# `grid_graph`

- Overview
- Creating a Grid Graph
- Indexing
- Grid Graph Member Functions

### Overview

A `grid_graph` represents a multi-dimensional, rectangular grid of vertices with user-defined dimension lengths and wrapping.

`grid_graph` models:

- Incidence Graph
- Adjacency Graph
- Vertex List Graph
- Edge List Graph
- Bidirectional Graph
- Adjacency Matrix

Defined in `boost/graph/grid_graph.hpp` with all functions in the `boost` namespace. All examples are available in a single program file in `libs/graph/example/grid_graph_example.cpp`

#### Template Parameters

    template <typename std::size_t Dimensions,
              typename VertexIndex = std::size_t,
              typename EdgeIndex = VertexIndex>
      class grid_graph;

- `Dimensions` - Number of dimensions in the graph, must be greater than 2
- `VertexIndex` - Type used for vertex indices, defaults to std::size_t
- `EdgeIndex` - Type used for edge indices, defaults to the same type as VertexIndex

### Creating a Grid Graph

The constructor to `grid_graph` has several overloads to aid in configuring each dimension:

    // Defines a grid_graph that does not wrap.
    grid_graph<...>(boost:array<VertexIndex, Dimensions> dimension_lengths);

    // Defines a grid_graph where all dimensions are either wrapped or unwrapped.
    grid_graph<...>(boost:array<VertexIndex, Dimensions> dimension_lengths,
                    bool wrap_all_dimensions);

    // Defines a grid_graph where the wrapping for each dimension is specified individually.
    grid_graph<...>(boost:array<VertexIndex, Dimensions> dimension_lengths,
                    boost:array<bool, Dimensions> wrap_dimension);

#### Example

    // Define dimension lengths, a 3x3 in this case
    boost::array<int, 2> lengths = { { 3, 3 } };

    // Create a 3x3 two-dimensional, unwrapped grid graph (Figure 1)
    grid_graph<2> graph(lengths);

    // Create a 3x3 two-dimensional, wrapped grid graph (Figure 2)
    grid_graph<2> graph(lengths, true);

Figure 1: A 3x3 two-dimensional, unwrapped grid graph

Figure 2: A 3x3 two-dimensional, wrapped grid graph

### Indexing

The `grid_graph` supports addressing vertices and edges by index. The following functions allow you to convert between vertices, edges, and their associated indices:

    typedef grid_graph<...> Graph;
    typedef graph_traits<Graph> Traits;

    // Get the vertex associated with vertex_index
    Traits::vertex_descriptor
    vertex(Traits::vertices_size_type vertex_index,
           const Graph& graph);

    // Get the index associated with vertex
    Traits::vertices_size_type
    get(boost::vertex_index_t,
        Traits::vertex_descriptor vertex,
        const Graph& graph);

    // Get the edge associated with edge_index
    Traits::edge_descriptor
    edge_at(Traits::edges_size_type edge_index,
            const Graph& graph);

    // Get the index associated with edge
    Traits::edges_size_type
    get(boost::edge_index_t,
        Traits::edge_descriptor edge,
        const Graph& graph);

    // Get the out-edge associated with vertex and out_edge_index
    Traits::edge_descriptor
    out_edge_at(Traits::vertex_descriptor vertex,
                Traits::degree_size_type out_edge_index,
                const Graph& graph);

    // Get the out-edge associated with vertex and in_edge_index
    Traits::edge_descriptor
    in_edge_at(Traits::vertex_descriptor vertex,
               Traits::degree_size_type in_edge_index,
               const Graph& graph);

#### Example

    typedef grid_graph<2> Graph;
    typedef graph_traits<Graph> Traits;

    // Create a 3x3, unwrapped grid_graph (Figure 3)
    boost::array<int, 2> lengths = { { 3, 3 } };
    Graph graph(lengths);

    // Do a round-trip test of the vertex index functions
    for (Traits::vertices_size_type v_index = 0;
         v_index < num_vertices(graph); ++v_index) {

