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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 (<u, w> ) </font></i>
<img src="image/text6-v.gif" width="572" height="153"></font></b></pre>
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