Summary: in this tutorial, you will learn about the PostgreSQL recursive query using recursive common table expressions or CTEs.

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Introduction to the PostgreSQL recursive query

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PostgreSQL provides the WITH statement that allows you to construct auxiliary statements for use in a query.

These statements are often referred to as common table expressions or CTEs. The CTEs are like temporary tables that exist only during the execution of the query.

A recursive query is a query that refers to a recursive CTE. The recursive queries are useful in many situations such as querying hierarchical data like organizational structure, bill of materials, etc.

The following illustrates the syntax of a recursive CTE:

A recursive CTE has three elements:

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• Non-recursive term: the non-recursive term is a CTE query definition that forms the base result set of the CTE structure.
• Recursive term: the recursive term is one or more CTE query definitions joined with the non-recursive term using the UNION or UNION ALL operator. The recursive term references the CTE name itself.
• Termination check: the recursion stops when no rows are returned from the previous iteration.

PostgreSQL executes a recursive CTE in the following sequence:

1. Execute the non-recursive term to create the base result set (R0).
2. Execute recursive term with Ri as an input to return the result set Ri+1 as the output.
3. Repeat step 2 until an empty set is returned. (termination check)
4. Return the final result set that is a UNION or UNION ALL of the result set R0, R1, … Rn

PostgreSQL recursive query example

We will create a new table to demonstrate the PostgreSQL recursive query.

The employees table has three columns: employee_id, manager_id, and full_name. The manager_id column specifies the manager id of an employee.

The following statement inserts sample data into the employees table.

The following query returns all subordinates of the manager with the id 2.

How it works:

• The recursive CTE, subordinates, defines one non-recursive term and one recursive term.
• The non-recursive term returns the base result set R0 that is the employee with the id 2.

The recursive term returns the direct subordinate(s) of the employee id 2. This is the result of joining between the employees table and the subordinates CTE. The first iteration of the recursive term returns the following result set:

PostgreSQL executes the recursive term repeatedly. The second iteration of the recursive member uses the result set above step as the input value, and returns this result set:

The third iteration returns an empty result set because there is no employee reporting to the employee with the id 16, 17, 18, 19, and 20.

PostgreSQL returns the final result set that is the union of all result sets in the first and second iterations generated by the non-recursive and recursive terms.

In this tutorial, you have learned how to use the recursive CTEs to construct the PostgreSQL recursive queries.

Numeric types consist of two-, four-, and eight-byte integers, four- and eight-byte floating-point numbers, and selectable-precision decimals. Table 8-2 lists the available types.

Table 8-2. Numeric Types

Name	Storage Size	Description	Range
smallint	2 bytes	small-range integer	-32768 to +32767
integer	4 bytes	typical choice for integer	-2147483648 to +2147483647
bigint	8 bytes	large-range integer	-9223372036854775808 to 9223372036854775807
decimal	variable	user-specified precision, exact	up to 131072 digits before the decimal point; up to 16383 digits after the decimal point
numeric	variable	user-specified precision, exact	up to 131072 digits before the decimal point; up to 16383 digits after the decimal point
real	4 bytes	variable-precision, inexact	6 decimal digits precision
double precision	8 bytes	variable-precision, inexact	15 decimal digits precision
serial	4 bytes	autoincrementing integer	1 to 2147483647
bigserial	8 bytes	large autoincrementing integer	1 to 9223372036854775807

The syntax of constants for the numeric types is described in Section 4.1.2. The numeric types have a full set of corresponding arithmetic operators and functions. Refer to Chapter 9 for more information. The following sections describe the types in detail.

8.1.1. Integer Types

The types smallint, integer, and bigint store whole numbers, that is, numbers without fractional components, of various ranges. Attempts to store values outside of the allowed range will result in an error.

The type integer is the common choice, as it offers the best balance between range, storage size, and performance. The smallint type is generally only used if disk space is at a premium. The bigint type should only be used if the range of the integer type is insufficient, because the latter is definitely faster.

On very minimal operating systems the bigint type might not function correctly, because it relies on compiler support for eight-byte integers. On such machines, bigint acts the same as integer, but still takes up eight bytes of storage. (We are not aware of any modern platform where this is the case.)

SQL only specifies the integer types integer (or int), smallint, and bigint. The type names int2, int4, and int8 are extensions, which are also used by some other SQL database systems.

8.1.2. Arbitrary Precision Numbers

The type numeric can store numbers with a very large number of digits and perform calculations exactly. It is especially recommended for storing monetary amounts and other quantities where exactness is required. However, arithmetic on numeric values is very slow compared to the integer types, or to the floating-point types described in the next section.

We use the following terms below: The scale of a numeric is the count of decimal digits in the fractional part, to the right of the decimal point. The precision of a numeric is the total count of significant digits in the whole number, that is, the number of digits to both sides of the decimal point. So the number 23.5141 has a precision of 6 and a scale of 4. Integers can be considered to have a scale of zero.

Both the maximum precision and the maximum scale of a numeric column can be configured. To declare a column of type numeric use the syntax:

The precision must be positive, the scale zero or positive. Alternatively:

selects a scale of 0. Specifying:

without any precision or scale creates a column in which numeric values of any precision and scale can be stored, up to the implementation limit on precision. A column of this kind will not coerce input values to any particular scale, whereas numeric columns with a declared scale will coerce input values to that scale. (The SQL standard requires a default scale of 0, i.e., coercion to integer precision. We find this a bit useless. If you're concerned about portability, always specify the precision and scale explicitly.)

Note: The maximum allowed precision when explicitly specified in the type declaration is 1000; NUMERIC without a specified precision is subject to the limits described in Table 8-2.

