通过与输入相同的boost图创建无向图

Create undirected graph by boost graph same as the input

本文关键字：boost 创建 输入      更新时间：2023-10-16

我想创建如下图，第一列是顶点，其他是邻接顶点

  • 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 7

我像这样把边添加到图中

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;
        }
    }
}

打印图形

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;
    }
}

我期望输出应该与输入相同，但事实并非如此结果为

  • 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 7连接

my expected results

  • 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连接4 6 7 8
  • 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

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

boost::adjacency_list的第一个模板参数是OutEdgeList，它控制某些图形行为，例如允许或不允许平行边。在无向MinCutG图的情况下，vecS被用作OutEdgeList，这将启用并行边。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1的adjacent_vertices()将包含顶点2两次，每条边(A和B)一次。

如文档中所述，可以通过对OutEdgeList使用setS或hash_setS选择器来禁用平行边。例如，修改:

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

: 

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

下面是一个使用原始代码的示例，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);
}

生成以下输出:

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

正如Tanner所解释的那样，你实际上是将每条边添加两次，首先作为(a,b)，然后作为(b,a)。避免这种情况的一种相当昂贵的方法是使用setS作为控制边缘容器的模板参数。这就是坦纳在他的回答中所暗示的。

另一种选择是在添加边之前检查边是否存在。它表示

这行
boost::add_edge(Vertex, *begin, graph);

应替换为

if (! edge(Vertex, *begin, graph).second ) //edge does not exist yet
    boost::add_edge(Vertex, *begin, graph);

在大多数情况下，这段代码可能更快，占用更少的内存。

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