# fn() depthFirstSearch
Implements a depth-first search on a graph.

Defined in | <seqan/graph_algorithms.h>
Signature | `void depthFirstSearch(predecessor, discovery, finish, g);`

## Parameters

`predecessor` | A property map.Predecessor subgraph produced by the depth-first search.
`discovery` | A property map.The discovery time of a vertex v.
`finish` | A property map.The time when v's adjacency list has been fully explored.
`g` | A graph. Types: Undirected Graph, Directed Graph

## Detailed Description

In contrast to a breadth-first search the depth-first search is repeated from multiple sources if the graph is not connected. Hence, depth-first search produces a depth-first forest. To ensure each vertex ends up in exactly one tree we need not just a distance but a discovery and finishing time.

### Example

    #include <iostream>
    #include <seqan/graph_algorithms.h>

    using namespace seqan;

    int main()
    {
        typedef Graph<Directed<> > TGraph;
        typedef VertexDescriptor<TGraph>::Type TVertexDescriptor;
        typedef Size<TGraph>::Type TSize;

        // Create graph with 8 directed edges (0,3), (0,1), ...
        TSize numEdges = 8;
        TVertexDescriptor edges[] = {0, 3, 0, 1, 1, 4, 2, 4, 2, 5, 3, 1, 4, 3, 5, 5};
        TGraph g;
        addEdges(g, edges, numEdges);
        // Print graph.
        std::cout << g << "\n";

        // Create external property map for the vertex names and assign to graph.
        char names[] = {'u', 'v', 'w', 'x', 'y', 'z'};
        String<char> nameMap;
        assignVertexMap(nameMap, g, names);

        // Perform a DFS search.
        String<unsigned int> predMap;
        String<unsigned int> discoveryTimeMap;
        String<unsigned int> finishingTimeMap;
        depthFirstSearch(predMap, discoveryTimeMap, finishingTimeMap, g);

        // Write the result to stdout.
        std::cout << "Depth-First search: \n";
        typedef Iterator<Graph<>, VertexIterator>::Type TVertexIterator;
        TVertexIterator it(g);
        while (!atEnd(it))
        {
            std::cout << "Vertex " << getProperty(nameMap, getValue(it)) << ": ";
            std::cout << "Discovery time = " << getProperty(discoveryTimeMap, getValue(it)) << ",";
            std::cout << "Finishing time = " << getProperty(finishingTimeMap, getValue(it)) << ",";
            typedef Value<String<unsigned int> >::Type TPredVal;
            TPredVal pre = getProperty(predMap, getValue(it));
            if (pre != getNil<TVertexDescriptor>())
                std::cout << "Predecessor = " << getProperty(nameMap, pre) << "\n";
            else
                std::cout << "Predecessor = nil" << "\n";
            goNext(it);
        }

        return 0;
    }

Demo: demos/dox/graph_algorithms/depth_first_search.cpp

    Adjacency list:
    0 -> 1,3,
    1 -> 4,
    2 -> 5,4,
    3 -> 1,
    4 -> 3,
    5 -> 5,
    Edge list:
    Source: 0,Target: 1 (Id: 1)
    Source: 0,Target: 3 (Id: 0)
    Source: 1,Target: 4 (Id: 2)
    Source: 2,Target: 5 (Id: 4)
    Source: 2,Target: 4 (Id: 3)
    Source: 3,Target: 1 (Id: 5)
    Source: 4,Target: 3 (Id: 6)
    Source: 5,Target: 5 (Id: 7)

    Depth-First search:
    Vertex u: Discovery time = 1,Finishing time = 8,Predecessor = nil
    Vertex v: Discovery time = 2,Finishing time = 7,Predecessor = u
    Vertex w: Discovery time = 9,Finishing time = 12,Predecessor = nil
    Vertex x: Discovery time = 4,Finishing time = 5,Predecessor = y
    Vertex y: Discovery time = 3,Finishing time = 6,Predecessor = v
    Vertex z: Discovery time = 10,Finishing time = 11,Predecessor = w

## Data Races

Thread safety unknown!

## See Also

- breadthFirstSearch

#### Dox Sources

    /*!
     * @fn depthFirstSearch
     *
     * @headerfile <seqan/graph_algorithms.h>
     *
     * @brief Implements a depth-first search on a graph.
     *
     * @signature void depthFirstSearch(predecessor, discovery, finish, g);
     *
     * @param[out] predecessor A property map.Predecessor subgraph produced by the
     *                         depth-first search.
     * @param[out] discovery A property map.The discovery time of a vertex v.
     * @param[out] finish A property map.The time when v's adjacency list has been
     *                    fully explored.
     * @param[in] g A graph. Types: Undirected Graph, Directed Graph
     *
     * In contrast to a breadth-first search the depth-first search is repeated from
     * multiple sources if the graph is not connected. Hence, depth-first search
     * produces a depth-first forest. To ensure each vertex ends up in exactly one
     * tree we need not just a distance but a discovery and finishing time.
     *
     * @section Example
     *
     * @include demos/dox/graph_algorithms/depth_first_search.cpp
     *
     * @include demos/dox/graph_algorithms/depth_first_search.cpp.stdout
     *
     * @see breadthFirstSearch
     */