      // The two indices should always be equal
      std::cout << "Index of vertex " << v_index << " is " <<
        get(boost::vertex_index, graph, vertex(v_index, graph)) << std::endl;

    }

    // Do a round-trip test of the edge index functions
    for (Traits::edges_size_type e_index = 0;
         e_index < num_edges(graph); ++e_index) {

      // The two indices should always be equal
      std::cout << "Index of edge " << e_index << " is " <<
        get(boost::edge_index, graph, edge_at(e_index, graph)) << std::endl;

    }

Figure 3: 3x3 unwrapped grid_graph with vertex and edge indices shown.

### Member Functions

There are several `grid_graph` specific member functions available:

    typedef grid_graph<...> Graph;
    typedef graph_traits<Graph> Traits;

    // Returns the number of dimensions
    std::size_t dimensions();

    // Returns the length of a dimension
    Traits::vertices_size_type length(std::size_t dimension);

    // Returns true if the dimension wraps, false if not
    bool wrapped(std::size_t dimension);

    // Returns the "next" vertex in a dimension at a given distance. If the dimension
    // is unwrapped, next will stop at the last vertex in the dimension.
    Traits::vertex_descriptor next(Traits::vertex_descriptor vertex,
                                   std::size_t dimension,
                                   Traits::vertices_size_type distance = 1);

    // Returns the "previous" vertex in a dimension at a given distance. If the
    // dimension is unwrapped, previous will stop at the beginning vertex in the dimension.
    Traits::vertex_descriptor previous(Traits::vertex_descriptor vertex,
                                       std::size_t dimension,
                                       Traits::vertices_size_type distance = 1);

#### Example

    typedef grid_graph<3> Graph;
    typedef graph_traits<Graph> Traits;

    // Define a 3x5x7 grid_graph where the second dimension doesn't wrap
    boost::array<std::size_t, 3> lengths = { { 3, 5, 7 } };
    boost::array<bool, 3> wrapped = { { true, false, true } };
    Graph graph(lengths, wrapped);

    // Print number of dimensions
    std::cout << graph.dimensions() << std::endl; // prints "3"

    // Print dimension lengths (same order as in the lengths array)
    std::cout << graph.length(0) << "x" << graph.length(1) <<
      "x" << graph.length(2) << std::endl; // prints "3x5x7"

    // Print dimension wrapping (W = wrapped, U = unwrapped)
    std::cout << graph.wrapped(0) ? "W" : "U" << ", " <<
      graph.wrapped(1) ? "W" : "U" << ", " <<
      graph.wrapped(2) ? "W" : "U" << std::endl; // prints "W, U, W"

    // Define a simple function to print vertices
    void print_vertex(Traits::vertex_descriptor vertex_to_print) {
      std::cout << "(" << vertex_to_print[0] << ", " << vertex_to_print[1] <<
        ", " << vertex_to_print[2] << ")" << std::endl;
    }

    // Start with the first vertex in the graph
    Traits::vertex_descriptor first_vertex = vertex(0, graph);
    print_vertex(first_vertex); // prints "(0, 0, 0)"

    // Print the next vertex in dimension 0
    print_vertex(graph.next(first_vertex, 0)); // prints "(1, 0, 0)"

    // Print the next vertex in dimension 1
    print_vertex(graph.next(first_vertex, 1)); // prints "(0, 1, 0)"

    // Print the 5th next vertex in dimension 2
    print_vertex(graph.next(first_vertex, 2, 5)); // prints "(0, 0, 5)"

    // Print the previous vertex in dimension 0 (wraps)
    print_vertex(graph.previous(first_vertex, 0)); // prints "(2, 0, 0)"

    // Print the previous vertex in dimension 1 (doesn't wrap, so it's the same)
    print_vertex(graph.previous(first_vertex, 1)); // prints "(0, 0, 0)"

    // Print the 20th previous vertex in dimension 2 (wraps around twice)
    print_vertex(graph.previous(first_vertex, 2, 20)); // prints "(0, 0, 1)"

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