xref: /macosx-10.10.1/tcl-105/tcl_ext/tcllib/tcllib/modules/struct/struct_list.man

[comment {-*- tcl -*- doctools manpage}]
[comment {$Id: struct_list.man,v 1.23 2009/01/29 06:16:20 andreas_kupries Exp $}]
[manpage_begin struct::list n 1.7]
[copyright {2003-2005 by Kevin B. Kenny. All rights reserved}]
[copyright {2003-2008 Andreas Kupries <andreas_kupries@users.sourceforge.net>}]
[moddesc {Tcl Data Structures}]
[titledesc {Procedures for manipulating lists}]
[category  {Data structures}]
[require Tcl 8.0]
[require struct::list [opt 1.7]]
[description]

[para]

The [cmd ::struct::list] namespace contains several useful commands
for processing Tcl lists. Generally speaking, they implement
algorithms more complex or specialized than the ones provided by Tcl
itself.

[para]

It exports only a single command, [cmd struct::list]. All
functionality provided here can be reached through a subcommand of
this command.

[section COMMANDS]
[list_begin definitions]

[call [cmd ::struct::list] [method longestCommonSubsequence] \
	[arg sequence1] [arg sequence2] [opt [arg maxOccurs]]]

Returns the longest common subsequence of elements in the two lists
[arg sequence1] and [arg sequence2]. If the [arg maxOccurs] parameter
is provided, the common subsequence is restricted to elements that
occur no more than [arg maxOccurs] times in [arg sequence2].

[para]

The return value is a list of two lists of equal length. The first
sublist is of indices into [arg sequence1], and the second sublist is
of indices into [arg sequence2].  Each corresponding pair of indices
corresponds to equal elements in the sequences; the sequence returned
is the longest possible.

[call [cmd ::struct::list] [method longestCommonSubsequence2] \
	[arg {sequence1 sequence2}] [opt [arg maxOccurs]]]

Returns an approximation to the longest common sequence of elements in
the two lists [arg sequence1] and [arg sequence2].

If the [arg maxOccurs] parameter is omitted, the subsequence computed
is exactly the longest common subsequence; otherwise, the longest
common subsequence is approximated by first determining the longest
common sequence of only those elements that occur no more than

[arg maxOccurs] times in [arg sequence2], and then using that result
to align the two lists, determining the longest common subsequences of
the sublists between the two elements.

[para]

As with [method longestCommonSubsequence], the return value is a list
of two lists of equal length.  The first sublist is of indices into
[arg sequence1], and the second sublist is of indices into

[arg sequence2].  Each corresponding pair of indices corresponds to
equal elements in the sequences.  The sequence approximates the
longest common subsequence.


[call [cmd ::struct::list] [method lcsInvert] [arg lcsData] [arg len1] [arg len2]]

This command takes a description of a longest common subsequence

([arg lcsData]), inverts it, and returns the result. Inversion means
here that as the input describes which parts of the two sequences are
identical the output describes the differences instead.

[para]

To be fully defined the lengths of the two sequences have to be known
and are specified through [arg len1] and [arg len2].

[para]

The result is a list where each element describes one chunk of the
differences between the two sequences. This description is a list
containing three elements, a type and two pairs of indices into

[arg sequence1] and [arg sequence2] respectively, in this order.

The type can be one of three values:

[list_begin definitions]
[def [const added]]

Describes an addition. I.e. items which are missing in [arg sequence1]
can be found in [arg sequence2].

The pair of indices into [arg sequence1] describes where the added
range had been expected to be in [arg sequence1]. The first index
refers to the item just before the added range, and the second index
refers to the item just after the added range.

The pair of indices into [arg sequence2] describes the range of items
which has been added to it. The first index refers to the first item
in the range, and the second index refers to the last item in the
range.

[def [const deleted]]

Describes a deletion. I.e. items which are in [arg sequence1] are
missing from [arg sequence2].

The pair of indices into [arg sequence1] describes the range of items
which has been deleted. The first index refers to the first item in
the range, and the second index refers to the last item in the range.

The pair of indices into [arg sequence2] describes where the deleted
range had been expected to be in [arg sequence2]. The first index
refers to the item just before the deleted range, and the second index
refers to the item just after the deleted range.

[def [const changed]]

Describes a general change. I.e a range of items in [arg sequence1]
has been replaced by a different range of items in [arg sequence2].

