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