relational algebra outer join operation

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tutorial on relational algebra: outer join operation

what is outer join?

in relational algebra, an **outer join** is an operation that combines records from two tables based on a related column between them, while also including records that do not have a match in one of the tables. this is in contrast to an inner join, which only includes records that have matching values in both tables.

there are three types of outer joins:

1. **left outer join**: returns all records from the left table and the matched records from the right table. if there is no match, null values are returned for columns from the right table.

2. **right outer join**: returns all records from the right table and the matched records from the left table. if there is no match, null values are returned for columns from the left table.

3. **full outer join**: returns all records when there is a match in either left or right table records. if there is no match, null values are returned for the missing side.

syntax of outer joins

given two relations (tables) r and s, the outer join operations can be represented as follows:

- **left outer join**:
\[
r \text{ left outer join } s
\]

- **right outer join**:
\[
r \text{ right outer join } s
\]

- **full outer join**:
\[
r \text{ full outer join } s
\]

example

let's illustrate outer joins with an example using sql-like syntax. we will use two tables: `employees` and `departments`.

**table: employees**

| employeeid | employeename | departmentid |
|------------|---------------|--------------|
| 1 | john doe | 1 |
| 2 | jane smith | 2 |
| 3 | emily johnson | null |
| 4 | michael brown | 3 |

**table: departments**

| departmentid | departmentname |
|--------------|----------------|
| 1 | hr |
| 2 | it |
| 3 | sales |
| 4 | marketing |

left outer jo ...

#RelationalAlgebra #OuterJoin #windows
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relational algebra
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left outer join
right outer join
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