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	<title>潘锦的空间 &#187; 矩阵连乘</title>
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		<title>矩阵连乘</title>
		<link>https://www.phppan.com/2009/08/matrix-multiplication/</link>
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		<pubDate>Mon, 31 Aug 2009 13:19:06 +0000</pubDate>
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				<category><![CDATA[程序相关]]></category>
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		<category><![CDATA[dynamic programming]]></category>
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		<category><![CDATA[矩阵连乘]]></category>

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		<description><![CDATA[【代码】 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 [&#8230;]]]></description>
				<content:encoded><![CDATA[<p>【代码】</p>

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</pre></td><td class="code"><pre class="c" style="font-family:monospace;"><span style="color: #339933;">#include &lt;stdio.h&gt; </span>
<span style="color: #339933;">#include &lt;string.h&gt; </span>
<span style="color: #339933;">#define N 100 </span>
<span style="color: #993333;">int</span> m<span style="color: #009900;">&#91;</span>N<span style="color: #009900;">&#93;</span><span style="color: #009900;">&#91;</span>N<span style="color: #009900;">&#93;</span><span style="color: #339933;">;</span> <span style="color: #666666; font-style: italic;">//m[i][j]表示从第i个矩阵连乘到第j个矩阵的最小计算次数 </span>
<span style="color: #993333;">int</span> s<span style="color: #009900;">&#91;</span>N<span style="color: #009900;">&#93;</span><span style="color: #009900;">&#91;</span>N<span style="color: #009900;">&#93;</span><span style="color: #339933;">;</span> <span style="color: #666666; font-style: italic;">//第i个矩阵连乘到第j个矩阵时在何处断开，用于构造最优解 </span>
<span style="color: #993333;">int</span> p<span style="color: #009900;">&#91;</span>N<span style="color: #009900;">&#93;</span><span style="color: #339933;">;</span>    <span style="color: #666666; font-style: italic;">//表示矩阵i为p[i-1]×p[i] </span>
&nbsp;
<span style="color: #993333;">void</span> MatrixChain<span style="color: #009900;">&#40;</span><span style="color: #993333;">int</span> n<span style="color: #009900;">&#41;</span> 
<span style="color: #009900;">&#123;</span> 
       <span style="color: #993333;">int</span> i<span style="color: #339933;">,</span>j<span style="color: #339933;">,</span>k<span style="color: #339933;">,</span>t<span style="color: #339933;">,</span>r<span style="color: #339933;">;</span> 
       <span style="color: #b1b100;">for</span><span style="color: #009900;">&#40;</span>i<span style="color: #339933;">=</span><span style="color: #0000dd;">1</span><span style="color: #339933;">;</span>i<span style="color: #339933;">&lt;=</span>n<span style="color: #339933;">;</span>i<span style="color: #339933;">++</span><span style="color: #009900;">&#41;</span> 
              m<span style="color: #009900;">&#91;</span>i<span style="color: #009900;">&#93;</span><span style="color: #009900;">&#91;</span>i<span style="color: #009900;">&#93;</span><span style="color: #339933;">=</span><span style="color: #0000dd;">0</span><span style="color: #339933;">;</span> 
       <span style="color: #b1b100;">for</span><span style="color: #009900;">&#40;</span>r<span style="color: #339933;">=</span><span style="color: #0000dd;">2</span><span style="color: #339933;">;</span>r<span style="color: #339933;">&lt;=</span>n<span style="color: #339933;">;</span>r<span style="color: #339933;">++</span><span style="color: #009900;">&#41;</span> 
       <span style="color: #009900;">&#123;</span> 
              <span style="color: #b1b100;">for</span><span style="color: #009900;">&#40;</span>i<span style="color: #339933;">=</span><span style="color: #0000dd;">1</span><span style="color: #339933;">;</span>i<span style="color: #339933;">&lt;=</span>n<span style="color: #339933;">-</span>r<span style="color: #339933;">+</span><span style="color: #0000dd;">1</span><span style="color: #339933;">;</span>i<span style="color: #339933;">++</span><span style="color: #009900;">&#41;</span> 
              <span style="color: #009900;">&#123;</span> 
                     j<span style="color: #339933;">=</span>i<span style="color: #339933;">+</span>r<span style="color: #339933;">-</span><span style="color: #0000dd;">1</span><span style="color: #339933;">;</span> 
