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34 .\" @(#)tsort.1 8.3 (Berkeley) 4/1/94
36 .Dd $Mdocdate: March 29 2012 $
41 .Nd topological sort of a directed graph
49 takes a list of pairs of node names representing directed arcs in
50 a graph and prints the nodes in topological order on standard output.
51 That is, the input describes a partial ordering relation, from which
53 computes a total order compatible with this partial ordering.
55 Input is taken from the named
57 or from standard input if no file
60 Node names in the input are separated by white space and there must
61 be an even number of node names.
63 Presence of a node in a graph can be represented by an arc from the node
65 This is useful when a node is not connected to any other nodes.
67 If the graph contains a cycle (and therefore cannot be properly sorted),
68 one of the arcs in the cycle is ignored and the sort continues.
69 Cycles are reported on standard error.
71 The options are as follows:
74 Resolve ambiguities by selecting nodes based on the order of appearance
75 of the first component of the pairs.
79 which holds an ordered list of nodes, to resolve ambiguities.
80 In case of duplicates, the first entry is chosen.
82 Search for and display the longest cycle.
83 Can take a very long time, as it may need to solve an NP-complete problem.
85 Do not display informational messages about cycles.
86 This is primarily intended for building libraries, where optimal ordering
87 is not critical, and cycles occur often.
89 Reverse the ordering relation.
91 Inform on the exact number of edges broken while breaking cycles.
92 If a hints file was used, inform on seen nodes absent from that file.
94 Exit with exit code the number of cycles
101 Faced with the input:
102 .Bd -literal -offset indent
112 .Bd -literal -offset indent
121 which is one total ordering compatible with the individual relations.
122 There is no unicity, another compatible total ordering would be:
123 .Bd -literal -offset indent
133 is commonly used to analyze dependencies and find a correct build order
134 in a static way, whereas
136 accomplishes the same task in a dynamic way.
143 .%B The Art of Computer Programming
151 utility is compliant with the
157 are extensions to that specification.
165 command was completely rewritten by Marc Espie for
167 to finally use the well-known optimal algorithms for topological sorting.