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# toposort

## Overview

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

`toposort(data)`

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.

## Testing

To test, run 'python setup.py test'. On python >= 3.0, this also runs the doctests.