list(n) Tcl Data Structures list(n)
NAME
list - Procedures for manipulating lists
SYNOPSIS
package require Tcl 8.00
package require struct ??1.4??
::::struct::::list longestCommonSubsequence sequence1 sequence2 ?maxOccurs?
::::struct::::list longestCommonSubsequence2 sequence1 sequence2 ?maxOc-
curs?
::::struct::::list lcsInvert lcsData len1 len2
::::struct::::list lcsInvert2 lcs1 lcs2 len1 len2
::::struct::::list lcsInverterge lcsData len1 len2
::::struct::::list lcsInverterge2 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 filter sequence cmdprefix
::::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? {key-
col table}...
::::struct::::list dbJoinKeyed ?-inner-left-right-full? ?-keys varname?
table...
DESCRIPTION
The ::::struct::::list namespace contains several useful commands for pro-
cessing 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 pro-
vided here can be reached through a subcommand of this command.
COMANDS
::::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 sub-
list 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 ?maxOc-
curs?
Returns an approximation to the longest common sequence of ele-
ments in the two lists sequence1 and sequence2. If the maxOc-
curs 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
maxOccurs 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:
]o An index of -1 in a deleted chunk refers to just before
the first element of the second sequence.
]o 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 longestCommonSubsequence this subcommand expects the
indices for the two sequences in two separate lists.
::::struct::::list lcsInverterge 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 lcsInverterge2 lcs1 lcs2 len1 len2
Similar to lcsInverterge. Instead of directly taking the result
of a call to longestCommonSubsequence 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 vari-
ables.
If there are more variables specified than there are elements in
the sequence the empty string will be assigned to the superflu-
ous variables.
If there are more elements in the sequence than variable names
specified the subcommand returns a list containing the unas-
signed 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 pre-
fix (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 $n}
tclsh> ::struct::list map {{a b c} {1 2 3} {d f g}} {projection 1}
b 2 f
::::struct::::list filter sequence cmdprefix
The subcommand takes a sequence to operate on and a command pre-
fix (cmdprefix) specifying an operation, applies the command
prefix to each element of the sequence and returns a sequence
consisting of all elements of the sequence for which the command
prefix returned true. In other words, this command filters out
all elements of the input sequence which fail the test the cmd-
prefix represents, and returns the remaining elements.
The command prefix will be evaluated with a single word appended
to it. The evaluation takes place in the context of the caller
of the subcommand.
tclsh> # removing all odd numbers from the input
tclsh> proc even {x} {expr {($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 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 com-
mand 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 speci-
fied 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 [00,,n). The element at index i of the list contain the
number i.
For "n == 00" 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 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" 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 deter-
mined 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? {key-
col table}...
The method performs a table join according to relational alge-
bra. The execution of any of the possible outer join operation
is triggered by the presence of either option -left, -right, or
-full. If none of these options is present a regular inner join
will be performed. This can also be triggered by specifying
-inner. The various 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 ta-
ble 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 00, which references the first col-
umn. 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 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 speci-
fication 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 ele-
ment is the regular list of column values and the first element
is the key to use.
LONGEST COMON SUBSEQUENCE AND FILE COMPARISON
The longestCommonSubsequence subcommand forms the core of a flexible
system for doing differential comparisons of files, similar to the
capability offered by the Unix command diff. While this procedure is
quite rapid for many tasks of file comparison, its performance degrades
severely 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 Reference 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 subsequence.
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
generate a huge intermediate result. To avoid this the cartesian prod-
uct 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 inter-
nally.
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
J. W. Hunt and M. D. McIlroy, "An algorithm for differential file com-
parison," Comp. Sci. Tech. Rep. #41, Bell Telephone Laboratories
(1976). Available on the Web at the second author's personal site:
http://www.cs.dartmouth.edu/~doug/
KEYWORDS
assign, common, comparison, diff, differential, equal, equality, fil-
ter, flatten, folding, full outer join, inner join, join, left outer
join, list, longest common subsequence, map, outer join, reduce,
repeating, repetition, reverse, right outer join, subsequence
COPYRIGHT
Copyright (c) 2003 by Kevin B. Kenny. All rights reserved
Copyright (c) 2003 Andreas Kupries
struct 1.4 list(n)
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