c++ - 通过与输入相同的 boost 图创建无向图

我想按如下方式创建图形，第一列是顶点，其他是邻接顶点


1 2 3 4 7
2 1 3 4
3 1 2 4
4 1 2 3 5
5 4 6 7 8
6 5 7 8
7 1 5 6 8
8 5 6 7


我这样将边添加到图形中

using MinCutG = boost::adjacency_list<boost::vecS, boost::vecS, boost::undirectedS>;

MinCutG graph;
std::vector<std::vector<int> > input{ {1,2,3,4,7}, {2,1,3,4}, {3,1,2,4},
            {4,1,2,3,5}, {5,4,6,7,8}, {6,5,7,8}, {7,1,5,6,8}, {8,5,6,7}};
for(auto const &data : input){
    auto begin = std::begin(data);
    auto end = std::end(data);
    if(begin != end){
        auto const Vertex = *begin;
        ++begin;
        while(begin != end){
            boost::add_edge(Vertex, *begin, graph);
            ++begin;
        }
    }
}

打印图

template<typename Graph>
void print_adjacent_vertex(Graph const &g)
{
    for (auto vertex = vertices(g); vertex.first != vertex.second; ++vertex.first){
        std::cout << *vertex.first << " is connected with ";
        for (auto neighbour = adjacent_vertices(*vertex.first, g);
             neighbour.first != neighbour.second; ++neighbour.first){
            std::cout << *neighbour.first << " ";
        }
        std::cout<<std::endl;
    }
}

我期望输出应与输入相同，但事实并非如此
结果是


1与2 3 4 7 2 3 4 7连接
2与1 1 3 4 3 4连接
3与1 2 1 2 4 4连接
4与1 2 3 1 2 3 5 5连接
5与4 4 6 7 8 6 7 8连接
6与5 5 7 8 7 8连接
7与1 5 6 1 5 6 8 8连接
8与5 6 7 5 6 7连接


我的预期结果


1与2 3 4 7连接
2与1 3 4连接
3与1 2 4连接
4与1 2 3 5连接
5与4 6 7 8连接
6与6 5 7 8连接
7与7 1 5 6 8连接
8与8 5 6 7连接

最佳答案

简而言之，对setS模板参数使用OutEdgeList将禁用平行边，从而得到所需的输出。

boost::adjacency_list的第一个模板参数是OutEdgeList，它控制某些图形行为，例如允许或禁止平行边。在无向MinCutG图的情况下，将vecS用作OutEdgeList，它将启用平行边。例如，如果无向图支持平行边，则使用：

add_edge(1, 2, graph); // Vertex 1 and 2 are adjacent to one another via edge A.
add_edge(2, 1, graph); // Vertex 1 and 2 are adjacent to one another via edge B,
                       // which is parallel to edge A.

顶点adjacent_vertices()的1将包含两次顶点2，每个边（A和B）一次。

如documentation中所述，可以通过为setS使用hash_setS或OutEdgeList选择器来禁用平行边。例如，更改：

using MinCutG = boost::adjacency_list<
  boost::vecS, // OutEdgeList with parallel edges
  boost::vecS,
  boost::undirectedS>;

至：

using MinCutG = boost::adjacency_list<
  boost::setS, // OutEdgeList with no parallel edges
  boost::vecS,
  boost::undirectedS>;

这是使用原始代码的example，仅将OutEdgeList从vecS更改为setS：

#include <iostream>
#include <vector>
#include <boost/graph/adjacency_list.hpp>

template<typename Graph>
void print_adjacent_vertex(Graph const &g)
{
    for (auto vertex = vertices(g); vertex.first != vertex.second;
         ++vertex.first){
        std::cout << *vertex.first << " is connected with ";
        for (auto neighbour = adjacent_vertices(*vertex.first, g);
             neighbour.first != neighbour.second; ++neighbour.first){
            std::cout << *neighbour.first << " ";
        }
        std::cout<<std::endl;
    }
}

int main()
{
    using MinCutG = boost::adjacency_list<
        boost::setS, boost::vecS, boost::undirectedS>;

    MinCutG graph;
    std::vector<std::vector<int> > input
    {
        {1,2,3,4,7},
        {2,1,3,4},
        {3,1,2,4},
        {4,1,2,3,5},
        {5,4,6,7,8},
        {6,5,7,8},
        {7,1,5,6,8},
        {8,5,6,7}
    };

    for(auto const &data : input){
        auto begin = std::begin(data);
        auto end = std::end(data);
        if(begin != end){
            auto const Vertex = *begin;
            ++begin;
            while(begin != end){
                boost::add_edge(Vertex, *begin, graph);
                ++begin;
            }
        }
    }
    print_adjacent_vertex(graph);
}

产生以下输出：

0 is connected with
1 is connected with 2 3 4 7
2 is connected with 1 3 4
3 is connected with 1 2 4
4 is connected with 1 2 3 5
5 is connected with 4 6 7 8
6 is connected with 5 7 8
7 is connected with 1 5 6 8
8 is connected with 5 6 7