c++ - 如何找到 BGL 图中两个顶点之间的最短路径？

Question

所以我目前正在研究一个单词阶梯问题的项目，我已经构建了用于在其中存储所有字典单词的图形并在其中添加了边，我使用 boost 图形库完成了此操作。

但令我困惑的是 breadth_first_search() 函数，似乎参数只采用起始顶点但没有结束顶点。

我检查了文档并注意到我可以为该搜索功能定义 BFS 访问者，但由于我是 boost 库的新手，我无法弄清楚它是如何工作的。

谁能解释一下如何实现寻找两个顶点之间的最短路径？我正在使用无向和未加权的图。

#include <iostream> // std::cout
#include <fstream>
#include <string>
#include <stdlib.h>
#include <utility> // std::pair
#include "headers.h"
#include <boost/graph/adjacency_list.hpp>
#include <boost/graph/dijkstra_shortest_paths.hpp>
#include <boost/graph/graph_utility.hpp>

using namespace std;

//Define a class that has the data you want to associate to every vertex and 
edge
//struct Vertex{ int foo;}
//  struct Edge{std::string blah;}

struct VertexProperties {
  string name;
  VertexProperties(string name) : name(name) {}
};

//typedef property<edge_weight_t, int> EdgeWeightProperty;
//typedef property<vertex_name_t, string> VertexNameProperty;

//Define the graph using those classes
typedef boost::adjacency_list<boost::setS, boost::listS, boost::undirectedS, 
VertexProperties> Graph;
typedef Graph::vertex_iterator Vit;
typedef Graph::vertex_descriptor Vde;
typedef Graph::edge_descriptor E;
typedef boost::graph_traits<Graph>::adjacency_iterator adjacency_it;


struct my_visitor : boost::default_dijkstra_visitor {
 using base = boost::default_dijkstra_visitor;
 struct done{};

my_visitor(Vde vd, size_t& visited) : destination(vd), visited(visited) {}

void finish_vertex(Vde v, Graph const& g) {
++visited;

if (v == destination)
  throw done{};

base::finish_vertex(v, g);
}

private:
Vde destination;
size_t &visited;
};

//Some typedefs for simplicity
//typedef boost::graph_traits<Graph>::vertex_descriptor vertex_t;
//typedef boost::graph_traits<Graph>::edge_descriptor edge_t;
int main()
{
ifstream dictionary("dictionary.txt");
string word;
Graph allWords;
//Vit begin,end;

if(dictionary.is_open())
{
  while(getline(dictionary,word))
    {
  word.pop_back();
      add_vertex(VertexProperties(word),allWords);
    }
 }
else 
cout<<"File openning failed."<<endl;

dictionary.close();
//cout<<num_vertices(allWords)<<endl;
Vit begin,end;
boost::tie(begin, end) = vertices(allWords);

vector<Graph::vertex_descriptor> vindex(begin, end);

int first=0;
int second=0;
for(Vit it=begin;it!=end;it++)
{
  for(Vit that=it;that!=end;that++)
    {
      if(isEditDistanceOne(allWords[*it].name,allWords[*that].name))
        add_edge(vindex[first],vindex[second],allWords);
      second++;
    }
  first++;
  second=first;
  cout<<first<<endl;
 }
//Vit temp=begin;
//temp++;   
//cout<<allWords[*begin].name<<"////////////////"<<endl;
adjacency_it neighbour, neighbour_end;
for (tie(neighbour, neighbour_end) = adjacent_vertices(*begin, allWords); 
    neighbour != neighbour_end; ++neighbour)
cout<<allWords[*neighbour].name<<endl;



string firstWord;
string secondWord;

int firstIndex=-1;
int secondIndex=-1;

cout<<"Enter first word:"<<endl;
cin>>firstWord;

cout<<"Enter second word:"<<endl;
cin>>secondWord;


Vit a=begin;
for(int i=0;i<num_vertices(allWords);i++)
{
  if(allWords[*a].name==firstWord)
    {
      firstIndex=i;
      break;
    }
  a++;
}

Vit b=begin;
for(int i=0;i<num_vertices(allWords);i++)
{
  if(allWords[*b].name==secondWord)
    {
      secondIndex=i;
      break;
    }
  b++;
}

if(firstIndex==-1)
  cout<<"First word not in graph."<<endl;

else if(secondIndex==-1)
  cout<<"Second word not in graph."<<endl;

else
{
  Vde start_vertex=vindex[firstIndex];
  Vde end_vertex=vindex[secondIndex];

  size_t visited;
  std::vector<boost::default_color_type> colors(num_vertices(allWords), 
  boost::default_color_type{});
  std::vector<Vde>                         _pred(num_vertices(allWords),   
  allWords.null_vertex());
  std::vector<size_t>                    _dist(num_vertices(allWords),   
  -1ull);

  my_visitor vis { end_vertex, visited };
  auto predmap = _pred.data(); // interior properties: 
  boost::get(boost::vertex_predecessor, g);
  auto distmap = _dist.data(); // interior properties: 
  boost::get(boost::vertex_distance, g);

  try {
  std::cout << "Searching from #" << start_vertex << " to #" << end_vertex 
  << 
  "...\n";
  boost::dijkstra_shortest_paths(allWords, start_vertex, 
                   boost::visitor(vis).
                   color_map(colors.data()).
                   distance_map(distmap).
                   predecessor_map(predmap).
                   weight_map(boost::make_constant_property<E>(1ul))
                   );

  std::cout << "No path found\n";
    return 0;
  } catch(my_visitor::done const&) {
  std::cout << "Percentage skipped: " << 
 (100.0*visited/num_vertices(allWords)) << "%\n";
  } 
 }


