Boost BGL BFS 查找从源到目标的所有唯一路径

Question

我正在使用 Boost BGL C++，我需要 Graph 来执行从源顶点到目标顶点的 BFS 并返回所有唯一路径。

现在，我想到了一种使用过滤图来获取包含从源到目标的路径的图的子集的方法，但我意识到它基本上不是过滤，因为过滤后的图包含访问但不是部分的顶点从源到目标的路径。有什么方法可以获取这些信息或其他方法更好吗？

参考代码：

boost::filtered_graph<DirectedGraph, boost::keep_all, std::function<bool(VertexDescr)>> Graph::getUniquePathsFromSource(VertexDescr source, VertexDescr target, DirectedGraph const & g)
{
    std::vector<double> distances(num_vertices(g));
    std::vector<boost::default_color_type> colormap(num_vertices(g));

    // Run BFS and record all distances from the source node
    breadth_first_search(g, source,
        visitor(make_bfs_visitor(boost::record_distances(distances.data(), boost::on_tree_edge())))
        .color_map(colormap.data())
    );

    for (auto vd : boost::make_iterator_range(vertices(g)))
        if (colormap.at(vd) == boost::default_color_type{})
            distances.at(vd) = -1;

    distances[source] = -2;

    boost::filtered_graph<DirectedGraph, boost::keep_all, std::function<bool(VertexDescr)>>
        fg(g, {}, [&](VertexDescr vd) { return distances[vd] != -1; });

    // Print edge list
    std::cout << "filtered out-edges:" << std::endl;
    std::cout << "Source Vertex: " << source << std::endl;

    auto ei = boost::edges(fg);

    typedef boost::property_map<DirectedGraph, boost::edge_weight_t>::type WeightMap;
    WeightMap weights = get(boost::edge_weight, fg);

    for (auto it = ei.first; it != ei.second; ++it)
    {
        if (source != boost::target(*it, g)) {
            std::cout << "Edge Probability " << *it << ": " << get(weights, *it) << std::endl;
        }
    }

    return fg;
}

输入（顶点1，顶点2，权重）：

0 1 0.001
0 2 0.1
0 3 0.001
1 5 0.001
2 3 0.001
3 4 0.1
1 482 0.1
482 635 0.001
4 705 0.1
705 5 0.1
1 1491 0.01
1 1727 0.01
1 1765 0.01

输出（源 = 0，目标 = 5）：

Source Vertex: 0
Edge Probability (0,1): 0.001
Edge Probability (0,2): 0.1
Edge Probability (0,3): 0.001
Edge Probability (1,5): 0.001
Edge Probability (1,482): 0.1
Edge Probability (1,1491): 0.01
Edge Probability (1,1727): 0.01
Edge Probability (1,1765): 0.01
Edge Probability (2,3): 0.001
Edge Probability (3,4): 0.1
Edge Probability (4,705): 0.1
Edge Probability (482,635): 0.001
Edge Probability (705,5): 0.1

预期输出：

0->1->5
0->3->4->705->5
0->2->3->4->705->5

Answer 1

我不会使用 BFS 算法，因为它使用颜色图来跟踪访问过的节点。但是，如果您想要 所有 个不同的路径，您将不想跳过已经访问过的节点（因为您可能会跳过替代路径）。

相反，我会实现一个蛮力广度优先递归算法，它只访问所有相邻节点除非它们已经在当前路径中。

所需的所有状态都是当前路径。

这里更详细地解释了这个想法：https://www.quora.com/How-should-I-find-all-distinct-simple-paths-between-2-given-nodes-in-an-undirected-graph

Live On Coliru

#include <boost/graph/adjacency_list.hpp>
#include <boost/graph/graph_utility.hpp> // print_graph
using namespace boost;
using Graph = adjacency_list<vecS, listS, directedS, property<vertex_index_t, int>, property<edge_weight_t, double> >;
Graph read_graph();

using Vertex = Graph::vertex_descriptor;
using Path = std::vector<Vertex>;

template <typename Report>
void all_paths_helper(Vertex from, Vertex to, Graph const& g, Path& path, Report const& callback) {
    path.push_back(from);

    if (from == to) {
        callback(path);
    } else {
        for (auto out : make_iterator_range(out_edges(from, g))) {
            auto v = target(out, g);
            if (path.end() == std::find(path.begin(), path.end(), v)) {
                all_paths_helper(v, to, g, path, callback);
            }
        }
    }

    path.pop_back();
}

template <typename Report>
void all_paths(Vertex from, Vertex to, Graph const& g, Report const& callback) {
    Path state;
    all_paths_helper(from, to, g, state, callback);
}

int main() {
    auto g = read_graph();
    print_graph(g, std::cout);

    auto by_vertex_id = [&](int id) {
        return *find_if(vertices(g), [&](Vertex vd) { return id == get(vertex_index, g, vd); });
    };

    all_paths(by_vertex_id(0), by_vertex_id(5), g, [&](Path const& path) {
            std::cout << "Found path ";
            for (auto v : path)
                std::cout << get(vertex_index, g, v) << " ";
            std::cout << "\n";
        });
    std::cout.flush();
}

// immaterial to the task, reading the graph
Graph read_graph() {
    std::istringstream iss(R"(
        0 1 0.001
        0 2 0.1
        0 3 0.001
        1 5 0.001
        2 3 0.001
        3 4 0.1
        1 482 0.1
        482 635 0.001
        4 705 0.1
        705 5 0.1
        1 1491 0.01
        1 1727 0.01
        1 1765 0.01)");

    Graph g;
    auto vertex = [&,idx=std::map<int,Vertex>{}](int id) mutable {
        auto it = idx.find(id);
        if (it != idx.end())
            return it->second;
        return idx.emplace(id, add_vertex(id, g)).first->second;
    };

    for (std::string line; getline(iss, line);) {
        std::istringstream ls(line);
        int s,t; double w;
        if (ls >> s >> t >> w) {
            add_edge(vertex(s), vertex(t), w, g);
        } else {
            std::cerr << "Skipped invalid line '" << line << "'\n";
        }
    }

    return g;
}

哪些打印：

1 --> 5 482 1491 1727 1765 
0 --> 1 2 3 
2 --> 3 
3 --> 4 
5 --> 
4 --> 705 
482 --> 635 
635 --> 
705 --> 5 
1491 --> 
1727 --> 
1765 --> 
Found path 0 1 5 
Found path 0 2 3 4 705 5 
Found path 0 3 4 705 5