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struct::list(n) Tcl Data Structures struct::list(n)
____________________________________________________________________________________________________________
NAME
struct::list - Procedures for manipulating lists
SYNOPSIS
package require Tcl 8.0
package require struct::list ?1.7?
::struct::list longestCommonSubsequence sequence1 sequence2 ?maxOccurs?
::struct::list longestCommonSubsequence2 sequence1 sequence2 ?maxOccurs?
::struct::list lcsInvert lcsData len1 len2
::struct::list lcsInvert2 lcs1 lcs2 len1 len2
::struct::list lcsInvertMerge lcsData len1 len2
::struct::list lcsInvertMerge2 lcs1 lcs2 len1 len2
::struct::list reverse sequence
::struct::list assign sequence varname ?varname?...
::struct::list flatten ?-full? ?--? sequence
::struct::list map sequence cmdprefix
::struct::list mapfor var sequence script
::struct::list filter sequence cmdprefix
::struct::list filterfor var sequence expr
::struct::list split sequence cmdprefix ?passVar failVar?
::struct::list fold sequence initialvalue cmdprefix
::struct::list shift listvar
::struct::list iota n
::struct::list equal a b
::struct::list repeat size element1 ?element2 element3...?
::struct::list repeatn value size...
::struct::list dbJoin ?-inner|-left|-right|-full? ?-keys varname? {keycol table}...
::struct::list dbJoinKeyed ?-inner|-left|-right|-full? ?-keys varname? table...
::struct::list swap listvar i j
::struct::list firstperm list
::struct::list nextperm perm
::struct::list permutations list
::struct::list foreachperm var list body
____________________________________________________________________________________________________________
DESCRIPTION
The ::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.
It exports only a single command, struct::list. All functionality provided here can be reached
through a subcommand of this command.
COMMANDS
::struct::list longestCommonSubsequence sequence1 sequence2 ?maxOccurs?
Returns the longest common subsequence of elements in the two lists sequence1 and sequence2.
If the maxOccurs parameter is provided, the common subsequence is restricted to elements that
occur no more than maxOccurs times in sequence2.
The return value is a list of two lists of equal length. The first sublist is of indices into
sequence1, and the second sublist is of indices into sequence2. Each corresponding pair of
indices corresponds to equal elements in the sequences; the sequence returned is the longest
possible.
::struct::list longestCommonSubsequence2 sequence1 sequence2 ?maxOccurs?
Returns an approximation to the longest common sequence of elements in the two lists sequence1
and sequence2. If the 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 maxOc-curs maxOccurs
curs times in sequence2, and then using that result to align the two lists, determining the
longest common subsequences of the sublists between the two elements.
As with longestCommonSubsequence, the return value is a list of two lists of equal length.
The first sublist is of indices into sequence1, and the second sublist is of indices into
sequence2. Each corresponding pair of indices corresponds to equal elements in the sequences.
The sequence approximates the longest common subsequence.
::struct::list lcsInvert lcsData len1 len2
This command takes a description of a longest common subsequence (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.
To be fully defined the lengths of the two sequences have to be known and are specified
through len1 and len2.
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 sequence1 and sequence2 respectively, in this order. The type can be one of
three values:
added Describes an addition. I.e. items which are missing in sequence1 can be found in
sequence2. The pair of indices into sequence1 describes where the added range had been
expected to be in 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 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.
deleted
Describes a deletion. I.e. items which are in sequence1 are missing from sequence2.
The pair of indices into 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 sequence2 describes where the
deleted range had been expected to be in 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.
changed
Describes a general change. I.e a range of items in sequence1 has been replaced by a
different range of items in sequence2. The pair of indices into 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 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.
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}}}
Notes:
• An index of -1 in a deleted chunk refers to just before the first element of the second
sequence.
• Also an index equal to the length of the first sequence in an added chunk refers to
just behind the end of the sequence.
::struct::list lcsInvert2 lcs1 lcs2 len1 len2
Similar to lcsInvert. Instead of directly taking the result of a call to longestCommonSubse-quence longestCommonSubsequence
quence this subcommand expects the indices for the two sequences in two separate lists.
::struct::list lcsInvertMerge lcsData len1 len2
Similar to lcsInvert. It returns essentially the same structure as that command, except that
it may contain chunks of type unchanged too.
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.
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}}}
::struct::list lcsInvertMerge2 lcs1 lcs2 len1 len2
Similar to lcsInvertMerge. Instead of directly taking the result of a call to longestCommon-Subsequence longestCommonSubsequence
Subsequence this subcommand expects the indices for the two sequences in two separate lists.
::struct::list reverse sequence
The subcommand takes a single sequence as argument and returns a new sequence containing the
elements of the input sequence in reverse order.
::struct::list assign sequence varname ?varname?...
The subcommand assigns the first n elements of the input sequence to the one or more variables
whose names were listed after the sequence, where n is the number of specified variables.
If there are more variables specified than there are elements in the sequence the empty string
will be assigned to the superfluous variables.