The pair of indices into [arg sequence1] describes the range of items
which has been replaced. The first index refers to the first item in
the range, and the second index refers to the last item in the range.

The pair of indices into [arg sequence2] describes the range of items
replacing the original range. Again the first index refers to the
first item in the range, and the second index refers to the last item
in the range.

[list_end]

[para]
[example {
    sequence 1 = {a b r a c a d a b r a}
    lcs 1      =   {1 2   4 5     8 9 10}
    lcs 2      =   {0 1   3 4     5 6 7}
    sequence 2 =   {b r i c a     b r a c}

    Inversion  = {{deleted  {0  0} {-1 0}}
                  {changed  {3  3}  {2 2}}
                  {deleted  {6  7}  {4 5}}
                  {added   {10 11}  {8 8}}}
}]

[emph Notes:]
[para]
[list_begin itemized]
[item]
An index of [const -1] in a [term deleted] chunk refers to just before
the first element of the second sequence.

[item]
Also an index equal to the length of the first sequence in an
[term added] chunk refers to just behind the end of the sequence.

[list_end]


[call [cmd ::struct::list] [method lcsInvert2] [arg lcs1] [arg lcs2] [arg len1] [arg len2]]

Similar to [method lcsInvert]. Instead of directly taking the result
of a call to [method longestCommonSubsequence] this subcommand expects
the indices for the two sequences in two separate lists.


[call [cmd ::struct::list] [method lcsInvertMerge] [arg lcsData] [arg len1] [arg len2]]

Similar to [method lcsInvert]. It returns essentially the same
structure as that command, except that it may contain chunks of type
[const unchanged] too.

[para]

These new chunks describe the parts which are unchanged between the
two sequences. This means that the result of this command describes
both the changed and unchanged parts of the two sequences in one
structure.

[para]
[example {
    sequence 1 = {a b r a c a d a b r a}
    lcs 1      =   {1 2   4 5     8 9 10}
    lcs 2      =   {0 1   3 4     5 6 7}
    sequence 2 =   {b r i c a     b r a c}

    Inversion/Merge  = {{deleted   {0  0} {-1 0}}
                        {unchanged {1  2}  {0 1}}
                        {changed   {3  3}  {2 2}}
                        {unchanged {4  5}  {3 4}}
                        {deleted   {6  7}  {4 5}}
                        {unchanged {8 10}  {5 7}}
                        {added    {10 11}  {8 8}}}
}]


[call [cmd ::struct::list] [method lcsInvertMerge2] [arg lcs1] [arg lcs2] [arg len1] [arg len2]]

Similar to [method lcsInvertMerge]. Instead of directly taking the
result of a call to [method longestCommonSubsequence] this subcommand
expects the indices for the two sequences in two separate lists.



[call [cmd ::struct::list] [method reverse] [arg sequence]]

The subcommand takes a single [arg sequence] as argument and returns a new
sequence containing the elements of the input sequence in reverse
order.


[call [cmd ::struct::list] [method assign] [arg sequence] [arg varname] [opt [arg varname]]...]

The subcommand assigns the first [var n] elements of the input

[arg sequence] to the one or more variables whose names were listed
after the sequence, where [var n] is the number of specified
variables.

[para]

If there are more variables specified than there are elements in the
[arg sequence] the empty string will be assigned to the superfluous
variables.

[para]

If there are more elements in the [arg sequence] than variable names
specified the subcommand returns a list containing the unassigned
elements. Else an empty list is returned.

[example {
    tclsh> ::struct::list assign {a b c d e} foo bar
    c d e
    tclsh> set foo
    a
    tclsh> set bar
    b
}]


[call [cmd ::struct::list] [method flatten] [opt [option -full]] [opt [option --]] [arg sequence]]

The subcommand takes a single [arg sequence] and returns a new
sequence where one level of nesting was removed from the input
sequence. In other words, the sublists in the input sequence are
replaced by their elements.

[para]

The subcommand will remove any nesting it finds if the option
[option -full] is specified.

