如何在BGL圖中找到兩個頂點之間的最短路徑？

Question

因此，我目前正在研究一個單詞梯子問題的項目，並且我已經建立了用於在其中存儲所有字典單詞並在其中添加邊的圖形，我使用了升壓圖形庫來實現。

但是令我感到困惑的是， breadth_first_search()函數似乎只接受起始頂點，而沒有終止頂點。

我查看了文檔，發現可以為該搜索功能定義BFS訪問者，但是由於我是Boost庫的新手，所以我不知道它是如何工作的。

誰能解釋一下如何實現找到兩個頂點之間的最短路徑？ 我正在使用無向和無權圖。

#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

找到目標后，只需中止搜索。

這是一個工作樣本

生活在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個頂點和400個邊的隨機無向圖。 對於特定的演示種子，它將輸出以下輸出：

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

如您所見，未訪問91％的節點。

筆記

文檔說當邊緣權重恆定時使用廣度優先搜索。 我很難過這項工作。

假設算法等價被斷言時，路徑仍然會最短使用早期輸出（假定邊緣權重是恆定）。