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    <title>Boost Graph Library: Grid Graph</title>
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    <img src="../../../boost.png" alt="C++ Boost" width="277" height="86" />
    <br />
    <h1>
      <tt>grid_graph</tt>
    </h1>

    <ul>
      <li><a href="#overview">Overview</a></li>
      <li><a href="#creating">Creating a Grid Graph</a></li>
      <li><a href="#indexing">Indexing</a></li>
      <li><a href="#member">Grid Graph Member Functions</a></li>
    </ul>

    <h3 id="overview">Overview</h3>  
    <p>
      A <tt>grid_graph</tt> represents a multi-dimensional,
      rectangular grid of vertices with user-defined dimension lengths
      and wrapping.

    </p>
    <p>
      <tt>grid_graph</tt> models:
      <ul>
        <li><a href="IncidenceGraph.html">Incidence Graph</a></li>
        <li><a href="AdjacencyGraph.html">Adjacency Graph</a></li>
        <li><a href="VertexListGraph.html">Vertex List Graph</a></li>
        <li><a href="EdgeListGraph.html">Edge List Graph</a></li>
        <li><a href="BidirectionalGraph.html">Bidirectional Graph</a></li>
        <li><a href="AdjacencyMatrix.html">Adjacency Matrix</a></li>
      </ul>
    </p>
    <p>
      Defined in
      <a href="../../../boost/graph/grid_graph.hpp"><tt>boost/graph/grid_graph.hpp</tt></a>
      with all functions in the <tt>boost</tt> namespace.  A simple examples of creating and iterating over a grid_graph is available here <a href="../../../libs/graph/example/grid_graph_example.cpp"><tt>libs/graph/example/grid_graph_example.cpp</tt></a>. An example of adding properties to a grid_graph is also available <a href="../../../libs/graph/example/grid_graph_example.cpp"><tt>libs/graph/example/grid_graph_properties.cpp</tt></a>
    </p>

    <h4>Template Parameters</h4>
    <pre class="code">
<span class="keyword">template</span> &lt;<span class="name">std</span>::<span class="type">size_t</span> <span class="name">Dimensions</span>,
          <span class="keyword">typename</span> <span class="name">VertexIndex</span> = <span class="name">std</span>::<span class="type">size_t</span>,
          <span class="keyword">typename</span> <span class="name">EdgeIndex</span> = <span class="name">VertexIndex</span>&gt;
  <span class="keyword">class</span> grid_graph;
    </pre>
    <ul>
      <li>
        <tt>Dimensions</tt> - Number of dimensions in the graph
      </li>
      <li>
        <tt>VertexIndex</tt> - Type used for vertex indices, defaults to <tt>std::size_t</tt>
      </li>
      <li>
        <tt>EdgeIndex</tt> - Type used for edge indices, defaults to the same type as <tt>VertexIndex</tt>
      </li>
    </ul>

    <h3 id="creating">Creating a Grid Graph</h3>
    <p>
      The constructor to <tt>grid_graph</tt> has several overloads to aid in configuring each dimension:
    </p>
    <pre class="code">
<span class="comment">// Defines a grid_graph that does not wrap.</span>
<span class="type">grid_graph</span>&lt;...&gt;(<span class="name">boost</span>:<span class="type">array</span>&lt;<span class="name">VertexIndex</span>, <span class="name">Dimensions</span>&gt; dimension_lengths);

<span class="comment">// Defines a grid_graph where all dimensions are either wrapped or unwrapped.</span>
<span class="type">grid_graph</span>&lt;...&gt;(<span class="name">boost</span>:<span class="type">array</span>&lt;<span class="name">VertexIndex</span>, <span class="name">Dimensions</span>&gt; dimension_lengths,
                <span class="keyword">bool</span> wrap_all_dimensions);

<span class="comment">// Defines a grid_graph where the wrapping for each dimension is specified individually.</span>
<span class="type">grid_graph</span>&lt;...&gt;(<span class="name">boost</span>:<span class="type">array</span>&lt;<span class="name">VertexIndex</span>, <span class="name">Dimensions</span>&gt; dimension_lengths,
                <span class="name">boost</span>:<span class="type">array</span>&lt;<span class="keyword">bool</span>, <span class="name">Dimensions</span>&gt; wrap_dimension);
    </pre>

    <h4>Example</h4>
    <pre class="code">
<span class="comment">// Define dimension lengths, a 3x3 in this case</span>
<span class="name">boost</span>::<span class="type">array</span>&lt;<span class="name">std</span>::<span class="type">size_t</span>, <span class="literal">2</span>&gt; lengths = { { <span class="literal">3</span>, <span class="literal">3</span> } };

