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来自「Data Structures And Algorithms With Obje」· HTML 代码 · 共 182 行 · 第 1/2 页

	    </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP>  <IMG WIDTH=13 HEIGHT=26 ALIGN=MIDDLE ALT="tex2html_wrap_inline71639" SRC="img2362.gif"  > </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP></TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> 0 </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP></TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP>--
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<TR><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> 
	<I>c</I> </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP></TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP>  <IMG WIDTH=14 HEIGHT=7 ALIGN=BOTTOM ALT="tex2html_wrap_inline68397" SRC="img1875.gif"  > </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP></TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP>
	    </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP></TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> 5 </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP></TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> <I>b</I>
	    </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP></TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> 4 </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP></TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> <I>a</I>
	    </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP>  <IMG WIDTH=13 HEIGHT=26 ALIGN=MIDDLE ALT="tex2html_wrap_inline71639" SRC="img2362.gif"  > </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP></TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> 4 </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP></TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> <I>a</I>
	    </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP>  <IMG WIDTH=13 HEIGHT=26 ALIGN=MIDDLE ALT="tex2html_wrap_inline71639" SRC="img2362.gif"  > </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP></TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> 4 </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP></TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> <I>a</I>
	    </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP>  <IMG WIDTH=13 HEIGHT=26 ALIGN=MIDDLE ALT="tex2html_wrap_inline71639" SRC="img2362.gif"  > </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP></TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> 4 </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP></TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> <I>a</I>
	    </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP>  <IMG WIDTH=13 HEIGHT=26 ALIGN=MIDDLE ALT="tex2html_wrap_inline71639" SRC="img2362.gif"  > </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP></TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> 4 </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP></TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> <I>a</I> </TD></TR>
<TR><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> 
	<I>d</I> </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP></TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP>  <IMG WIDTH=14 HEIGHT=7 ALIGN=BOTTOM ALT="tex2html_wrap_inline68397" SRC="img1875.gif"  > </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP></TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP>
	    </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP></TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP>  <IMG WIDTH=14 HEIGHT=7 ALIGN=BOTTOM ALT="tex2html_wrap_inline68397" SRC="img1875.gif"  > </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP></TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP>
	    </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP></TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP>  <IMG WIDTH=14 HEIGHT=7 ALIGN=BOTTOM ALT="tex2html_wrap_inline68397" SRC="img1875.gif"  > </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP></TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP>
	    </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP></TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> 6 </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP></TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> <I>c</I>
	    </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP>  <IMG WIDTH=13 HEIGHT=26 ALIGN=MIDDLE ALT="tex2html_wrap_inline71639" SRC="img2362.gif"  > </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP></TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> 6 </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP></TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP><I>c</I>
	    </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP>  <IMG WIDTH=13 HEIGHT=26 ALIGN=MIDDLE ALT="tex2html_wrap_inline71639" SRC="img2362.gif"  > </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP></TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> 6 </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP></TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP><I>c</I>
	    </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP>  <IMG WIDTH=13 HEIGHT=26 ALIGN=MIDDLE ALT="tex2html_wrap_inline71639" SRC="img2362.gif"  > </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP></TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> 6 </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP></TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP><I>c</I> </TD></TR>
<TR><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> 
	<I>e</I> </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP></TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> <IMG WIDTH=14 HEIGHT=7 ALIGN=BOTTOM ALT="tex2html_wrap_inline68397" SRC="img1875.gif"  > </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP></TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP>
	    </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP></TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> <IMG WIDTH=14 HEIGHT=7 ALIGN=BOTTOM ALT="tex2html_wrap_inline68397" SRC="img1875.gif"  > </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP></TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP>
	    </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP></TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> <IMG WIDTH=14 HEIGHT=7 ALIGN=BOTTOM ALT="tex2html_wrap_inline68397" SRC="img1875.gif"  > </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP></TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP>
	    </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP></TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> 8 </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP></TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP><I>c</I>
	    </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP></TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> 8 </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP></TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP><I>c</I>
	    </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP>  <IMG WIDTH=13 HEIGHT=26 ALIGN=MIDDLE ALT="tex2html_wrap_inline71639" SRC="img2362.gif"  > </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP></TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> 8 </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP></TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP><I>c</I>
	    </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP>  <IMG WIDTH=13 HEIGHT=26 ALIGN=MIDDLE ALT="tex2html_wrap_inline71639" SRC="img2362.gif"  > </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP></TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> 8 </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP></TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP><I>c</I> </TD></TR>
<TR><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> 
	<I>f</I> </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP></TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP>  <IMG WIDTH=14 HEIGHT=7 ALIGN=BOTTOM ALT="tex2html_wrap_inline68397" SRC="img1875.gif"  > </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP></TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP>
	    </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP></TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP>  <IMG WIDTH=14 HEIGHT=7 ALIGN=BOTTOM ALT="tex2html_wrap_inline68397" SRC="img1875.gif"  > </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP></TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP>
	    </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP></TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP>  <IMG WIDTH=14 HEIGHT=7 ALIGN=BOTTOM ALT="tex2html_wrap_inline68397" SRC="img1875.gif"  > </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP></TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP>
	    </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP></TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP>  <IMG WIDTH=14 HEIGHT=7 ALIGN=BOTTOM ALT="tex2html_wrap_inline68397" SRC="img1875.gif"  > </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP></TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP>
	    </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP></TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> 11 </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP></TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> <I>d</I>
	    </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP></TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> 9 </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP></TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> <I>e</I>
	    </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP>  <IMG WIDTH=13 HEIGHT=26 ALIGN=MIDDLE ALT="tex2html_wrap_inline71639" SRC="img2362.gif"  ></TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP></TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP>9</TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP></TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP><I>e</I>  </TD></TR>
</TBODY>
<CAPTION ALIGN=BOTTOM><STRONG>Table:</STRONG> Operation of Dijkstra's algorithm.</CAPTION></TABLE>
</P></DIV><P>
<P>
Initially all the tentative distances are  <IMG WIDTH=14 HEIGHT=7 ALIGN=BOTTOM ALT="tex2html_wrap_inline68397" SRC="img1875.gif"  >,
except for vertex <I>b</I> which has tentative distance zero.