[example {
    tclsh> ::struct::list flatten {1 2 3 {4 5} {6 7} {{8 9}} 10}
    1 2 3 4 5 6 7 {8 9} 10
    tclsh> ::struct::list flatten -full {1 2 3 {4 5} {6 7} {{8 9}} 10}
    1 2 3 4 5 6 7 8 9 10
}]


[call [cmd ::struct::list] [method map] [arg sequence] [arg cmdprefix]]

The subcommand takes a [arg sequence] to operate on and a command
prefix ([arg cmdprefix]) specifying an operation, applies the command
prefix to each element of the sequence and returns a sequence
consisting of the results of that application.

[para]

The command prefix will be evaluated with a single word appended to
it. The evaluation takes place in the context of the caller of the
subcommand.

[para]

[example {
    tclsh> # squaring all elements in a list

    tclsh> proc sqr {x} {expr {$x*$x}}
    tclsh> ::struct::list map {1 2 3 4 5} sqr
    1 4 9 16 25

    tclsh> # Retrieving the second column from a matrix
    tclsh> # given as list of lists.

    tclsh> proc projection {n list} {::lindex $list $n}
    tclsh> ::struct::list map {{a b c} {1 2 3} {d f g}} {projection 1}
    b 2 f
}]


[call [cmd ::struct::list] [method mapfor] [arg var] [arg sequence] [arg script]]

The subcommand takes a [arg sequence] to operate on and a tcl [arg script],
applies the script to each element of the sequence and returns a sequence
consisting of the results of that application.

[para]

The script will be evaluated as is, and has access to the current list element
through the specified iteration variable [arg var]. The evaluation takes place
in the context of the caller of the subcommand.

[para]

[example {
    tclsh> # squaring all elements in a list

    tclsh> ::struct::list mapfor x {1 2 3 4 5} {
	expr {$x * $x}
    }
    1 4 9 16 25

    tclsh> # Retrieving the second column from a matrix
    tclsh> # given as list of lists.

    tclsh> ::struct::list mapfor x {{a b c} {1 2 3} {d f g}} {
	lindex $x 1
    }
    b 2 f
}]


[call [cmd ::struct::list] [method filter] [arg sequence] [arg cmdprefix]]

The subcommand takes a [arg sequence] to operate on and a command
prefix ([arg cmdprefix]) specifying an operation, applies the command
prefix to each element of the sequence and returns a sequence
consisting of all elements of the [arg sequence] for which the command
prefix returned [const true].

In other words, this command filters out all elements of the input
[arg sequence] which fail the test the [arg cmdprefix] represents, and
returns the remaining elements.

[para]

The command prefix will be evaluated with a single word appended to
it. The evaluation takes place in the context of the caller of the
subcommand.

[para]

[example {
    tclsh> # removing all odd numbers from the input

    tclsh> proc even {x} {expr {($x % 2) == 0}}
    tclsh> ::struct::list filter {1 2 3 4 5} even
    2 4
}]

[para]

[emph Note:] The [method filter] is a specialized application of
[method fold] where the result is extended with the current item or
not, depending o nthe result of the test.


[call [cmd ::struct::list] [method filterfor] [arg var] [arg sequence] [arg expr]]

The subcommand takes a [arg sequence] to operate on and a tcl expression
([arg expr]) specifying a condition, applies the conditionto each element
of the sequence and returns a sequence consisting of all elements of the
[arg sequence] for which the expression returned [const true].

In other words, this command filters out all elements of the input
[arg sequence] which fail the test the condition [arg expr] represents, and
returns the remaining elements.

[para]

The expression will be evaluated as is, and has access to the current list
element through the specified iteration variable [arg var]. The evaluation
takes place in the context of the caller of the subcommand.

[para]

[example {
    tclsh> # removing all odd numbers from the input

    tclsh> ::struct::list filterfor x {1 2 3 4 5} {($x % 2) == 0}
    2 4
}]


[call [cmd ::struct::list] [method split] [arg sequence] [arg cmdprefix] [opt "[arg passVar] [arg failVar]"]]

This is a variant of method [method filter], see above. Instead of
returning just the elements passing the test we get lists of both
passing and failing elements.

[para]

If no variable names are specified then the result of the command will
be a list containing the list of passing elements, and the list of
failing elements, in this order. Otherwise the lists of passing and
failing elements are stored into the two specified variables, and the
result will be a list containing two numbers, the number of elements
passing the test, and the number of elements failing, in this order.

[para]

The interface to the test is the same as used by [method filter].