<span class="comment">// Create a 3x3 two-dimensional, unwrapped grid graph (Figure 1)</span>
<span class="type">grid_graph</span>&lt;<span class="literal">2</span>&gt; graph(lengths);

<span class="comment">// Create a 3x3 two-dimensional, wrapped grid graph (Figure 2)</span>
<span class="type">grid_graph</span>&lt;<span class="literal">2</span>&gt; graph(lengths, <span class="keyword">true</span>);

    </pre>
    <p style="margin-left: 10px;">
      <img src="figs/grid_graph_unwrapped.png" />
      <br />
      <em style="font-size: 0.8em"><b>Figure 1:</b> A 3x3 two-dimensional, unwrapped grid graph</em>
    </p>
    <br />
    <p style="margin-left: 10px;">
      <img src="figs/grid_graph_wrapped.png" />
      <br />
      <em style="font-size: 0.8em"><b>Figure 2:</b> A 3x3 two-dimensional, wrapped grid graph</em>
    </p> 
    <br />

    <h3 id="indexing">Indexing</h3>
    <p>
      The <tt>grid_graph</tt> supports addressing vertices and edges
      by index. The following functions allow you to convert between
      vertices, edges, and their associated indices:
    </p>

    <pre class="code">
<span class="keyword">typedef</span> <span class="type">grid_graph</span>&lt;...&gt; <span class="name">Graph</span>;
<span class="keyword">typedef</span> <span class="type">graph_traits</span>&lt;<span class="name">Graph</span>&gt; <span class="name">Traits</span>;

<span class="comment">// Get the vertex associated with vertex_index</span>
<span class="name">Traits</span>::<span class="type">vertex_descriptor</span>
vertex(<span class="name">Traits</span>::<span class="type">vertices_size_type</span> vertex_index,
       <span class="keyword">const</span> <span class="name">Graph&amp;</span> graph);

<span class="comment">// Get the index associated with vertex</span>
<span class="name">Traits</span>::<span class="type">vertices_size_type</span>
get(<span class="name">boost</span>::<span class="type">vertex_index_t</span>,
    <span class="keyword">const</span> <span class="name">Graph&amp;</span> graph,
    <span class="name">Traits</span>::<span class="type">vertex_descriptor</span> vertex);

<span class="comment">// Get the edge associated with edge_index</span>
<span class="name">Traits</span>::<span class="type">edge_descriptor</span>
edge_at(<span class="name">Traits</span>::<span class="type">edges_size_type</span> edge_index,
        <span class="keyword">const</span> <span class="name">Graph&amp;</span> graph);

<span class="comment">// Get the index associated with edge</span>
<span class="name">Traits</span>::<span class="type">edges_size_type</span>
get(<span class="name">boost</span>::<span class="type">edge_index_t</span>,
    <span class="keyword">const</span> <span class="name">Graph&amp;</span> graph,
    <span class="name">Traits</span>::<span class="type">edge_descriptor</span> edge);

<span class="comment">// Get the out-edge associated with vertex and out_edge_index</span>
<span class="name">Traits</span>::<span class="type">edge_descriptor</span>
out_edge_at(<span class="name">Traits</span>::<span class="type">vertex_descriptor</span> vertex,
            <span class="name">Traits</span>::<span class="type">degree_size_type</span> out_edge_index,
            <span class="keyword">const</span> <span class="name">Graph&amp;</span> graph);

<span class="comment">// Get the out-edge associated with vertex and in_edge_index</span>
<span class="name">Traits</span>::<span class="type">edge_descriptor</span>
in_edge_at(<span class="name">Traits</span>::<span class="type">vertex_descriptor</span> vertex,
           <span class="name">Traits</span>::<span class="type">degree_size_type</span> in_edge_index,
           <span class="keyword">const</span> <span class="name">Graph&amp;</span> graph);
    </pre>

    <h4>Example</h4>
    <pre class="code">
<span class="keyword">typedef</span> <span class="type">grid_graph</span>&lt;2&gt; <span class="name">Graph</span>;
<span class="keyword">typedef</span> <span class="type">graph_traits</span>&lt;<span class="name">Graph</span>&gt; <span class="name">Traits</span>;

<span class="comment">// Create a 3x3, unwrapped grid_graph (Figure 3)</span>
<span class="name">boost</span>::<span class="type">array</span>&lt;<span class="name">std</span>::<span class="type">size_t</span>, <span class="literal">2</span>&gt; lengths = { { <span class="literal">3</span>, <span class="literal">3</span> } };
<span class="name">Graph</span> graph(lengths);

