
FROM HumanResources.Employee EMP 
, HumanResources.Employee MNG 
WHERE EMP.ManagerID *= MNG.EmployeeID 

Note:
       In order to built the whole hierarchy, starting with SQL Server 2005 instead of using multiple self joins could be used common tables expressions (CTE), they offering more flexibility and better performance.

References:
[1] David M.M., (1999). Advanced ANSI SQL Data Modeling and Structure Processing. Artech House. ISBN: 1-58053-038-9