[call [cmd ::struct::list] [method fold] [arg sequence] [arg initialvalue] [arg cmdprefix]]

The subcommand takes a [arg sequence] to operate on, an arbitrary
string [arg {initial value}] and a command prefix ([arg cmdprefix])
specifying an operation.

[para]

The command prefix will be evaluated with two words appended to
it. The second of these words will always be an element of the
sequence. The evaluation takes place in the context of the caller of
the subcommand.

[para]

It then reduces the sequence into a single value through repeated
application of the command prefix and returns that value. This
reduction is done by

[list_begin definitions]
[def [const 1]]

Application of the command to the initial value and the first element
of the list.

[def [const 2]]

Application of the command to the result of the last call and the
second element of the list.

[def [const ...]]
[def [const i]]

Application of the command to the result of the last call and the
[var i]'th element of the list.

[def [const ...]]
[def [const end]]

Application of the command to the result of the last call and the last
element of the list. The result of this call is returned as the result
of the subcommand.

[list_end]
[para]
[example {
    tclsh> # summing the elements in a list.
    tclsh> proc + {a b} {expr {$a + $b}}
    tclsh> ::struct::list fold {1 2 3 4 5} 0 +
    15
}]


[call [cmd ::struct::list] [method shift] [arg listvar]]

The subcommand takes the list contained in the variable named by

[arg listvar] and shifts it down one element.

After the call [arg listvar] will contain a list containing the second
to last elements of the input list. The first element of the ist is
returned as the result of the command. Shifting the empty list does
nothing.


[call [cmd ::struct::list] [method iota] [arg n]]

The subcommand returns a list containing the integer numbers
in the range [const {[0,n)}]. The element at index [var i]
of the list contain the number [const i].

[para]

For "[arg n] == [const 0]" an empty list will be returned.


[call [cmd ::struct::list] [method equal] [arg a] [arg b]]

The subcommand compares the two lists [arg a] and [arg b] for
equality. In other words, they have to be of the same length and have
to contain the same elements in the same order. If an element is a
list the same definition of equality applies recursively.

[para]

A boolean value will be returned as the result of the command.
This value will be [const true] if the two lists are equal, and
[const false] else.


[call [cmd ::struct::list] [method repeat] [arg size] [arg element1] [opt "[arg element2] [arg element3]..."]]

The subcommand creates a list of length

"[arg size] * [emph {number of elements}]" by repeating [arg size]
times the sequence of elements
[arg element1] [arg element2] [arg ...].

[arg size] must be a positive integer, [arg element][var n] can be any
Tcl value.

Note that [cmd {repeat 1 arg ...}]  is identical to
[cmd {list arg ...}], though the [arg arg] is required
with [method repeat].

[para]
[emph Examples:]
[para]
[example {
    tclsh> ::struct::list repeat 3 a
    a a a
    tclsh> ::struct::list repeat 3 [::struct::list repeat 3 0]
    {0 0 0} {0 0 0} {0 0 0}
    tclsh> ::struct::list repeat 3 a b c
    a b c a b c a b c
    tclsh> ::struct::list repeat 3 [::struct::list repeat 2 a] b c
    {a a} b c {a a} b c {a a} b c
}]

[call [cmd ::struct::list] [method repeatn] [arg value] [arg size]...]

The subcommand creates a (nested) list containing the [arg value] in
all positions. The exact size and degree of nesting is determined by
the [arg size] arguments, all of which have to be integer numbers
greater than or equal to zero.

[para]

A single argument [arg size] which is a list of more than one element
will be treated as if more than argument [arg size] was specified.

[para]

If only one argument [arg size] is present the returned list will not
be nested, of length [arg size] and contain [arg value] in all
positions.

If more than one [arg size] argument is present the returned
list will be nested, and of the length specified by the last
[arg size] argument given to it. The elements of that list
are defined as the result of [cmd Repeat] for the same arguments,
but with the last [arg size] value removed.

[para]

An empty list will be returned if no [arg size] arguments are present.