 //cout<<adjacency_list[*begin]<<"\t";
 return 0;
 }

Answer 1

只要发现目标就中止搜索。

这是一个工作示例

Live On Coliru

#include <boost/graph/adjacency_list.hpp>
#include <boost/graph/graph_utility.hpp>
#include <boost/graph/dijkstra_shortest_paths.hpp>
#include <boost/graph/random.hpp>
#include <random>
#include <iostream>

using G = boost::adjacency_list<boost::vecS, boost::vecS, boost::undirectedS>;
using V = G::vertex_descriptor;
using E = G::edge_descriptor;

struct my_visitor : boost::default_dijkstra_visitor {
    using base = boost::default_dijkstra_visitor;
    struct done{};

    my_visitor(V vd, size_t& visited) : destination(vd), visited(visited) {}

    void finish_vertex(V v, G const& g) {
        ++visited;

        if (v == destination)
            throw done{};

        base::finish_vertex(v, g);
    }

  private:
    V destination;
    size_t &visited;
};

int main() {
#if 1
    auto seed = 2912287549; // fixed seed for demo
#else
    auto seed = std::random_device{}();
    std::cout << "SEED: " << seed << "\n";
#endif
    std::mt19937 prng { seed };
    G g;
    generate_random_graph(g, 100, 400, prng);
    print_graph(g);

    V start_vertex = prng()%num_vertices(g);
    V end_vertex   = prng()%num_vertices(g);

    size_t visited;
    std::vector<boost::default_color_type> colors(num_vertices(g), boost::default_color_type{});
    std::vector<V>                         _pred(num_vertices(g),   g.null_vertex());
    std::vector<size_t>                    _dist(num_vertices(g),   -1ull);

    my_visitor vis { end_vertex, visited };
    auto predmap = _pred.data(); // interior properties: boost::get(boost::vertex_predecessor, g);
    auto distmap = _dist.data(); // interior properties: boost::get(boost::vertex_distance, g);

    try {
        std::cout << "Searching from #" << start_vertex << " to #" << end_vertex << "...\n";
        boost::dijkstra_shortest_paths(g, start_vertex, 
                boost::visitor(vis).
                color_map(colors.data()).
                distance_map(distmap).
                predecessor_map(predmap).
                weight_map(boost::make_constant_property<E>(1ul))
            );

        std::cout << "No path found\n";
        return 0;
    } catch(my_visitor::done const&) {
        std::cout << "Percentage skipped: " << (100.0*visited/num_vertices(g)) << "%\n";
    }

    size_t distance = distmap[end_vertex];
    std::cout << "Distance from #" << start_vertex << " to #" << end_vertex << ": " << distance << "\n";

    if (distance != size_t(-1)) {
        std::deque<V> path;
        for (V current = end_vertex; 
                current != g.null_vertex() 
                && predmap[current] != current 
                && current != start_vertex;) 
        {
            path.push_front(predmap[current]);
            current = predmap[current];
        }

        std::cout << "Path from #" << start_vertex << " to #" << end_vertex << ": ";
        std::copy(path.begin(), path.end(), std::ostream_iterator<V>(std::cout, ", "));
        std::cout << end_vertex << "\n";
    }
}

它生成具有 100 个顶点和 400 条边的随机无向图。对于特定的演示种子，它会打印以下输出:

