[666] | 1 | /*! |
---|
| 2 | |
---|
| 3 | \page graphs How to use graphs |
---|
| 4 | |
---|
[756] | 5 | The primary data structures of HugoLib are the graph classes. They all |
---|
| 6 | provide a node list - edge list interface, i.e. they have |
---|
| 7 | functionalities to list the nodes and the edges of the graph as well |
---|
| 8 | as in incoming and outgoing edges of a given node. |
---|
| 9 | |
---|
| 10 | |
---|
[873] | 11 | Each graph should meet the |
---|
| 12 | \ref hugo::skeleton::StaticGraphSkeleton "StaticGraph" concept. |
---|
| 13 | This concept does not |
---|
[756] | 14 | makes it possible to change the graph (i.e. it is not possible to add |
---|
| 15 | or delete edges or nodes). Most of the graph algorithms will run on |
---|
| 16 | these graphs. |
---|
| 17 | |
---|
[873] | 18 | The graphs meeting the |
---|
| 19 | \ref hugo::skeleton::ExtendableGraphSkeleton "ExtendableGraph" |
---|
| 20 | concept allow node and |
---|
[756] | 21 | edge addition. You can also "clear" (i.e. erase all edges and nodes) |
---|
| 22 | such a graph. |
---|
| 23 | |
---|
[873] | 24 | In case of graphs meeting the full feature |
---|
| 25 | \ref hugo::skeleton::ErasableGraphSkeleton "ErasableGraph" |
---|
| 26 | concept |
---|
[756] | 27 | you can also erase individual edges and node in arbitrary order. |
---|
| 28 | |
---|
| 29 | The implemented graph structures are the following. |
---|
| 30 | \li \ref hugo::ListGraph "ListGraph" is the most versatile graph class. It meets |
---|
[873] | 31 | the hugo::skeleton::ErasableGraphSkeleton "ErasableGraph" concept |
---|
| 32 | and it also have some convenience features. |
---|
[756] | 33 | \li \ref hugo::SmartGraph "SmartGraph" is a more memory |
---|
| 34 | efficient version of \ref hugo::ListGraph "ListGraph". The |
---|
[873] | 35 | price of it is that it only meets the |
---|
| 36 | \ref hugo::skeleton::ExtendableGraphSkeleton "ExtendableGraph" concept, |
---|
[756] | 37 | so you cannot delete individual edges or nodes. |
---|
| 38 | \li \ref hugo::SymListGraph "SymListGraph" and |
---|
| 39 | \ref hugo::SymSmartGraph "SymSmartGraph" classes are very similar to |
---|
| 40 | \ref hugo::ListGraph "ListGraph" and \ref hugo::SmartGraph "SmartGraph". |
---|
| 41 | The difference is that whenever you add a |
---|
| 42 | new edge to the graph, it actually adds a pair of oppositely directed edges. |
---|
| 43 | They are linked together so it is possible to access the counterpart of an |
---|
| 44 | edge. An even more important feature is that using these classes you can also |
---|
| 45 | attach data to the edges in such a way that the stored data |
---|
| 46 | are shared by the edge pairs. |
---|
| 47 | \li \ref hugo::FullGraph "FullGraph" |
---|
| 48 | implements a full graph. It is a \ref ConstGraph, so you cannot |
---|
| 49 | change the number of nodes once it is constructed. It is extremely memory |
---|
| 50 | efficient: it uses constant amount of memory independently from the number of |
---|
| 51 | the nodes of the graph. Of course, the size of the \ref maps "NodeMap"'s and |
---|
| 52 | \ref maps "EdgeMap"'s will depend on the number of nodes. |
---|
| 53 | |
---|
| 54 | \li \ref hugo::NodeSet "NodeSet" implements a graph with no edges. This class |
---|
| 55 | can be used as a base class of \ref hugo::EdgeSet "EdgeSet". |
---|