[para]
[example {
    tclsh> ::struct::list repeatn  0 3 4
    {0 0 0} {0 0 0} {0 0 0} {0 0 0}
    tclsh> ::struct::list repeatn  0 {3 4}
    {0 0 0} {0 0 0} {0 0 0} {0 0 0}
    tclsh> ::struct::list repeatn  0 {3 4 5}
    {{0 0 0} {0 0 0} {0 0 0} {0 0 0}} {{0 0 0} {0 0 0} {0 0 0} {0 0 0}} {{0 0 0} {0 0 0} {0 0 0} {0 0 0}} {{0 0 0} {0 0 0} {0 0 0} {0 0 0}} {{0 0 0} {0 0 0} {0 0 0} {0 0 0}}
}]


[call [cmd ::struct::list] [method dbJoin] [opt [option -inner]|[option -left]|[option -right]|[option -full]] [opt "[option -keys] [arg varname]"] \{[arg keycol] [arg table]\}...]

The method performs a table join according to relational algebra. The
execution of any of the possible outer join operation is triggered by
the presence of either option [option -left], [option -right], or
[option -full]. If none of these options is present a regular inner
join will be performed. This can also be triggered by specifying
[option -inner]. The various possible join operations are explained in
detail in section [sectref {TABLE JOIN}].

[para]

If the [option -keys] is present its argument is the name of a
variable to store the full list of found keys into. Depending on the
exact nature of the input table and the join mode the output table may
not contain all the keys by default. In such a case the caller can
declare a variable for this information and then insert it into the
output table on its own, as she will have more information about the
placement than this command.

[para]

What is left to explain is the format of the arguments.

[para]

The [arg keycol] arguments are the indices of the columns in the
tables which contain the key values to use for the joining. Each
argument applies to the table following immediately after it. The
columns are counted from [const 0], which references the first
column. The table associated with the column index has to have at
least [arg keycol]+1 columns. An error will be thrown if there are
less.

[para]

The [arg table] arguments represent a table or matrix of rows and
columns of values. We use the same representation as generated and
consumed by the methods [method {get rect}] and [method {set rect}] of
[cmd matrix] objects. In other words, each argument is a list,
representing the whole matrix.  Its elements are lists too, each
representing a single rows of the matrix. The elements of the
row-lists are the column values.

[para]

The table resulting from the join operation is returned as the result
of the command. We use the same representation as described above for
the input [arg table]s.



[call [cmd ::struct::list] [method dbJoinKeyed] [opt [option -inner]|[option -left]|[option -right]|[option -full]] [opt "[option -keys] [arg varname]"] [arg table]...]

The operations performed by this method are the same as described
above for [method dbJoin]. The only difference is in the specification
of the keys to use. Instead of using column indices separate from the
table here the keys are provided within the table itself. The row
elements in each [arg table] are not the lists of column values, but a
two-element list where the second element is the regular list of
column values and the first element is the key to use.

[call [cmd ::struct::list] [method swap] [arg listvar] [arg i] [arg j]]

The subcommand exchanges the elements at the indices [arg i] and
[arg j] in the list stored in the variable named by [arg listvar]. The
list is modified in place, and also returned as the result of the
subcommand.


[call [cmd ::struct::list] [method firstperm] [arg list]]

This subcommand returns the lexicographically first permutation of the
input [arg list].


[call [cmd ::struct::list] [method nextperm] [arg perm]]

This subcommand accepts a permutation of a set of elements (provided
by [arg perm]) and returns the next permutatation in lexicographic
sequence.

[para]
The algorithm used here is by Donal E. Knuth, see section
[sectref REFERENCES] for details.


[call [cmd ::struct::list] [method permutations] [arg list]]

This subcommand returns a list containing all permutations of the
input [arg list] in lexicographic order.


[call [cmd ::struct::list] [method foreachperm] [arg var] [arg list] [arg body]]

This subcommand executes the script [arg body] once for each
permutation of the specified [arg list]. The permutations are visited
in lexicographic order, and the variable [arg var] is set to the
permutation for which [arg body] is currently executed. The result of
the loop command is the empty string.

[list_end]

[section {LONGEST COMMON SUBSEQUENCE AND FILE COMPARISON}]

[para]

The [method longestCommonSubsequence] subcommand forms the core of a
flexible system for doing differential comparisons of files, similar
to the capability offered by the Unix command [syscmd diff].

While this procedure is quite rapid for many tasks of file comparison,
its performance degrades severely if [arg sequence2] contains many
equal elements (as, for instance, when using this procedure to compare
two files, a quarter of whose lines are blank.  This drawback is
intrinsic to the algorithm used (see the Reference for details).

[para]

One approach to dealing with the performance problem that is sometimes
effective in practice is arbitrarily to exclude elements that appear
more than a certain number of times. 

