1 //=======================================================================
2 // Copyright (c) 2018 Yi Ji
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
10 #include <iostream>
11 #include <vector>
12 #include <string>
13 #include <boost/graph/adjacency_list.hpp>
14 #include <boost/graph/maximum_weighted_matching.hpp>
15
16 using namespace boost;
17
18 typedef property< edge_weight_t, float, property< edge_index_t, int > >
19 EdgeProperty;
20 typedef adjacency_list< vecS, vecS, undirectedS, no_property, EdgeProperty >
21 my_graph;
22
main(int argc,const char * argv[])23 int main(int argc, const char* argv[])
24 {
25 graph_traits< my_graph >::vertex_iterator vi, vi_end;
26 const int n_vertices = 18;
27 my_graph g(n_vertices);
28
29 // vertices can be refered by integers because my_graph use vector to store
30 // them
31
32 add_edge(1, 2, EdgeProperty(5), g);
33 add_edge(0, 4, EdgeProperty(1), g);
34 add_edge(1, 5, EdgeProperty(4), g);
35 add_edge(2, 6, EdgeProperty(1), g);
36 add_edge(3, 7, EdgeProperty(4), g);
37 add_edge(4, 5, EdgeProperty(7), g);
38 add_edge(6, 7, EdgeProperty(5), g);
39 add_edge(4, 8, EdgeProperty(2), g);
40 add_edge(5, 9, EdgeProperty(5), g);
41 add_edge(6, 10, EdgeProperty(6), g);
42 add_edge(7, 11, EdgeProperty(5), g);
43 add_edge(10, 11, EdgeProperty(4), g);
44 add_edge(8, 13, EdgeProperty(4), g);
45 add_edge(9, 14, EdgeProperty(4), g);
46 add_edge(10, 15, EdgeProperty(7), g);
47 add_edge(11, 16, EdgeProperty(6), g);
48 add_edge(14, 15, EdgeProperty(6), g);
49 add_edge(12, 13, EdgeProperty(2), g);
50 add_edge(16, 17, EdgeProperty(5), g);
51
52 // print the ascii graph into terminal (better to use fixed-width font)
53 // this graph has a maximum cardinality matching of size 8
54 // but maximum weighted matching is of size 7
55
56 std::vector< std::string > ascii_graph_weighted;
57
58 ascii_graph_weighted.push_back(" 5 ");
59 ascii_graph_weighted.push_back(" A B---C D ");
60 ascii_graph_weighted.push_back(" 1\\ 7 /4 1\\ 5 /4 ");
61 ascii_graph_weighted.push_back(" E---F G---H ");
62 ascii_graph_weighted.push_back(" 2| |5 6| |5 ");
63 ascii_graph_weighted.push_back(" I J K---L ");
64 ascii_graph_weighted.push_back(" 4/ 3\\ 7/ 4 \\6 ");
65 ascii_graph_weighted.push_back(" M---N O---P Q---R ");
66 ascii_graph_weighted.push_back(" 2 6 5 ");
67
68 // our maximum weighted matching and result
69
70 std::cout << "In the following graph:" << std::endl << std::endl;
71
72 for (std::vector< std::string >::iterator itr
73 = ascii_graph_weighted.begin();
74 itr != ascii_graph_weighted.end(); ++itr)
75 std::cout << *itr << std::endl;
76
77 std::cout << std::endl;
78
79 std::vector< graph_traits< my_graph >::vertex_descriptor > mate1(
80 n_vertices),
81 mate2(n_vertices);
82 maximum_weighted_matching(g, &mate1[0]);
83
84 std::cout << "Found a weighted matching:" << std::endl;
85 std::cout << "Matching size is " << matching_size(g, &mate1[0])
86 << ", total weight is " << matching_weight_sum(g, &mate1[0])
87 << std::endl;
88 std::cout << std::endl;
89
90 std::cout << "The matching is:" << std::endl;
91 for (boost::tie(vi, vi_end) = vertices(g); vi != vi_end; ++vi)
92 if (mate1[*vi] != graph_traits< my_graph >::null_vertex()
93 && *vi < mate1[*vi])
94 std::cout << "{" << *vi << ", " << mate1[*vi] << "}" << std::endl;
95 std::cout << std::endl;
96
97 // now we check the correctness by compare the weight sum to a brute-force
98 // matching result note that two matchings may be different because of
99 // multiple optimal solutions
100
101 brute_force_maximum_weighted_matching(g, &mate2[0]);
102
103 std::cout << "Found a weighted matching by brute-force searching:"
104 << std::endl;
105 std::cout << "Matching size is " << matching_size(g, &mate2[0])
106 << ", total weight is " << matching_weight_sum(g, &mate2[0])
107 << std::endl;
108 std::cout << std::endl;
109
110 std::cout << "The brute-force matching is:" << std::endl;
111 for (boost::tie(vi, vi_end) = vertices(g); vi != vi_end; ++vi)
112 if (mate2[*vi] != graph_traits< my_graph >::null_vertex()
113 && *vi < mate2[*vi])
114 std::cout << "{" << *vi << ", " << mate2[*vi] << "}" << std::endl;
115 std::cout << std::endl;
116
117 assert(
118 matching_weight_sum(g, &mate1[0]) == matching_weight_sum(g, &mate2[0]));
119
120 return 0;
121 }
122