If there are more elements in the sequence than variable names specified the subcommand
returns a list containing the unassigned elements. Else an empty list is returned.
tclsh> ::struct::list assign {a b c d e} foo bar
c d e
tclsh> set foo
a
tclsh> set bar
b
::struct::list flatten ?-full? ?--? sequence
The subcommand takes a single 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.
The subcommand will remove any nesting it finds if the option -full is specified.
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
::struct::list map sequence cmdprefix
The subcommand takes a sequence to operate on and a command prefix (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.
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.
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 $n}
tclsh> ::struct::list map {{a b c} {1 2 3} {d f g}} {projection 1}
b 2 f
::struct::list mapfor var sequence script
The subcommand takes a sequence to operate on and a tcl script, applies the script to each
element of the sequence and returns a sequence consisting of the results of that application.
The script will be evaluated as is, and has access to the current list element through the
specified iteration variable var. The evaluation takes place in the context of the caller of
the subcommand.
tclsh> # squaring all elements in a list
tclsh> ::struct::list mapfor x {1 2 3 4 5} {
expr {$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 $x 1
}
b 2 f
::struct::list filter sequence cmdprefix
The subcommand takes a sequence to operate on and a command prefix (cmdprefix) specifying an
operation, applies the command prefix to each element of the sequence and returns a sequence
consisting of all elements of the sequence for which the command prefix returned true. In
other words, this command filters out all elements of the input sequence which fail the test
the cmdprefix represents, and returns the remaining elements.
The command prefix will be evaluated with a single word appended to it. The evaluation takes
place in the context of the caller of the subcommand.
tclsh> # removing all odd numbers from the input
tclsh> proc even {x} {expr {($x % 2) == 0}}
tclsh> ::struct::list filter {1 2 3 4 5} even
2 4
Note: The filter is a specialized application of fold where the result is extended with the
current item or not, depending o nthe result of the test.
::struct::list filterfor var sequence expr
The subcommand takes a sequence to operate on and a tcl expression (expr) specifying a condi-tion, condition,
tion, applies the conditionto each element of the sequence and returns a sequence consisting
of all elements of the sequence for which the expression returned true. In other words, this
command filters out all elements of the input sequence which fail the test the condition expr
represents, and returns the remaining elements.
The expression will be evaluated as is, and has access to the current list element through the
specified iteration variable var. The evaluation takes place in the context of the caller of
the subcommand.
tclsh> # removing all odd numbers from the input
tclsh> ::struct::list filterfor x {1 2 3 4 5} {($x % 2) == 0}
2 4
::struct::list split sequence cmdprefix ?passVar failVar?
This is a variant of method filter, see above. Instead of returning just the elements passing
the test we get lists of both passing and failing elements.
If no variable names are specified then the result of the command will be a list containing
the list of passing elements, and the list of failing elements, in this order. Otherwise the
lists of passing and failing elements are stored into the two specified variables, and the
result will be a list containing two numbers, the number of elements passing the test, and the
number of elements failing, in this order.
The interface to the test is the same as used by filter.
::struct::list fold sequence initialvalue cmdprefix
The subcommand takes a sequence to operate on, an arbitrary string initial value and a command
prefix (cmdprefix) specifying an operation.
The command prefix will be evaluated with two words appended to it. The second of these words
will always be an element of the sequence. The evaluation takes place in the context of the
caller of the subcommand.
It then reduces the sequence into a single value through repeated application of the command
prefix and returns that value. This reduction is done by
1 Application of the command to the initial value and the first element of the list.
2 Application of the command to the result of the last call and the second element of the
list.
i
Application of the command to the result of the last call and the i'th element
of the list.
end
Application of the command to the result of the last call and the
last element of the list. The result of this call is returned as
the result of the subcommand.
tclsh> # summing the elements in a list.
tclsh> proc + {a b} {expr {$a + $b}}
tclsh> ::struct::list fold {1 2 3 4 5} 0 +
15
::struct::list shift listvar
The subcommand takes the list contained in the variable named by
listvar and shifts it down one element. After the call 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.
::struct::list iota n
The subcommand returns a list containing the integer numbers in
the range [0,n). The element at index i of the list contain the
number i.
For "n == 0" an empty list will be returned.
::struct::list equal a b
The subcommand compares the two lists a and b for equality. In
other words, they have to be of the same length and have to con-tain contain
tain the same elements in the same order. If an element is a list
the same definition of equality applies recursively.
A boolean value will be returned as the result of the command.
This value will be true if the two lists are equal, and false
else.
::struct::list repeat size element1 ?element2 element3...?
The subcommand creates a list of length "size * number of ele-ments" elements"
ments" by repeating size times the sequence of elements element1
element2 .... size must be a positive integer, elementn can be
any Tcl value. Note that repeat 1 arg ... is identical to list
arg ..., though the arg is required with repeat.
Examples:
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
::struct::list repeatn value size...
