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Implements a topological sort algorithm.

Project Description


Implements a topological sort algorithm.

>From Wikipedia: In computer science, a topological sort (sometimes abbreviated topsort or toposort) or topological ordering of a directed graph is a linear ordering of its vertices such that for every directed edge uv from vertex u to vertex v, u comes before v in the ordering.

Input data description

The input to the toposort function is a dict describing the dependencies among the input nodes. Each key is a dependent node, the corresponding value is a set containing the dependent nodes.

Note that toposort does not care what the input node values mean: it just compares them for equality. The examples here usually use integers, but they could be any hashable type.

Typical usage

The interpretation of the input data here is: If 2 depends on 11; 9 depends on 11, 8 and 10; 10 depends on 11 and 3 (and so on), then in what order should we process the items such that all nodes are processed before any of their dependencies?:

>>> from toposort import toposort, toposort_flatten
>>> list(toposort({2: {11},
...                9: {11, 8, 10},
...                10: {11, 3},
...                11: {7, 5},
...                8: {7, 3},
...               }))
[{3, 5, 7}, {8, 11}, {2, 10}, {9}]

And the answer is: process 3, 5, and 7 (in any order); then process 8 and 11; then process 2 and 10; then process 9. Note that 3, 5, and 7 are returned first because they do not depend on anything. They are then removed from consideration, and then 8 and 11 don’t depend on anything remaining. This process continues until all nodes are returned, or a circular dependency is detected.

Circular dependencies

A circular dependency will raise a CyclicDependencyError, which is derived from ValueError. Here 1 depends on 2, and 2 depends on 1:

>>> list(toposort({1: {2},
...                2: {1},
...               }))
Traceback (most recent call last):
toposort.CircularDependencyError: Circular dependencies exist among these items: {1:{2}, 2:{1}}

In addition, the ‘data’ attribute of the raised CyclicDependencyError will contain a dict containing the subset of the input data involved in the circular dependency.

Module contents


Returns an iterator describing the dependencies among nodes in the input data. Each returned item will be a set. Each member of this set has no dependencies in this set, or in any set previously returned.

toposort_flatten(data, sort=True)

Like toposort(data), except that it returns a list of all of the depend values, in order. If sort is true, the returned nodes are sorted within each group before they are appended to the result:

>>> toposort_flatten({2: {11},
...                   9: {11, 8, 10},
...                   10: {11, 3},
...                   11: {7, 5},
...                   8: {7, 3},
...                  })
[3, 5, 7, 8, 11, 2, 10, 9]

Note that this result is the same as the first example: [{3, 5, 7}, {8, 11}, {2, 10}, {9}], except that the result is flattened, and within each set the nodes are sorted.


To test, run ‘python test’. On python >= 3.0, this also runs the doctests.

Change log

1.5 2016-10-24 Eric V. Smith

  • When a circular dependency error is detected, raise a specific exception, CircularDependencyError, which is a subclass of ValueError. The ‘data’ attribute of the exception will contain the data involved in the circular dependency (issue #2). Thanks lilydjwg for the initial patch.
  • To make building wheels easier, always require setuptools in (issue #5).
  • Mark wheel as being universal, that is, supporting both Python 2.7 and 3.x (issue #7).

1.4 2015-05-16 Eric V. Smith

  • Removed ‘test’ package, so it won’t get installed by bdist_*. It’s still included in sdists.
  • No code changes.

1.3 2015-05-15 Eric V. Smith

  • Fixed change log date.
  • No code changes.

1.2 2015-05-15 Eric V. Smith

  • Changed RPM name to python3-toposort if running with python 3.
  • No code changes.

1.1 2014-07-24 Eric V. Smith

  • Release version 1.1. No code changes.
  • Add a README.txt entry on running the test suite.
  • Fix missing test/ in the sdist.

1.0 2014-03-14 Eric V. Smith

  • Release version 1.0. The API is stable.
  • Add to, so that it is created in the sdist (issue #1).

0.2 2014-02-11 Eric V. Smith

  • Modify to produce a RPM name of python-toposort for bdist_rpm.

0.1 2014-02-10 Eric V. Smith

  • Initial release.

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