c++ - 通过与输入相同的boost图创建无向图

Question

我想创建如下图，第一列是顶点，其他的是邻接顶点

• 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

我像这样将边添加到图中

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;
        }
    }
}

打印图表

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;
    }
}

我希望输出与输入相同，但事实并非如此 结果是

• 1 与 2 3 4 7 2 3 4 7 相连
• 2 与 1 1 3 4 3 4 相连
• 3 与 1 2 1 2 4 4 相连
• 4 与 1 2 3 1 2 3 5 5 相连
• 5 与 4 4 6 7 8 6 7 8 相连
• 6 与 5 5 7 8 7 8 相连
• 7 与 1 5 6 1 5 6 8 8 相连
• 8 与 5 6 7 5 6 7 相连

我的预期结果

• 1 与 2 3 4 7 相连
• 2 与 1 3 4 相连
• 3 与 1 2 4 相连
• 4 与 1 2 3 5 相连
• 5 与 4 6 7 8 相连
• 6 与 6 5 7 8 相连
• 7 与 7 1 5 6 8 相连
• 8 与 8 5 6 7 相连

Answer 1

简而言之，对 OutEdgeList 模板参数使用 setS 将禁用平行边，从而产生所需的输出。

第一个模板参数为boost::adjacency_list是 OutEdgeList 并且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，vecS 用作将启用平行边的 OutEdgeList。例如，如果无向图支持平行边，则:

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.

adjacent_vertices()对于顶点 1 将包含顶点 2 两次，每条边一次(A 和 B)。

如 documentation 中所述，可以通过为 OutEdgeList 使用 setS 或 hash_setS 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>;

到:

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

---

这是一个 example使用原始代码，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