| 56 | \li \ref hugo::EdgeSet "EdgeSet" can be used to create a new graph on |
---|
[873] | 57 | the node set of another graph. The base graph can be an arbitrary graph and it |
---|
[756] | 58 | is possible to attach several \ref hugo::EdgeSet "EdgeSet"'s to a base graph. |
---|
| 59 | |
---|
| 60 | \todo Don't we need SmartNodeSet and SmartEdgeSet? |
---|
| 61 | \todo Some cross-refs are wrong. |
---|
| 62 | |
---|
[873] | 63 | \bug This file must be updated accordig to the new style iterators. |
---|
[756] | 64 | |
---|
| 65 | The graph structures itself can not store data attached |
---|
| 66 | to the edges and nodes. However they all provide |
---|
| 67 | \ref maps "map classes" |
---|
| 68 | to dynamically attach data the to graph components. |
---|
| 69 | |
---|
[666] | 70 | The following program demonstrates the basic features of HugoLib's graph |
---|
| 71 | structures. |
---|
| 72 | |
---|
| 73 | \code |
---|
| 74 | #include <iostream> |
---|
| 75 | #include <hugo/list_graph.h> |
---|
| 76 | |
---|
| 77 | using namespace hugo; |
---|
| 78 | |
---|
| 79 | int main() |
---|
| 80 | { |
---|
| 81 | typedef ListGraph Graph; |
---|
| 82 | \endcode |
---|
| 83 | |
---|
| 84 | ListGraph is one of HugoLib's graph classes. It is based on linked lists, |
---|
| 85 | therefore iterating throuh its edges and nodes is fast. |
---|
| 86 | |
---|
| 87 | \code |
---|
| 88 | typedef Graph::Edge Edge; |
---|
| 89 | typedef Graph::InEdgeIt InEdgeIt; |
---|
| 90 | typedef Graph::OutEdgeIt OutEdgeIt; |
---|
| 91 | typedef Graph::EdgeIt EdgeIt; |
---|
| 92 | typedef Graph::Node Node; |
---|
| 93 | typedef Graph::NodeIt NodeIt; |
---|
| 94 | |
---|
| 95 | Graph g; |
---|
| 96 | |
---|
| 97 | for (int i = 0; i < 3; i++) |
---|
| 98 | g.addNode(); |
---|
| 99 | |
---|
| 100 | for (NodeIt i(g); g.valid(i); g.next(i)) |
---|
| 101 | for (NodeIt j(g); g.valid(j); g.next(j)) |
---|
| 102 | if (i != j) g.addEdge(i, j); |
---|
| 103 | \endcode |
---|
| 104 | |
---|
| 105 | After some convenience typedefs we create a graph and add three nodes to it. |
---|
| 106 | Then we add edges to it to form a full graph. |
---|
| 107 | |
---|
| 108 | \code |
---|
| 109 | std::cout << "Nodes:"; |
---|
| 110 | for (NodeIt i(g); g.valid(i); g.next(i)) |
---|
| 111 | std::cout << " " << g.id(i); |
---|
| 112 | std::cout << std::endl; |
---|
| 113 | \endcode |
---|
| 114 | |
---|
| 115 | Here we iterate through all nodes of the graph. We use a constructor of the |
---|
| 116 | node iterator to initialize it to the first node. The next member function is |
---|
| 117 | used to step to the next node, and valid is used to check if we have passed the |
---|
| 118 | last one. |
---|
| 119 | |
---|
| 120 | \code |
---|
| 121 | std::cout << "Nodes:"; |
---|
| 122 | NodeIt n; |
---|
| 123 | for (g.first(n); n != INVALID; g.next(n)) |
---|
| 124 | std::cout << " " << g.id(n); |
---|
| 125 | std::cout << std::endl; |
---|
| 126 | \endcode |
---|
| 127 | |
---|
| 128 | Here you can see an alternative way to iterate through all nodes. Here we use a |
---|
| 129 | member function of the graph to initialize the node iterator to the first node |
---|
| 130 | of the graph. Using next on the iterator pointing to the last node invalidates |
---|
| 131 | the iterator i.e. sets its value to INVALID. Checking for this value is |
---|
