弗洛伊德(Floyd)算法 主要是用于计算图中所有顶点对之间的最短距离长度的算法，如果是要求某一个特定点到图中所有顶点之间的最短距离可以用Dijkstra(迪杰斯特拉)算法来求。

弗洛伊德(Floyd)算法的算法过程是：



1、从任意一条单边路径开始。所有两点之间的距离是边的权，如果两点之间没有边相连，则权为无穷大。



2、对于每一对顶点 u 和 v，看看是否存在一个顶点 w 使得从 u 到 w 再到 v 比已知的路径更短。如果是更新它。



把图用邻接矩阵G表示出来，如果从Vi到Vj有路可达，则G[i,j]=d，d表示该路的长度；否则G[i,j]=无穷大。定义一个矩阵D用来记录所插入点的信息，D[i,j]表示从Vi到Vj需要经过的点，初始化D[i,j]=j。把各个顶点插入图中，比较插点后的距离与原来的距离，G[i,j] = min( G[i,j], G[i,k]+G[k,j] )，如果G[i,j]的值变小，则D[i,j]=k。在G中包含有两点之间最短道路的信息，而在D中则包含了最短路径的信息。



比如，要寻找从V5到V1的路径。根据D，假如D(5,1)=3则说明从V5到V1经过V3，路径为{V5,V3,V1}，如果D(5,3)=3，说明V5与V3直接相连，如果D(3,1)=1，说明V3与V1直接相连。 -Floyd (Floyd) algorithm is mainly used to calculate the length of the shortest distance between the drawing algorithm between all pairs of vertices, if the requirements of a specific point to the diagram all the shortest distance between vertices can Dijkstra (Dinger Stella) algorithm to find.

  Floyd algorithm process (Floyd) algorithm is:



1, starting　any one-sided way. The distance between two points is all right edge, if there is no edge connected between two points, the right to infinity.



2. For every pair of vertices u and v, and see if there is a vertex w such that w　u to v and then shorter than the known path. If you are updating it.



Figure that out of the adjacency matrix G, if there is a road up　Vi to Vj, then G [i, j] = d, d represents the length of the path　otherwise G [i, j] = infinity. Define a matrix D used to record the information of the inserted point, D [i, j] represents　Vi to Vj need to go through the points, initialize D [i, j] = j. The inset in e