ceph/src/boost/libs/graph/example/weighted_matching_example.cpp

   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
  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
 111
 112