0 <--> 45 46 15 83 69 32 38 68 37 
1 <--> 29 52 99 85 10 19 30 78 
2 <--> 42 7 35 80 25 9 23 23 
3 <--> 29 9 15 77 7 58 42 
4 <--> 75 56 98 24 14 40 97 34 84 37 80 30 62 
5 <--> 58 46 80 71 
6 <--> 89 12 47 88 80 
7 <--> 62 69 2 86 88 74 8 33 13 76 3 9 86 48 
8 <--> 64 26 31 7 94 95 77 
9 <--> 83 53 76 3 43 55 7 2 67 72 
10 <--> 51 16 21 20 1 63 31 
11 <--> 38 50 19 88 16 52 
12 <--> 46 6 85 21 61 39 
13 <--> 95 24 17 51 7 
14 <--> 24 4 43 53 
15 <--> 0 51 70 3 43 34 
16 <--> 72 10 23 99 28 35 22 11 96 99 19 38 39 
17 <--> 84 25 13 54 74 96 28 
18 <--> 90 54 88 78 
19 <--> 63 11 61 20 73 22 1 63 90 75 16 
20 <--> 70 57 79 35 19 10 65 79 45 
21 <--> 49 89 43 50 10 38 12 26 67 
22 <--> 41 49 95 99 25 39 23 16 19 81 
23 <--> 35 16 22 95 2 69 2 
24 <--> 76 85 13 42 14 4 85 88 
25 <--> 98 17 22 72 92 60 2 51 
26 <--> 65 48 62 8 50 86 44 37 21 48 
27 <--> 42 82 
28 <--> 92 46 89 16 50 53 59 17 94 
29 <--> 1 33 3 46 91 96 46 48 
30 <--> 60 96 70 79 1 48 4 
31 <--> 37 66 50 8 59 72 32 87 10 67 
32 <--> 84 77 49 71 0 31 81 75 98 66 
33 <--> 29 83 66 7 69 74 80 79 
34 <--> 90 59 73 61 47 4 75 87 15 
35 <--> 51 23 46 20 16 2 68 
36 <--> 70 
37 <--> 31 41 77 68 70 26 70 4 0 60 
38 <--> 11 65 74 0 21 39 50 94 16 86 
39 <--> 48 88 38 22 12 89 16 
40 <--> 81 92 86 4 55 
41 <--> 22 37 74 64 63 63 79 
42 <--> 27 2 24 84 90 65 67 76 72 93 3 
43 <--> 51 75 21 54 9 65 14 53 44 15 
44 <--> 74 82 26 43 
45 <--> 0 86 70 46 94 89 20 
46 <--> 0 12 28 35 45 96 5 29 29 
47 <--> 96 51 6 82 62 34 88 78 
48 <--> 26 99 39 50 59 78 30 29 7 26 
49 <--> 21 22 52 32 99 61 55 69 66 57 
50 <--> 82 11 31 21 26 65 28 48 38 94 55 
51 <--> 43 35 10 47 15 55 13 55 88 25 69 84 
52 <--> 86 49 66 1 93 55 11 74 90 
53 <--> 89 76 9 76 82 28 77 43 14 
54 <--> 87 43 17 98 59 18 66 
55 <--> 68 76 51 65 51 81 52 9 49 92 50 40 
56 <--> 4 82 95 88 80 
57 <--> 20 87 66 62 49 
58 <--> 5 3 
59 <--> 34 75 71 28 31 48 54 70 96 
60 <--> 81 30 81 87 61 61 25 37 
61 <--> 78 62 97 19 49 34 12 60 60 
62 <--> 7 26 69 87 61 70 92 57 47 90 4 
63 <--> 19 41 41 10 72 19 
64 <--> 8 92 41 95 86 
65 <--> 26 38 50 42 55 43 83 79 20 79 
66 <--> 52 31 33 57 87 54 32 49 
67 <--> 97 42 98 9 31 21 
68 <--> 55 74 96 37 0 98 35 
69 <--> 7 97 62 0 97 33 70 49 75 51 23 
70 <--> 20 83 45 78 15 69 30 37 62 37 59 78 77 36 
71 <--> 83 74 59 32 5 88 
72 <--> 16 74 31 25 85 83 42 63 9 
73 <--> 74 34 87 19 
74 <--> 68 73 41 44 72 71 7 38 17 96 33 82 52 
75 <--> 4 43 59 86 32 34 19 69 85 
76 <--> 24 53 55 53 9 42 7 
77 <--> 32 37 79 53 3 70 96 90 8 
78 <--> 61 70 70 48 1 18 47 
79 <--> 20 77 41 30 98 65 20 33 65 82 
80 <--> 82 81 86 93 56 5 33 2 6 4 
81 <--> 40 60 60 80 91 55 32 22 
82 <--> 80 50 44 56 88 53 47 27 74 79 
83 <--> 9 70 71 0 33 95 72 65 
84 <--> 32 17 42 86 4 51 
85 <--> 24 96 12 87 24 1 72 89 87 75 
86 <--> 52 45 40 7 84 26 75 80 7 64 38 
87 <--> 54 57 73 85 62 60 66 31 85 34 
88 <--> 7 39 82 56 11 6 51 24 18 47 71 
89 <--> 53 21 6 28 99 92 45 85 39 
90 <--> 34 42 96 18 77 19 62 52 
91 <--> 81 29 
92 <--> 28 40 64 62 25 89 55 
93 <--> 52 80 42 
94 <--> 8 45 50 28 38 
95 <--> 22 13 83 56 23 64 8 
96 <--> 85 47 30 68 46 90 74 17 16 77 29 59 
97 <--> 69 67 61 69 4 
98 <--> 25 4 54 79 68 67 32 
99 <--> 22 48 16 89 1 49 16 
Searching from #20 to #27...
Percentage skipped: 91%
Distance from #20 to #27: 3
Path from #20 to #27: 20, 65, 42, 27

如您所见，91% 的节点未被访问。

注意事项

文档说当边缘权重恒定时使用广度优先搜索。遗憾的是我无法完成这项工作。

假设算法等价性被断言，使用早出的路径仍然是最短的(假设边缘权重是常数)。