Therefore, vertex <I>b</I> is selected in the first pass.
The mark  <IMG WIDTH=13 HEIGHT=26 ALIGN=MIDDLE ALT="tex2html_wrap_inline71639" SRC="img2362.gif"  > beside an entry in Table&nbsp;<A HREF="page565.html#tblgraphsdijkstra"><IMG  ALIGN=BOTTOM ALT="gif" SRC="../icons/cross_ref_motif.gif"></A>
indicates that the shortest path is <em>known</em> ( <IMG WIDTH=69 HEIGHT=22 ALIGN=MIDDLE ALT="tex2html_wrap_inline71767" SRC="img2364.gif"  >).
<P>
Next we follow the edges emanating from vertex <I>b</I>,
 <IMG WIDTH=39 HEIGHT=11 ALIGN=BOTTOM ALT="tex2html_wrap_inline71771" SRC="img2365.gif"  > and  <IMG WIDTH=38 HEIGHT=11 ALIGN=BOTTOM ALT="tex2html_wrap_inline71773" SRC="img2366.gif"  >,
and update the distances accordingly.
The new tentative distances for <I>a</I> becomes 3
and the new tentative distance for <I>c</I> is 5.
In both cases, the next-to-last vertex on the shortest path is vertex <I>b</I>.
<P>
In the second pass, vertex <I>a</I> is selected and
its entry is marked with  <IMG WIDTH=13 HEIGHT=26 ALIGN=MIDDLE ALT="tex2html_wrap_inline71639" SRC="img2362.gif"  > indicating the shortest path is known.
There is one edge emanating from <I>a</I>,  <IMG WIDTH=41 HEIGHT=8 ALIGN=BOTTOM ALT="tex2html_wrap_inline71791" SRC="img2367.gif"  >.
The distance to <I>c</I> via <I>a</I> is 4.
Since this is less than the tentative distance to <I>c</I>,
vertex <I>c</I> is given the new tentative distance 4
and its predecessor on the shortest-path is set to <I>a</I>.
The algorithm continues in this fashion
for a total of  <IMG WIDTH=11 HEIGHT=12 ALIGN=BOTTOM ALT="tex2html_wrap_inline70551" SRC="img2167.gif"  > passes
until all the shortest paths have been found.
<P>
The shortest-path information contained in the right-most column
of Table&nbsp;<A HREF="page565.html#tblgraphsdijkstra"><IMG  ALIGN=BOTTOM ALT="gif" SRC="../icons/cross_ref_motif.gif"></A>
can be represented in the form of a vertex-weighted graph
as shown in Figure&nbsp;<A HREF="page565.html#figgraph13"><IMG  ALIGN=BOTTOM ALT="gif" SRC="../icons/cross_ref_motif.gif"></A>.
<P>
<P><A NAME="52051">&#160;</A><A NAME="figgraph13">&#160;</A> <IMG WIDTH=575 HEIGHT=186 ALIGN=BOTTOM ALT="figure51680" SRC="img2368.gif"  ><BR>
<STRONG>Figure:</STRONG> The shortest-path graph for  <IMG WIDTH=24 HEIGHT=23 ALIGN=MIDDLE ALT="tex2html_wrap_inline71499" SRC="img2337.gif"  >.<BR>
<P>
<P>
This graph contains the same set of vertices as the problem graph  <IMG WIDTH=24 HEIGHT=23 ALIGN=MIDDLE ALT="tex2html_wrap_inline71499" SRC="img2337.gif"  >.
Each vertex <I>v</I> is labeled with the length  <IMG WIDTH=14 HEIGHT=22 ALIGN=MIDDLE ALT="tex2html_wrap_inline71553" SRC="img2348.gif"  >
of the shortest path from <I>b</I> to <I>v</I>.
Each vertex (except <I>b</I>) has a single emanating edge
that connects the vertex to the next-to-last vertex on the shortest-path.
By following the edges in this graph from any vertex <I>v</I> to vertex <I>b</I>,
we can construct the shortest path from <I>b</I> to <I>v</I> in reverse.
<P>
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