1 //=======================================================================
2 // Copyright (c) 2005 Aaron Windsor
3 //
4 // Distributed under the Boost Software License, Version 1.0.
5 // (See accompanying file LICENSE_1_0.txt or copy at
6 // http://www.boost.org/LICENSE_1_0.txt)
7 //
8 //=======================================================================
9 #include <string>
10 #include <iostream>
11 #include <boost/graph/adjacency_list.hpp>
12 #include <cassert>
13
14 #include <boost/graph/max_cardinality_matching.hpp>
15
16
17 using namespace boost;
18
19 typedef adjacency_list<vecS, vecS, undirectedS> my_graph;
20
main()21 int main()
22 {
23
24 // Create the following graph: (it'll look better when output
25 // to the terminal in a fixed width font...)
26
27 const int n_vertices = 18;
28
29 std::vector<std::string> ascii_graph;
30
31 ascii_graph.push_back(" 0 1---2 3 ");
32 ascii_graph.push_back(" \\ / \\ / ");
33 ascii_graph.push_back(" 4---5 6---7 ");
34 ascii_graph.push_back(" | | | | ");
35 ascii_graph.push_back(" 8---9 10---11 ");
36 ascii_graph.push_back(" / \\ / \\ ");
37 ascii_graph.push_back(" 12 13 14---15 16 17 ");
38
39 // It has a perfect matching of size 8. There are two isolated
40 // vertices that we'll use later...
41
42 my_graph g(n_vertices);
43
44 // our vertices are stored in a vector, so we can refer to vertices
45 // by integers in the range 0..15
46
47 add_edge(1,2,g);
48 add_edge(0,4,g);
49 add_edge(1,5,g);
50 add_edge(2,6,g);
51 add_edge(3,7,g);
52 add_edge(4,5,g);
53 add_edge(6,7,g);
54 add_edge(4,8,g);
55 add_edge(5,9,g);
56 add_edge(6,10,g);
57 add_edge(7,11,g);
58 add_edge(8,9,g);
59 add_edge(10,11,g);
60 add_edge(8,13,g);
61 add_edge(9,14,g);
62 add_edge(10,15,g);
63 add_edge(11,16,g);
64 add_edge(14,15,g);
65
66 std::vector<graph_traits<my_graph>::vertex_descriptor> mate(n_vertices);
67
68 // find the maximum cardinality matching. we'll use a checked version
69 // of the algorithm, which takes a little longer than the unchecked
70 // version, but has the advantage that it will return "false" if the
71 // matching returned is not actually a maximum cardinality matching
72 // in the graph.
73
74 bool success = checked_edmonds_maximum_cardinality_matching(g, &mate[0]);
75 assert(success);
76
77 std::cout << "In the following graph:" << std::endl << std::endl;
78
79 for(std::vector<std::string>::iterator itr = ascii_graph.begin(); itr != ascii_graph.end(); ++itr)
80 std::cout << *itr << std::endl;
81
82 std::cout << std::endl << "Found a matching of size " << matching_size(g, &mate[0]) << std::endl;
83
84 std::cout << "The matching is:" << std::endl;
85
86 graph_traits<my_graph>::vertex_iterator vi, vi_end;
87 for(boost::tie(vi,vi_end) = vertices(g); vi != vi_end; ++vi)
88 if (mate[*vi] != graph_traits<my_graph>::null_vertex() && *vi < mate[*vi])
89 std::cout << "{" << *vi << ", " << mate[*vi] << "}" << std::endl;
90
91 std::cout << std::endl;
92
93 //now we'll add two edges, and the perfect matching has size 9
94
95 ascii_graph.pop_back();
96 ascii_graph.push_back(" 12---13 14---15 16---17 ");
97
98 add_edge(12,13,g);
99 add_edge(16,17,g);
100
101 success = checked_edmonds_maximum_cardinality_matching(g, &mate[0]);
102 assert(success);
103
104 std::cout << "In the following graph:" << std::endl << std::endl;
105
106 for(std::vector<std::string>::iterator itr = ascii_graph.begin(); itr != ascii_graph.end(); ++itr)
107 std::cout << *itr << std::endl;
108
109 std::cout << std::endl << "Found a matching of size " << matching_size(g, &mate[0]) << std::endl;
110
111 std::cout << "The matching is:" << std::endl;
112
113 for(boost::tie(vi,vi_end) = vertices(g); vi != vi_end; ++vi)
114 if (mate[*vi] != graph_traits<my_graph>::null_vertex() && *vi < mate[*vi])
115 std::cout << "{" << *vi << ", " << mate[*vi] << "}" << std::endl;
116
117 return 0;
118 }
119