This number is provided as the [arg maxOccurs] parameter.  If frequent
lines are excluded in this manner, they will not appear in the common
subsequence that is computed; the result will be the longest common
subsequence of infrequent elements.

The procedure [method longestCommonSubsequence2] implements this
heuristic.

It functions as a wrapper around [method longestCommonSubsequence]; it
computes the longest common subsequence of infrequent elements, and
then subdivides the subsequences that lie between the matches to
approximate the true longest common subsequence.


[section {TABLE JOIN}]

This is an operation from relational algebra for relational databases.

[para]

The easiest way to understand the regular inner join is that it
creates the cartesian product of all the tables involved first and
then keeps only all those rows in the resulting table for which the
values in the specified key columns are equal to each other.

[para]

Implementing this description naively, i.e. as described above will
generate a [emph huge] intermediate result. To avoid this the
cartesian product and the filtering of row are done at the same
time. What is required is a fast way to determine if a key is present
in a table. In a true database this is done through indices. Here we
use arrays internally.

[para]

An [term outer] join is an extension of the inner join for two
tables. There are three variants of outerjoins, called [term left],
[term right], and [term full] outer joins. Their result always
contains all rows from an inner join and then some additional rows.

[list_begin enumerated]
[enum]

For the left outer join the additional rows are all rows from the left
table for which there is no key in the right table. They are joined to
an empty row of the right table to fit them into the result.

[enum]

For the right outer join the additional rows are all rows from the right
table for which there is no key in the left table. They are joined to
an empty row of the left table to fit them into the result.


[enum]

The full outer join combines both left and right outer join. In other
words, the additional rows are as defined for left outer join, and
right outer join, combined.

[list_end]

[para]

We extend all the joins from two to [var n] tables ([var n] > 2) by
executing

[example {
    (...((table1 join table2) join table3) ...) join tableN
}]

[para]

Examples for all the joins:

[example {
    Inner Join

    {0 foo}              {0 bagel}    {0 foo   0 bagel}
    {1 snarf} inner join {1 snatz}  = {1 snarf 1 snatz}
    {2 blue}             {3 driver}

    Left Outer Join

    {0 foo}                   {0 bagel}    {0 foo   0 bagel}
    {1 snarf} left outer join {1 snatz}  = {1 snarf 1 snatz}
    {2 blue}                  {3 driver}   {2 blue  {} {}}

    Right Outer Join

    {0 foo}                    {0 bagel}    {0 foo   0 bagel}
    {1 snarf} right outer join {1 snatz}  = {1 snarf 1 snatz}
    {2 blue}                   {3 driver}   {{} {}   3 driver}

    Full Outer Join

    {0 foo}                   {0 bagel}    {0 foo   0 bagel}
    {1 snarf} full outer join {1 snatz}  = {1 snarf 1 snatz}
    {2 blue}                  {3 driver}   {2 blue  {} {}}
                                           {{} {}   3 driver}
}]




[section REFERENCES]

[list_begin enumerated]

[enum]
J. W. Hunt and M. D. McIlroy, "An algorithm for differential 
file comparison," Comp. Sci. Tech. Rep. #41, Bell Telephone 
Laboratories (1976). Available on the Web at the second
author's personal site: [uri http://www.cs.dartmouth.edu/~doug/]

[enum]
Donald E. Knuth, "Fascicle 2b of 'The Art of Computer Programming'
volume 4". Available on the Web at the author's personal site:
[uri http://www-cs-faculty.stanford.edu/~knuth/fasc2b.ps.gz].

[list_end]

[section {BUGS, IDEAS, FEEDBACK}]

This document, and the package it describes, will undoubtedly contain
bugs and other problems.

Please report such in the category [emph {struct :: list}] of the
[uri {http://sourceforge.net/tracker/?group_id=12883} {Tcllib SF Trackers}].

Please also report any ideas for enhancements you may have for either
package and/or documentation.


[keywords list diff differential comparison common subsequence]
[keywords {longest common subsequence}]
[keywords reverse]
[keywords assign]
[keywords flatten]
[keywords map filter]
[keywords folding reduce]
[keywords equality equal repetition repeating]
[keywords {inner join} {left outer join} {right outer join} {full outer join} {outer join} join]
[keywords swapping permutation {first permutation} {next permutation} {generate permutations}]
[manpage_end]