Tsort
The tsort program is a command line utility on Unix and Unix-like platforms, that performs a topological sort on its input. It is part of the POSIX.1 standard. and has been since The Single [UNIX Specification, Version 2].
History
According to its info page, this command was initially written for providing an ordering of object files that allowed the linker to process them sequentially. The FreeBSD manual page dates its appearance to Version 7 Unix.Note that the following description is describing the behavior of the FreeBSD implementation of tsort and mentions GNU features where they may exist. Other implementations or versions may differ.
Syntax
tsortFreeBSD options can be:
-d turn on debugging
-l search for and display the longest cycle.
-q Do not display informational messages about cycles.
GNU provides the following options only:
--help display help message and exit
--version display version information and exit
There are no options prescribed by POSIX.
Behavior
tsort reads its input as pairs of strings, separated by blanks, indicating a partial ordering. The output is a total ordering that corresponds to the given partial ordering.In other words: for a directed acyclic graph, tsort produces a listing of the
vertices so that for all edges 'a->b', 'a' comes before 'b' in the listing.
Examples
tsort lists the vertices of a directed acyclic graph in such an order that all ordering/direction relations are respected:$ tsort < > 3 10 > 5 11 > 7 8 > 7 11 > 8 9 > 11 2 > 11 9 > 11 10 > EOF 11 10 | Image:Directed [acyclic graph 2.svg|right|frame|sample DAG] |
Call graph
tsort can help rearranging functions in a source file so that as many as possible are defined before they are used :$ cat call-graph main parse_options main tail_file main tail_forever tail_file pretty_name tail_file write_header tail_file tail tail_forever recheck tail_forever pretty_name tail_forever write_header tail_forever dump_remainder tail tail_lines tail tail_bytes tail_lines start_lines tail_lines dump_remainder tail_lines file_lines tail_lines pipe_lines tail_bytes xlseek tail_bytes start_bytes tail_bytes dump_remainder tail_bytes pipe_bytes file_lines dump_remainder recheck pretty_name | $ # note: 'tac' reverses the order $ tsort call-graph | tac dump_remainder start_lines file_lines pipe_lines xlseek start_bytes pipe_bytes tail_lines tail_bytes pretty_name write_header tail recheck parse_options tail_file tail_forever main |
Library
The traditional ld requires that its library inputs be sorted in topological order, since it processes files in a single pass. This applies both to static libraries and dynamic libraries, and in the case of static libraries preferably for the individual object files contained within.BSD UNIX uses tsort as a common part of the typical ar & ranlib command invocations :
lib$.a: $ $
@$ building static $ library
@$ cq $ `lorder $ $ | tsort -q` $
$ $
Here is used to generate the inter-file dependency list by inspecting the symbol table.
Usage notes
Notice the interchangeability of white space separators so the following inputs are equivalent:a b b c | a b b c | a b b c | a b b c | a b b c |
Pairs of identical items indicate presence of a vertex, but not ordering :
a a
Strictly speaking there is no topological ordering of a graph that contains one or more cycles. However tsort prints a warning and GNU tsort prints the detected cycles to standard error :
$ tsort <
> b c
> c a
> EOF
UX: tsort: INFORM: cycle in data
tsort: a
tsort: b
tsort: c