                     m<span style="color: #009900;">&#91;</span>i<span style="color: #009900;">&#93;</span><span style="color: #009900;">&#91;</span>j<span style="color: #009900;">&#93;</span><span style="color: #339933;">=</span>m<span style="color: #009900;">&#91;</span>i<span style="color: #339933;">+</span><span style="color: #0000dd;">1</span><span style="color: #009900;">&#93;</span><span style="color: #009900;">&#91;</span>j<span style="color: #009900;">&#93;</span><span style="color: #339933;">+</span>p<span style="color: #009900;">&#91;</span>i<span style="color: #339933;">-</span><span style="color: #0000dd;">1</span><span style="color: #009900;">&#93;</span><span style="color: #339933;">*</span>p<span style="color: #009900;">&#91;</span>i<span style="color: #009900;">&#93;</span><span style="color: #339933;">*</span>p<span style="color: #009900;">&#91;</span>j<span style="color: #009900;">&#93;</span><span style="color: #339933;">;</span> 
                     s<span style="color: #009900;">&#91;</span>i<span style="color: #009900;">&#93;</span><span style="color: #009900;">&#91;</span>j<span style="color: #009900;">&#93;</span><span style="color: #339933;">=</span>i<span style="color: #339933;">;</span> 
                     <span style="color: #b1b100;">for</span><span style="color: #009900;">&#40;</span>k<span style="color: #339933;">=</span>i<span style="color: #339933;">+</span><span style="color: #0000dd;">1</span><span style="color: #339933;">;</span>k<span style="color: #339933;">&lt;</span>j<span style="color: #339933;">;</span>k<span style="color: #339933;">++</span><span style="color: #009900;">&#41;</span> 
                     <span style="color: #009900;">&#123;</span> 
                            t<span style="color: #339933;">=</span>m<span style="color: #009900;">&#91;</span>i<span style="color: #009900;">&#93;</span><span style="color: #009900;">&#91;</span>k<span style="color: #009900;">&#93;</span><span style="color: #339933;">+</span>m<span style="color: #009900;">&#91;</span>k<span style="color: #339933;">+</span><span style="color: #0000dd;">1</span><span style="color: #009900;">&#93;</span><span style="color: #009900;">&#91;</span>j<span style="color: #009900;">&#93;</span><span style="color: #339933;">+</span>p<span style="color: #009900;">&#91;</span>i<span style="color: #339933;">-</span><span style="color: #0000dd;">1</span><span style="color: #009900;">&#93;</span><span style="color: #339933;">*</span>p<span style="color: #009900;">&#91;</span>k<span style="color: #009900;">&#93;</span><span style="color: #339933;">*</span>p<span style="color: #009900;">&#91;</span>j<span style="color: #009900;">&#93;</span><span style="color: #339933;">;</span> 
                            <span style="color: #b1b100;">if</span><span style="color: #009900;">&#40;</span>t<span style="color: #339933;">&lt;</span>m<span style="color: #009900;">&#91;</span>i<span style="color: #009900;">&#93;</span><span style="color: #009900;">&#91;</span>j<span style="color: #009900;">&#93;</span><span style="color: #009900;">&#41;</span> 
                            <span style="color: #009900;">&#123;</span> 
                                   m<span style="color: #009900;">&#91;</span>i<span style="color: #009900;">&#93;</span><span style="color: #009900;">&#91;</span>j<span style="color: #009900;">&#93;</span><span style="color: #339933;">=</span>t<span style="color: #339933;">;</span> 
                                   s<span style="color: #009900;">&#91;</span>i<span style="color: #009900;">&#93;</span><span style="color: #009900;">&#91;</span>j<span style="color: #009900;">&#93;</span><span style="color: #339933;">=</span>k<span style="color: #339933;">;</span> 
                            <span style="color: #009900;">&#125;</span> 
                     <span style="color: #009900;">&#125;</span> 
              <span style="color: #009900;">&#125;</span> 
       <span style="color: #009900;">&#125;</span> 
<span style="color: #009900;">&#125;</span> 
&nbsp;
<span style="color: #993333;">void</span> TraceBack<span style="color: #009900;">&#40;</span><span style="color: #993333;">int</span> i<span style="color: #339933;">,</span><span style="color: #993333;">int</span> j<span style="color: #009900;">&#41;</span> 
<span style="color: #009900;">&#123;</span> 
       <span style="color: #b1b100;">if</span><span style="color: #009900;">&#40;</span>i<span style="color: #339933;">==</span>j<span style="color: #009900;">&#41;</span> <span style="color: #b1b100;">return</span><span style="color: #339933;">;</span> 
