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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 45 行

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<b><font face="Arial, Helvetica, sans-serif" size="4" color="#000000">⑵<font color="#FF0000">	All pairs shortest paths </font>
        Using the above  shortestpath algorithm , find the shortest path
        between all pairs of vertices ,   <img src="image/vivj.gif" width="148" height="28" align="middle">
         <font color="#FF0000">   complexity</font> =   <img src="image/text6-y.gif" width="196" height="26" align="middle">

<font color="#FF0000">G</font>  ~  cost adjacency matrix 
  <img src="image/text6-z.gif" width="66" height="20" align="middle">  ~  the cost of the shortest path from i to j, using only these
                  intermediate vertices with an index  &lt;=k  .
  <img src="image/text6-a1.gif" width="75" height="19" align="middle"> ~  the cost of the shortest path from i to j
  <img src="image/text6-a3.gif" width="70" height="20" align="middle"> =  cost [i ] [j ]

<font color="#FF0000">Rules </font>for    <img src="image/text6-a4.gif" width="76" height="20">   ----->        <img src="image/text6-z.gif" width="66" height="20">  

(1) the shortest path from i to j going through no vertices with 
      index greater than k does not go through the vertex with index 
      k and so its cost is <img src="image/text6-a4.gif" width="76" height="20" align="middle"> .
(2) the shortest such path does go through vertex k, 
      path i to j =  path i to k  + path k to j  ( indices <= k-1)
    
       </font></b><img src="image/text6-a1c.gif" width="597" height="27">
    <b><font face="Arial, Helvetica, sans-serif" size="4" color="#000000"><img src="image/text6-a3.gif" width="88" height="26" align="middle"></font></b>  <b><font face="Arial, Helvetica, sans-serif" size="4" color="#000000">=  cost [i ] [j ]</font></b></pre>
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