关于Floyd-Warshall，Dijkstra和Bellman-Ford算法之间的区别，我是否正确？

我一直在研究这三个，并在下面说明了他们的推论。有人可以告诉我我是否足够正确地理解它们？谢谢。

1. Dijkstra的算法仅在您只有一个来源并且想知道从一个节点到另一个节点的最小路径时使用，但是在这种情况下会失败

2. 当所有节点中的任何一个都可以作为源时，将使用Floyd-Warshall算法，因此您希望从任何源节点到任何目标节点的距离最短。仅在出现负循环时失败

（这是最重要的一个。我的意思是，这是我最不确定的一个：）

3，贝尔曼·福特（Bellman-Ford）和迪杰斯特拉（Dijkstra）一样，只有一个来源。它可以处理负数权重，其工作方式与Floyd-Warshall相同，只是有一个来源，对吗？

如果需要看一下，相应的算法是（由维基百科提供）：

贝尔曼福特：

 procedure BellmanFord(list vertices, list edges, vertex source)
   // This implementation takes in a graph, represented as lists of vertices
   // and edges, and modifies the vertices so that their distance and
   // predecessor attributes store the shortest paths.

   // Step 1: initialize graph
   for each vertex v in vertices:
       if v is source then v.distance := 0
       else v.distance := infinity
       v.predecessor := null

   // Step 2: relax edges repeatedly
   for i from 1 to size(vertices)-1:
       for each edge uv in edges: // uv is the edge from u to v
           u := uv.source
           v := uv.destination
           if u.distance + uv.weight < v.distance:
               v.distance := u.distance + uv.weight
               v.predecessor := u

   // Step 3: check for negative-weight cycles
   for each edge uv in edges:
       u := uv.source
       v := uv.destination
       if u.distance + uv.weight < v.distance:
           error "Graph contains a negative-weight cycle"

Dijkstra：

 1  function Dijkstra(Graph, source):
 2      for each vertex v in Graph:                                // Initializations
 3          dist[v] := infinity ;                                  // Unknown distance function from 
 4                                                                 // source to v
 5          previous[v] := undefined ;                             // Previous node in optimal path
 6                                                                 // from source
 7      
 8      dist[source] := 0 ;                                        // Distance from source to source
 9      Q := the set of all nodes in Graph ;                       // All nodes in the graph are
10                                                                 // unoptimized - thus are in Q
11      while Q is not empty:                                      // The main loop
12          u := vertex in Q with smallest distance in dist[] ;    // Start node in first case
13          if dist[u] = infinity:
14              break ;                                            // all remaining vertices are
15                                                                 // inaccessible from source
16          
17          remove u from Q ;
18          for each neighbor v of u:                              // where v has not yet been 
19                                                                                 removed from Q.
20              alt := dist[u] + dist_between(u, v) ;
21              if alt < dist[v]:                                  // Relax (u,v,a)
22                  dist[v] := alt ;
23                  previous[v] := u ;
24                  decrease-key v in Q;                           // Reorder v in the Queue
25      return dist;

弗洛伊德·沃希尔（Floyd-Warshall）：

 1 /* Assume a function edgeCost(i,j) which returns the cost of the edge from i to j
 2    (infinity if there is none).
 3    Also assume that n is the number of vertices and edgeCost(i,i) = 0
 4 */
 5
 6 int path[][];
 7 /* A 2-dimensional matrix. At each step in the algorithm, path[i][j] is the shortest path
 8    from i to j using intermediate vertices (1..k−1).  Each path[i][j] is initialized to
 9    edgeCost(i,j).
10 */
11
12 procedure FloydWarshall ()
13    for k := 1 to n
14       for i := 1 to n
15          for j := 1 to n
16             path[i][j] = min ( path[i][j], path[i][k]+path[k][j] );

如果我正确理解您，则您的理解是正确的。

• Djikstra的查找找到了从源节点到图中每个其他节点的最小成本路径，除非权重边为负。（只要将Dijkstra找到目标节点，然后将其更改为停止并添加启发式方法，就可以轻松地将其转换为A *算法。）
• Bellman-Ford与Dijkstra的一样，但速度较慢。但它可以处理负重边缘。
• Floyd-Warshall找到从每个节点到每个其他节点的最小成本路径的成本。（它返回一个数值矩阵。）它比Djikstra或Bellman-Ford都要慢得多。与您编写的内容不同，它不会在出现负循环时失败，它只会向自己报告某个节点的成本毫无意义的负数。