The subcommand creates a (nested) list containing the value in all
positions. The exact size and degree of nesting is determined by
the size arguments, all of which have to be integer numbers
greater than or equal to zero.
A single argument size which is a list of more than one element
will be treated as if more than argument size was specified.
If only one argument size is present the returned list will not be
nested, of length size and contain value in all positions. If
more than one size argument is present the returned list will be
nested, and of the length specified by the last size argument
given to it. The elements of that list are defined as the result
of Repeat for the same arguments, but with the last size value
removed.
An empty list will be returned if no size arguments are present.
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}}
::struct::list dbJoin ?-inner|-left|-right|-full? ?-keys varname? {keycol
table}...
The method performs a table join according to relational algebra.
The execution of any of the possible outer join operation is trig-gered triggered
gered by the presence of either option -left, -right, or -full. If
none of these options is present a regular inner join will be per-formed. performed.
formed. This can also be triggered by specifying -inner. The vari-ous various
ous possible join operations are explained in detail in section
TABLE JOIN.
If the -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.
What is left to explain is the format of the arguments.
The 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 0, which references the first column. The table
associated with the column index has to have at least keycol+1
columns. An error will be thrown if there are less.
The table arguments represent a table or matrix of rows and col-umns columns
umns of values. We use the same representation as generated and
consumed by the methods get rect and set rect of 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.
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 tables.
::struct::list dbJoinKeyed ?-inner|-left|-right|-full? ?-keys varname?
table...
The operations performed by this method are the same as described
above for 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 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.
::struct::list swap listvar i j
The subcommand exchanges the elements at the indices i and j in
the list stored in the variable named by listvar. The list is mod-ified modified
ified in place, and also returned as the result of the subcommand.
::struct::list firstperm list
This subcommand returns the lexicographically first permutation of
the input list.
::struct::list nextperm perm
This subcommand accepts a permutation of a set of elements (pro-vided (provided
vided by perm) and returns the next permutatation in lexicographic
sequence.
The algorithm used here is by Donal E. Knuth, see section REFER-ENCES REFERENCES
ENCES for details.
::struct::list permutations list
This subcommand returns a list containing all permutations of the
input list in lexicographic order.
::struct::list foreachperm var list body
This subcommand executes the script body once for each permutation
of the specified list. The permutations are visited in lexico-graphic lexicographic
graphic order, and the variable var is set to the permutation for
which body is currently executed. The result of the loop command
is the empty string.
LONGEST COMMON SUBSEQUENCE AND FILE COMPARISON
The longestCommonSubsequence subcommand forms the core of a flexible sys-tem system
tem for doing differential comparisons of files, similar to the capabil-ity capability
ity offered by the Unix command diff. While this procedure is quite
rapid for many tasks of file comparison, its performance degrades severe-ly severely
ly if 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 Refer-ence Reference
ence for details).
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 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
longestCommonSubsequence2 implements this heuristic. It functions as a
wrapper around 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 sub-sequence. subsequence.
sequence.
TABLE JOIN
This is an operation from relational algebra for relational databases.
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.
Implementing this description naively, i.e. as described above will gen-erate generate
erate a 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.
An outer join is an extension of the inner join for two tables. There are
three variants of outerjoins, called left, right, and full outer joins.
Their result always contains all rows from an inner join and then some
additional rows.
[1] 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.
[2] 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.
[3] 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.
We extend all the joins from two to n tables (n > 2) by executing
(...((table1 join table2) join table3) ...) join tableN
Examples for all the joins:
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}
REFERENCES
[1] J. W. Hunt and M. D. McIlroy, "An algorithm for differential file
comparison," Comp. Sci. Tech. Rep. #41, Bell Telephone Laborato-ries Laboratories
ries (1976). Available on the Web at the second author's personal
site: http://www.cs.dartmouth.edu/~doug/
[2] Donald E. Knuth, "Fascicle 2b of 'The Art of Computer Programming'
volume 4". Available on the Web at the author's personal site:
http://www-cs-faculty.stanford.edu/~knuth/fasc2b.ps.gz.
BUGS, IDEAS, FEEDBACK
This document, and the package it describes, will undoubtedly contain
bugs and other problems. Please report such in the category struct ::
list of the Tcllib SF Trackers [http://source -
forge.net/tracker/? group_id=12883]. Please also report any ideas for
enhancements you may have for either package and/or documentation.
KEYWORDS
assign, common, comparison, diff, differential, equal, equality, filter,
first permutation, flatten, folding, full outer join, generate permuta-tions, permutations,
tions, inner join, join, left outer join, list, longest common subse-quence, subsequence,
quence, map, next permutation, outer join, permutation, reduce, repeat-ing, repeating,
ing, repetition, reverse, right outer join, subsequence, swapping
CATEGORY
Data structures
COPYRIGHT
Copyright (c) 2003-2005 by Kevin B. Kenny. All rights reserved
Copyright (c) 2003-2008 Andreas Kupries <andreas_kupries@users.sourceforge.net>
struct 1.7 struct::list(n)
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