113 lines
4.6 KiB
C++
113 lines
4.6 KiB
C++
//=======================================================================
|
|
// Copyright (c) 2018 Yi Ji
|
|
//
|
|
// Distributed under the Boost Software License, Version 1.0.
|
|
// (See accompanying file LICENSE_1_0.txt or copy at
|
|
// http://www.boost.org/LICENSE_1_0.txt)
|
|
//
|
|
//=======================================================================
|
|
|
|
#include <iostream>
|
|
#include <vector>
|
|
#include <string>
|
|
#include <boost/graph/adjacency_list.hpp>
|
|
#include <boost/graph/maximum_weighted_matching.hpp>
|
|
|
|
using namespace boost;
|
|
|
|
typedef property<edge_weight_t, float, property<edge_index_t, int> > EdgeProperty;
|
|
typedef adjacency_list<vecS, vecS, undirectedS, no_property, EdgeProperty> my_graph;
|
|
|
|
int main(int argc, const char * argv[])
|
|
{
|
|
graph_traits<my_graph>::vertex_iterator vi, vi_end;
|
|
const int n_vertices = 18;
|
|
my_graph g(n_vertices);
|
|
|
|
// vertices can be refered by integers because my_graph use vector to store them
|
|
|
|
add_edge(1, 2, EdgeProperty(5), g);
|
|
add_edge(0, 4, EdgeProperty(1), g);
|
|
add_edge(1, 5, EdgeProperty(4), g);
|
|
add_edge(2, 6, EdgeProperty(1), g);
|
|
add_edge(3, 7, EdgeProperty(4), g);
|
|
add_edge(4, 5, EdgeProperty(7), g);
|
|
add_edge(6, 7, EdgeProperty(5), g);
|
|
add_edge(4, 8, EdgeProperty(2), g);
|
|
add_edge(5, 9, EdgeProperty(5), g);
|
|
add_edge(6, 10, EdgeProperty(6), g);
|
|
add_edge(7, 11, EdgeProperty(5), g);
|
|
add_edge(10, 11, EdgeProperty(4), g);
|
|
add_edge(8, 13, EdgeProperty(4), g);
|
|
add_edge(9, 14, EdgeProperty(4), g);
|
|
add_edge(10, 15, EdgeProperty(7), g);
|
|
add_edge(11, 16, EdgeProperty(6), g);
|
|
add_edge(14, 15, EdgeProperty(6), g);
|
|
add_edge(12, 13, EdgeProperty(2), g);
|
|
add_edge(16, 17, EdgeProperty(5), g);
|
|
|
|
|
|
// print the ascii graph into terminal (better to use fixed-width font)
|
|
// this graph has a maximum cardinality matching of size 8
|
|
// but maximum weighted matching is of size 7
|
|
|
|
std::vector<std::string> ascii_graph_weighted;
|
|
|
|
ascii_graph_weighted.push_back(" 5 ");
|
|
ascii_graph_weighted.push_back(" A B---C D ");
|
|
ascii_graph_weighted.push_back(" 1\\ 7 /4 1\\ 5 /4 ");
|
|
ascii_graph_weighted.push_back(" E---F G---H ");
|
|
ascii_graph_weighted.push_back(" 2| |5 6| |5 ");
|
|
ascii_graph_weighted.push_back(" I J K---L ");
|
|
ascii_graph_weighted.push_back(" 4/ 3\\ 7/ 4 \\6 ");
|
|
ascii_graph_weighted.push_back(" M---N O---P Q---R ");
|
|
ascii_graph_weighted.push_back(" 2 6 5 ");
|
|
|
|
|
|
// our maximum weighted matching and result
|
|
|
|
std::cout << "In the following graph:" << std::endl << std::endl;
|
|
|
|
for(std::vector<std::string>::iterator itr = ascii_graph_weighted.begin(); itr != ascii_graph_weighted.end(); ++itr)
|
|
std::cout << *itr << std::endl;
|
|
|
|
std::cout << std::endl;
|
|
|
|
std::vector<graph_traits<my_graph>::vertex_descriptor> mate1(n_vertices), mate2(n_vertices);
|
|
maximum_weighted_matching(g, &mate1[0]);
|
|
|
|
std::cout << "Found a weighted matching:" << std::endl;
|
|
std::cout << "Matching size is " << matching_size(g, &mate1[0]) << ", total weight is " << matching_weight_sum(g, &mate1[0]) << std::endl;
|
|
std::cout << std::endl;
|
|
|
|
std::cout << "The matching is:" << std::endl;
|
|
for (boost::tie(vi,vi_end) = vertices(g); vi != vi_end; ++vi)
|
|
if (mate1[*vi] != graph_traits<my_graph>::null_vertex() && *vi < mate1[*vi])
|
|
std::cout << "{" << *vi << ", " << mate1[*vi] << "}" << std::endl;
|
|
std::cout << std::endl;
|
|
|
|
|
|
// now we check the correctness by compare the weight sum to a brute-force matching result
|
|
// note that two matchings may be different because of multiple optimal solutions
|
|
|
|
brute_force_maximum_weighted_matching(g, &mate2[0]);
|
|
|
|
std::cout << "Found a weighted matching by brute-force searching:" << std::endl;
|
|
std::cout << "Matching size is " << matching_size(g, &mate2[0]) << ", total weight is " << matching_weight_sum(g, &mate2[0]) << std::endl;
|
|
std::cout << std::endl;
|
|
|
|
std::cout << "The brute-force matching is:" << std::endl;
|
|
for (boost::tie(vi,vi_end) = vertices(g); vi != vi_end; ++vi)
|
|
if (mate2[*vi] != graph_traits<my_graph>::null_vertex() && *vi < mate2[*vi])
|
|
std::cout << "{" << *vi << ", " << mate2[*vi] << "}" << std::endl;
|
|
std::cout << std::endl;
|
|
|
|
assert(matching_weight_sum(g, &mate1[0]) == matching_weight_sum(g, &mate2[0]));
|
|
|
|
|
|
return 0;
|
|
}
|
|
|
|
|
|
|