       TraceBack<span style="color: #009900;">&#40;</span>i<span style="color: #339933;">,</span>s<span style="color: #009900;">&#91;</span>i<span style="color: #009900;">&#93;</span><span style="color: #009900;">&#91;</span>j<span style="color: #009900;">&#93;</span><span style="color: #009900;">&#41;</span><span style="color: #339933;">;</span> 
       TraceBack<span style="color: #009900;">&#40;</span>s<span style="color: #009900;">&#91;</span>i<span style="color: #009900;">&#93;</span><span style="color: #009900;">&#91;</span>j<span style="color: #009900;">&#93;</span><span style="color: #339933;">+</span><span style="color: #0000dd;">1</span><span style="color: #339933;">,</span>j<span style="color: #009900;">&#41;</span><span style="color: #339933;">;</span> 
       <span style="color: #000066;">printf</span><span style="color: #009900;">&#40;</span><span style="color: #ff0000;">&quot;Multiply A%d,%d and A%d,%dn&quot;</span><span style="color: #339933;">,</span>i<span style="color: #339933;">,</span>s<span style="color: #009900;">&#91;</span>i<span style="color: #009900;">&#93;</span><span style="color: #009900;">&#91;</span>j<span style="color: #009900;">&#93;</span><span style="color: #339933;">,</span>s<span style="color: #009900;">&#91;</span>i<span style="color: #009900;">&#93;</span><span style="color: #009900;">&#91;</span>j<span style="color: #009900;">&#93;</span><span style="color: #339933;">+</span><span style="color: #0000dd;">1</span><span style="color: #339933;">,</span>j<span style="color: #009900;">&#41;</span><span style="color: #339933;">;</span>                                               
&nbsp;
<span style="color: #009900;">&#125;</span> 
&nbsp;
<span style="color: #993333;">int</span> main<span style="color: #009900;">&#40;</span><span style="color: #009900;">&#41;</span> 
&nbsp;
<span style="color: #009900;">&#123;</span> 
       <span style="color: #993333;">int</span> i<span style="color: #339933;">,</span>n<span style="color: #339933;">;</span> 
       <span style="color: #000066;">memset</span><span style="color: #009900;">&#40;</span>m<span style="color: #339933;">,</span><span style="color: #0000dd;">0</span><span style="color: #339933;">,</span><span style="color: #993333;">sizeof</span><span style="color: #009900;">&#40;</span>m<span style="color: #009900;">&#41;</span><span style="color: #009900;">&#41;</span><span style="color: #339933;">;</span> 
       <span style="color: #000066;">scanf</span><span style="color: #009900;">&#40;</span><span style="color: #ff0000;">&quot;%d&quot;</span><span style="color: #339933;">,&amp;</span>n<span style="color: #009900;">&#41;</span><span style="color: #339933;">;</span> 
       <span style="color: #b1b100;">for</span><span style="color: #009900;">&#40;</span>i<span style="color: #339933;">=</span><span style="color: #0000dd;">0</span><span style="color: #339933;">;</span>i<span style="color: #339933;">&lt;=</span>n<span style="color: #339933;">;</span>i<span style="color: #339933;">++</span><span style="color: #009900;">&#41;</span> 
              <span style="color: #000066;">scanf</span><span style="color: #009900;">&#40;</span><span style="color: #ff0000;">&quot;%d&quot;</span><span style="color: #339933;">,&amp;</span>p<span style="color: #009900;">&#91;</span>i<span style="color: #009900;">&#93;</span><span style="color: #009900;">&#41;</span><span style="color: #339933;">;</span> 
       MatrixChain<span style="color: #009900;">&#40;</span>n<span style="color: #009900;">&#41;</span><span style="color: #339933;">;</span> 
       <span style="color: #000066;">printf</span><span style="color: #009900;">&#40;</span><span style="color: #ff0000;">&quot;%dn&quot;</span><span style="color: #339933;">,</span>m<span style="color: #009900;">&#91;</span><span style="color: #0000dd;">1</span><span style="color: #009900;">&#93;</span><span style="color: #009900;">&#91;</span>n<span style="color: #009900;">&#93;</span><span style="color: #009900;">&#41;</span><span style="color: #339933;">;</span> 
       TraceBack<span style="color: #009900;">&#40;</span><span style="color: #0000dd;">1</span><span style="color: #339933;">,</span>n<span style="color: #009900;">&#41;</span><span style="color: #339933;">;</span> 
       <span style="color: #b1b100;">return</span> <span style="color: #0000dd;">0</span><span style="color: #339933;">;</span> 
<span style="color: #009900;">&#125;</span></pre></td></tr></table></div>

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