<span class="comment">// Do a round-trip test of the vertex index functions</span>
<span class="keyword">for</span> (<span class="name">Traits</span>::<span class="type">vertices_size_type</span> v_index = <span class="literal">0</span>;
     v_index &lt; num_vertices(graph); ++v_index) {

  <span class="comment">// The two indices should always be equal</span>
  <span class="name">std</span>::cout &lt;&lt; <span class="literal">&quot;Index of vertex &quot;</span> &lt;&lt; v_index &lt;&lt; <span class="literal">&quot; is &quot;</span> &lt;&lt;
    get(<span class="name">boost</span>::vertex_index, graph, vertex(v_index, graph)) &lt;&lt; <span class="name">std</span>::endl;

}

<span class="comment">// Do a round-trip test of the edge index functions</span>
<span class="keyword">for</span> (<span class="name">Traits</span>::<span class="type">edges_size_type</span> e_index = <span class="literal">0</span>;
     e_index &lt; num_edges(graph); ++e_index) {

  <span class="comment">// The two indices should always be equal</span>
  <span class="name">std</span>::cout &lt;&lt; <span class="literal">&quot;Index of edge &quot;</span> &lt;&lt; e_index &lt;&lt; <span class="literal">&quot; is &quot;</span> &lt;&lt;
    get(<span class="name">boost</span>::edge_index, graph, edge_at(e_index, graph)) &lt;&lt; <span class="name">std</span>::endl;

}
    </pre>

    <p style="margin-left: 10px;">
      <img src="figs/grid_graph_indexed.png" />
      <br />
      <em style="font-size: 0.8em"><b>Figure 3:</b> 3x3 unwrapped grid_graph with vertex and edge indices shown.</em>
    </p>
    <br />

    <h3 id="member">Member Functions</h3>
    <p>
      There are several <tt>grid_graph</tt> specific member functions available:
    </p>
    <pre class="code">
<span class="keyword">typedef</span> <span class="type">grid_graph</span>&lt;...&gt; <span class="name">Graph</span>;
<span class="keyword">typedef</span> <span class="type">graph_traits</span>&lt;<span class="name">Graph</span>&gt; <span class="name">Traits</span>;

<span class="comment">// Returns the number of dimensions</span>
<span class="name">std</span>::<span class="type">size_t</span> dimensions();

<span class="comment">// Returns the length of a dimension</span>
<span class="name">Traits</span>::<span class="type">vertices_size_type</span> length(<span class="name">std</span>::<span class="type">size_t</span> dimension);

<span class="comment">// Returns true if the dimension wraps, false if not</span>
<span class="keyword">bool</span> wrapped(<span class="name">std</span>::<span class="type">size_t</span> dimension);

<span class="comment">// Returns the &quot;next&quot; vertex in a dimension at a given distance. If the dimension
// is unwrapped, next will stop at the last vertex in the dimension.
</span><span class="name">Traits</span>::<span class="type">vertex_descriptor</span> next(<span class="name">Traits</span>::<span class="type">vertex_descriptor</span> vertex,
                               <span class="name">std</span>::<span class="type">size_t</span> dimension,
                               <span class="name">Traits</span>::<span class="type">vertices_size_type</span> distance = <span class="literal">1</span>);

<span class="comment">// Returns the &quot;previous&quot; vertex in a dimension at a given distance. If the
// dimension is unwrapped, previous will stop at the beginning vertex in the dimension.
</span><span class="name">Traits</span>::<span class="type">vertex_descriptor</span> previous(<span class="name">Traits</span>::<span class="type">vertex_descriptor</span> vertex,
                                   <span class="name">std</span>::<span class="type">size_t</span> dimension,
                                   <span class="name">Traits</span>::<span class="type">vertices_size_type</span> distance = <span class="literal">1</span>); 
    </pre>

    <h4>Example</h4>
    <pre class="code">
<span class="keyword">typedef</span> <span class="type">grid_graph</span>&lt;<span class="literal">3</span>&gt; <span class="name">Graph</span>;
<span class="keyword">typedef</span> <span class="type">graph_traits</span>&lt;<span class="name">Graph</span>&gt; <span class="name">Traits</span>;

<span class="comment">// Define a 3x5x7 grid_graph where the second dimension doesn&apos;t wrap</span>
<span class="name">boost</span>::<span class="type">array</span>&lt;<span class="name">std</span>::<span class="type">size_t</span>, <span class="literal">3</span>&gt; lengths = { { <span class="literal">3</span>, <span class="literal">5</span>, <span class="literal">7</span> } };
<span class="name">boost</span>::<span class="type">array</span>&lt;<span class="keyword">bool</span>, <span class="literal">3</span>&gt; wrapped = { { <span class="keyword">true</span>, <span class="keyword">false</span>, <span class="keyword">true</span> } };
<span class="name">Graph</span> graph(lengths, wrapped);

