NAME

tsort — topological sort of a directed graph

SYNOPSIS

DESCRIPTION

tsort takes a list of pairs of node names representing directed arcs in a graph and prints the nodes in topological order on standard output. That is, the input describes a partial ordering relation, from which tsort computes a total order compatible with this partial ordering.

Input is taken from the named file, or from standard input if no file is given.

Node names in the input are separated by white space and there must be an even number of node names.

Presence of a node in a graph can be represented by an arc from the node to itself. This is useful when a node is not connected to any other nodes.

If the graph contains a cycle (and therefore cannot be properly sorted), one of the arcs in the cycle is ignored and the sort continues. Cycles are reported on standard error.

The options are as follows:

-f

Resolve ambiguities by selecting nodes based on the order of appearance of the first component of the pairs.

-h file

Use file, which holds an ordered list of nodes, to resolve ambiguities. In case of duplicates, the first entry is chosen.

-l

Search for and display the longest cycle. Can take a very long time, as it may need to solve an NP-complete problem.

-q

Do not display informational messages about cycles. This is primarily intended for building libraries, where optimal ordering is not critical, and cycles occur often.

-r

Reverse the ordering relation.

-v

Inform on the exact number of edges broken while breaking cycles. If a hints file was used, inform on seen nodes absent from that file.

-w

Exit with exit code the number of cycles tsort had to break.

EXIT STATUS

The tsort utility exits 0 on success, and >0 if an error occurs.

EXAMPLES

Faced with the input:

a b
b c
b d
d f
c e

tsort outputs:

a
b
c
e
d
f

which is one total ordering compatible with the individual relations. There is no unicity, another compatible total ordering would be:

a
b
c
d
e
f

tsort is commonly used to analyze dependencies and find a correct build order in a static way, whereas make(1) accomplishes the same task in a dynamic way.

SEE ALSO

ar(1), lorder(1), make(1)

Donald E. Knuth, The Art of Computer Programming, Vol. 1, pp. 258–268, 1973.

STANDARDS

The tsort utility is compliant with the IEEE Std 1003.1-2008 (“POSIX.1”) specification.

The flags [-fhlqrvw] are extensions to that specification.

HISTORY

A tsort command appeared in Version 7 AT&T UNIX. This tsort command was completely rewritten by Marc Espie for OpenBSD, to finally use the well-known optimal algorithms for topological sorting.