# `topological_sort`

    template <typename VertexListGraph, typename OutputIterator,
              typename P, typename T, typename R>
    void topological_sort(VertexListGraph& g, OutputIterator result,
        const bgl_named_params<P, T, R>& params = all defaults)

The topological sort algorithm creates a linear ordering of the vertices such that if edge (u,v) appears in the graph, then v comes before u in the ordering. The graph must be a directed acyclic graph (DAG). The implementation consists mainly of a call to `depth_first_search()`.

### Where Defined:

`boost/graph/topological_sort.hpp`

### Parameters

IN: `VertexListGraph& g`

> A directed acylic graph (DAG). The graph type must be a model of Vertex List Graph and Incidence Graph. If the graph is not a DAG then a `not_a_dag` exception will be thrown and the user should discard the contents of `result` range.
> Python: The parameter is named `graph`.

OUT: `OutputIterator result`

> The vertex descriptors of the graph will be output to the `result` output iterator in reverse topological order. The iterator type must model Output Iterator.
> Python: This parameter is not used in Python. Instead, a Python `list` containing the vertices in topological order is returned.

### Named Parameters

UTIL/OUT: `color_map(ColorMap color)`

> This is used by the algorithm to keep track of its progress through the graph. The type `ColorMap` must be a model of Read/Write Property Map and its key type must be the graph's vertex descriptor type and the value type of the color map must model ColorValue.
> Default: an iterator_property_map created from a `std::vector` of `default_color_type` of size `num_vertices(g)` and using the `i_map` for the index map.
> Python: The color map must be a `vertex_color_map` for the graph.

IN: `vertex_index_map(VertexIndexMap i_map)`

> This maps each vertex to an integer in the range `[0, num_vertices(g))`. This parameter is only necessary when the default color property map is used. The type `VertexIndexMap` must be a model of Readable Property Map. The value type of the map must be an integer type. The vertex descriptor type of the graph needs to be usable as the key type of the map.
> Default: `get(vertex_index, g)` Note: if you use this default, make sure your graph has an internal `vertex_index` property. For example, `adjacenty_list` with `VertexList=listS` does not have an internal `vertex_index` property.
> Python: Unsupported parameter.

### Complexity

The time complexity is O(V + E).

### Example

Calculate a topological ordering of the vertices.

      typedef adjacency_list< vecS, vecS, directedS, color_property<> > Graph;
      typedef boost::graph_traits<Graph>::vertex_descriptor Vertex;
      Pair edges[6] = { Pair(0,1), Pair(2,4),
                        Pair(2,5),
                        Pair(0,3), Pair(1,4),
                        Pair(4,3) };
      Graph G(6, edges, edges + 6);

      typedef std::vector< Vertex > container;
      container c;
      topological_sort(G, std::back_inserter(c));

      cout << "A topological ordering: ";
      for ( container::reverse_iterator ii=c.rbegin(); ii!=c.rend(); ++ii)
        cout << index(*ii) << " ";
      cout << endl;

The output is:

      A topological ordering: 2 5 0 1 4 3

Copyright © 2000-2001 | Jeremy Siek, Indiana University (jsiek@osl.iu.edu)