| 132 | equivalent to using the valid member function. |
---|
| 133 | |
---|
| 134 | Both of the previous code fragments print out the same: |
---|
| 135 | |
---|
| 136 | \code |
---|
| 137 | Nodes: 2 1 0 |
---|
| 138 | \endcode |
---|
| 139 | |
---|
| 140 | \code |
---|
| 141 | std::cout << "Edges:"; |
---|
| 142 | for (EdgeIt i(g); g.valid(i); g.next(i)) |
---|
| 143 | std::cout << " (" << g.id(g.tail(i)) << "," << g.id(g.head(i)) << ")"; |
---|
| 144 | std::cout << std::endl; |
---|
| 145 | \endcode |
---|
| 146 | |
---|
| 147 | \code |
---|
| 148 | Edges: (0,2) (1,2) (0,1) (2,1) (1,0) (2,0) |
---|
| 149 | \endcode |
---|
| 150 | |
---|
| 151 | We can also iterate through all edges of the graph very similarly. The head and |
---|
| 152 | tail member functions can be used to access the endpoints of an edge. |
---|
| 153 | |
---|
| 154 | \code |
---|
| 155 | NodeIt first_node(g); |
---|
| 156 | |
---|
| 157 | std::cout << "Out-edges of node " << g.id(first_node) << ":"; |
---|
| 158 | for (OutEdgeIt i(g, first_node); g.valid(i); g.next(i)) |
---|
| 159 | std::cout << " (" << g.id(g.tail(i)) << "," << g.id(g.head(i)) << ")"; |
---|
| 160 | std::cout << std::endl; |
---|
| 161 | |
---|
| 162 | std::cout << "In-edges of node " << g.id(first_node) << ":"; |
---|
| 163 | for (InEdgeIt i(g, first_node); g.valid(i); g.next(i)) |
---|
| 164 | std::cout << " (" << g.id(g.tail(i)) << "," << g.id(g.head(i)) << ")"; |
---|
| 165 | std::cout << std::endl; |
---|
| 166 | \endcode |
---|
| 167 | |
---|
| 168 | \code |
---|
| 169 | Out-edges of node 2: (2,0) (2,1) |
---|
| 170 | In-edges of node 2: (0,2) (1,2) |
---|
| 171 | \endcode |
---|
| 172 | |
---|
| 173 | We can also iterate through the in and out-edges of a node. In the above |
---|
| 174 | example we print out the in and out-edges of the first node of the graph. |
---|
| 175 | |
---|
| 176 | \code |
---|
| 177 | Graph::EdgeMap<int> m(g); |
---|
| 178 | |
---|
| 179 | for (EdgeIt e(g); g.valid(e); g.next(e)) |
---|
| 180 | m.set(e, 10 - g.id(e)); |
---|
| 181 | |
---|
| 182 | std::cout << "Id Edge Value" << std::endl; |
---|
| 183 | for (EdgeIt e(g); g.valid(e); g.next(e)) |
---|
| 184 | std::cout << g.id(e) << " (" << g.id(g.tail(e)) << "," << g.id(g.head(e)) |
---|
| 185 | << ") " << m[e] << std::endl; |
---|
| 186 | \endcode |
---|
| 187 | |
---|
| 188 | \code |
---|
| 189 | Id Edge Value |
---|
| 190 | 4 (0,2) 6 |
---|
| 191 | 2 (1,2) 8 |
---|
| 192 | 5 (0,1) 5 |
---|
| 193 | 0 (2,1) 10 |
---|
| 194 | 3 (1,0) 7 |
---|
| 195 | 1 (2,0) 9 |
---|
| 196 | \endcode |
---|
| 197 | |
---|
[873] | 198 | As we mentioned above, graphs are not containers rather |
---|
[666] | 199 | incidence structures which are iterable in many ways. HugoLib introduces |
---|
| 200 | concepts that allow us to attach containers to graphs. These containers are |
---|
| 201 | called maps. |
---|
| 202 | |
---|
| 203 | In the example above we create an EdgeMap which assigns an int value to all |
---|
| 204 | edges of the graph. We use the set member function of the map to write values |
---|
| 205 | into the map and the operator[] to retrieve them. |
---|
| 206 | |
---|
| 207 | Here we used the maps provided by the ListGraph class, but you can also write |
---|
| 208 | your own maps. You can read more about using maps \ref maps "here". |
---|
| 209 | |
---|
| 210 | */ |
---|