<span class="comment">// Print number of dimensions</span>
<span class="name">std</span>::cout &lt;&lt; graph.dimensions() &lt;&lt; <span class="name">std</span>::endl; <span class="comment">// prints &quot;3&quot;</span>

<span class="comment">// Print dimension lengths (same order as in the lengths array)</span>
<span class="name">std</span>::cout &lt;&lt; graph.length(<span class="literal">0</span>) &lt;&lt; <span class="literal">&quot;x&quot;</span> &lt;&lt; graph.length(<span class="literal">1</span>) <<
  <span class="literal">&quot;x&quot;</span> &lt;&lt; graph.length(<span class="literal">2</span>) &lt;&lt; <span class="name">std</span>::endl; <span class="comment">// prints &quot;3x5x7&quot;</span>

<span class="comment">// Print dimension wrapping (W = wrapped, U = unwrapped)</span>
<span class="name">std</span>::cout &lt;&lt; graph.wrapped(<span class="literal">0</span>) ? <span class="literal">&quot;W&quot;</span> : <span class="literal">&quot;U&quot;</span> &lt;&lt; <span class="literal">&quot;, &quot;</span> <<
  graph.wrapped(<span class="literal">1</span>) ? <span class="literal">&quot;W&quot;</span> : <span class="literal">&quot;U&quot;</span> &lt;&lt; <span class="literal">&quot;, &quot;</span> <<
  graph.wrapped(<span class="literal">2</span>) ? <span class="literal">&quot;W&quot;</span> : <span class="literal">&quot;U&quot;</span> &lt;&lt; <span class="name">std</span>::endl; <span class="comment">// prints &quot;W, U, W&quot;</span>

<span class="comment">// Define a simple function to print vertices</span>
<span class="keyword">void</span> print_vertex(<span class="name">Traits</span>::<span class="type">vertex_descriptor</span> vertex_to_print) {
  <span class="name">std</span>::cout &lt;&lt; <span class="literal">&quot;(&quot;</span> &lt;&lt; vertex_to_print[<span class="literal">0</span>] &lt;&lt; <span class="literal">&quot;, &quot;</span> &lt;&lt; vertex_to_print[<span class="literal">1</span>] <<
    <span class="literal">&quot;, &quot;</span> &lt;&lt; vertex_to_print[<span class="literal">2</span>] &lt;&lt; <span class="literal">&quot;)&quot;</span> &lt;&lt; <span class="name">std</span>::endl;
}

<span class="comment">// Start with the first vertex in the graph</span>
<span class="name">Traits</span>::<span class="type">vertex_descriptor</span> first_vertex = vertex(<span class="literal">0</span>, graph);
print_vertex(first_vertex); <span class="comment">// prints &quot;(0, 0, 0)&quot;</span>

<span class="comment">// Print the next vertex in dimension 0</span>
print_vertex(graph.next(first_vertex, <span class="literal">0</span>)); <span class="comment">// prints &quot;(1, 0, 0)&quot;</span>

<span class="comment">// Print the next vertex in dimension 1</span>
print_vertex(graph.next(first_vertex, <span class="literal">1</span>)); <span class="comment">// prints &quot;(0, 1, 0)&quot;</span>

<span class="comment">// Print the 5th next vertex in dimension 2</span>
print_vertex(graph.next(first_vertex, <span class="literal">2</span>, <span class="literal">5</span>)); <span class="comment">// prints &quot;(0, 0, 5)&quot;</span>

<span class="comment">// Print the previous vertex in dimension 0 (wraps)</span>
print_vertex(graph.previous(first_vertex, <span class="literal">0</span>)); <span class="comment">// prints &quot;(2, 0, 0)&quot;</span>

<span class="comment">// Print the previous vertex in dimension 1 (doesn&apos;t wrap, so it&apos;s the same)</span>
print_vertex(graph.previous(first_vertex, <span class="literal">1</span>)); <span class="comment">// prints &quot;(0, 0, 0)&quot;</span>

<span class="comment">// Print the 20th previous vertex in dimension 2 (wraps around twice)</span>
print_vertex(graph.previous(first_vertex, <span class="literal">2</span>, <span class="literal">20</span>)); <span class="comment">// prints &quot;(0, 0, 1)&quot;</span>
    </pre>

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