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来自「浙江大学计算机学院数据结构课程的教学课件」· HTM 代码 · 共 55 行

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<b><font face="Arial, Helvetica, sans-serif" size="5" color="#FF0000">6.4 Shortest path and transitive closure
</font><font face="Arial, Helvetica, sans-serif" size="4" color="#000000">      ※ Is there a path from A to B ?
      ※ If there is more than one path from A to B,  
                 <font color="#FF0000">which path is the  shortest ?</font>

⑴	<font color="#FF0000">Single source all destinations</font>

<i><font color="#0033CC">problem :</font></i> given a directed graph, G = (V, E), a weighting function,
 w(e), w(e) > 0, for the edges of G, and a source vertex v0, determine
 shortest path from v0 to each of the remaining vertices of G.

<img src="image/text6-v0.gif" width="278" height="73" hspace="200">
<font color="#FF0000">greedy method:</font>
  1. Let S denote the set of vertices, including v0, whose
      shortest paths have been found
  2. For w in not in S, let distance[w] be the length of the 
      shortest path starting from v0, going through vertices only
      in S, and ending in w.
                   <font color="#FF0000"> S<font color="#000000"> (v0) </font>   </font>            <font color="#FF0000"> W<font color="#000000">(v1,v2,v3, .......,Vn)</font></font>

<font color="#FF0000">□ </font>If the next shortest path is to vertex u, then the path from v0 to u 
     goes through only those vertices that are in S.
<font color="#FF0000">□</font> Vertex u is chosen so that it has the minimum distance, 
     distance[u], among all the vertices not in S.
<font color="#FF0000">□ </font>Once we have selected u and generated the shortest path from 
     v0 to u, u becomes a member of  S. (w is not currently in S)
        the<font color="#FF0000"> shortest path </font> = <i><font color="#FF0000"> distance [ u ] + length (&lt;u, w&gt; ) </font></i>

                   <img src="image/text6-v.gif" width="572" height="153"></font></b></pre>
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