If the scale of a value to be stored is greater than the declared scale of the column, the system will round the value to the specified number of fractional digits. Then, if the number of digits to the left of the decimal point exceeds the declared precision minus the declared scale, an error is raised.

Numeric values are physically stored without any extra leading or trailing zeroes. Thus, the declared precision and scale of a column are maximums, not fixed allocations. (In this sense the numeric type is more akin to varchar(n) than to char(n).) The actual storage requirement is two bytes for each group of four decimal digits, plus three to eight bytes overhead.

In addition to ordinary numeric values, the numeric type allows the special value NaN, meaning 'not-a-number'. Any operation on NaN yields another NaN. When writing this value as a constant in an SQL command, you must put quotes around it, for example UPDATE table SET x = 'NaN'. On input, the string NaN is recognized in a case-insensitive manner.

Note: In most implementations of the 'not-a-number' concept, NaN is not considered equal to any other numeric value (including NaN). In order to allow numeric values to be sorted and used in tree-based indexes, PostgreSQL treats NaN values as equal, and greater than all non-NaN values.

The types decimal and numeric are equivalent. Both types are part of the SQL standard.

8.1.3. Floating-Point Types

The data types real and double precision are inexact, variable-precision numeric types. In practice, these types are usually implementations of IEEE Standard 754 for Binary Floating-Point Arithmetic (single and double precision, respectively), to the extent that the underlying processor, operating system, and compiler support it.

Inexact means that some values cannot be converted exactly to the internal format and are stored as approximations, so that storing and retrieving a value might show slight discrepancies. Managing these errors and how they propagate through calculations is the subject of an entire branch of mathematics and computer science and will not be discussed here, except for the following points:

• If you require exact storage and calculations (such as for monetary amounts), use the numeric type instead.

• If you want to do complicated calculations with these types for anything important, especially if you rely on certain behavior in boundary cases (infinity, underflow), you should evaluate the implementation carefully.

• Comparing two floating-point values for equality might not always work as expected.

On most platforms, the real type has a range of at least 1E-37 to 1E+37 with a precision of at least 6 decimal digits. The double precision type typically has a range of around 1E-307 to 1E+308 with a precision of at least 15 digits. Values that are too large or too small will cause an error. Rounding might take place if the precision of an input number is too high. Numbers too close to zero that are not representable as distinct from zero will cause an underflow error.

Note: The extra_float_digits setting controls the number of extra significant digits included when a floating point value is converted to text for output. With the default value of 0, the output is the same on every platform supported by PostgreSQL. Increasing it will produce output that more accurately represents the stored value, but may be unportable.

In addition to ordinary numeric values, the floating-point types have several special values:

Infinity
-Infinity
NaN

These represent the IEEE 754 special values 'infinity', 'negative infinity', and 'not-a-number', respectively. (On a machine whose floating-point arithmetic does not follow IEEE 754, these values will probably not work as expected.) When writing these values as constants in an SQL command, you must put quotes around them, for example UPDATE table SET x = 'Infinity'. On input, these strings are recognized in a case-insensitive manner.

Note: IEEE754 specifies that NaN should not compare equal to any other floating-point value (including NaN). In order to allow floating-point values to be sorted and used in tree-based indexes, PostgreSQL treats NaN values as equal, and greater than all non-NaN values.

PostgreSQL also supports the SQL-standard notations float and float(p) for specifying inexact numeric types. Here, p specifies the minimum acceptable precision in binary digits. PostgreSQL accepts float(1) to float(24) as selecting the real type, while float(25) to float(53) select double precision. Values of p outside the allowed range draw an error. float with no precision specified is taken to mean double precision.

Note: Prior to PostgreSQL 7.4, the precision in float(p) was taken to mean so many decimal digits. This has been corrected to match the SQL standard, which specifies that the precision is measured in binary digits. The assumption that real and double precision have exactly 24 and 53 bits in the mantissa respectively is correct for IEEE-standard floating point implementations. On non-IEEE platforms it might be off a little, but for simplicity the same ranges of p are used on all platforms.

8.1.4. Serial Types

The data types serial and bigserial are not true types, but merely a notational convenience for creating unique identifier columns (similar to the AUTO_INCREMENT property supported by some other databases). In the current implementation, specifying:

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is equivalent to specifying:

Thus, we have created an integer column and arranged for its default values to be assigned from a sequence generator. A NOT NULL constraint is applied to ensure that a null value cannot be inserted. (In most cases you would also want to attach a UNIQUE or PRIMARY KEY constraint to prevent duplicate values from being inserted by accident, but this is not automatic.) Lastly, the sequence is marked as 'owned by' the column, so that it will be dropped if the column or table is dropped.

Note: Because smallserial, serial and bigserial are implemented using sequences, there may be 'holes' or gaps in the sequence of values which appears in the column, even if no rows are ever deleted. A value allocated from the sequence is still 'used up' even if a row containing that value is never successfully inserted into the table column. This may happen, for example, if the inserting transaction rolls back. See nextval() in Section 9.15 for details.

Note: Prior to PostgreSQL 7.3, serial implied UNIQUE. This is no longer automatic. If you wish a serial column to have a unique constraint or be a primary key, it must now be specified, just like any other data type.

To insert the next value of the sequence into the serial column, specify that the serial column should be assigned its default value. This can be done either by excluding the column from the list of columns in the INSERT statement, or through the use of the DEFAULT key word.

The type names serial and serial4 are equivalent: both create integer columns. The type names bigserial and serial8 work the same way, except that they create a bigint column. bigserial should be used if you anticipate the use of more than 2³¹ identifiers over the lifetime of the table.

The sequence created for a serial column is automatically dropped when the owning column is dropped. You can drop the sequence without dropping the column, but this will force removal of the column default expression.