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	<title>潘锦的空间 &#187; pku1160</title>
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		<title>Post Office pku1160 邮局</title>
		<link>https://www.phppan.com/2009/08/post-office-pku1160/</link>
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		<pubDate>Sat, 29 Aug 2009 01:20:32 +0000</pubDate>
		<dc:creator><![CDATA[admin]]></dc:creator>
				<category><![CDATA[程序相关]]></category>
		<category><![CDATA[ACM]]></category>
		<category><![CDATA[DP]]></category>
		<category><![CDATA[dynamic programming]]></category>
		<category><![CDATA[pku1160]]></category>
		<category><![CDATA[动态规划]]></category>

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		<description><![CDATA[package pku1160; /*在一条高速公路边上有V个村庄，用一条坐标轴来描述这条公路，每个村庄的坐标 [&#8230;]]]></description>
				<content:encoded><![CDATA[<p>package pku1160;</p>
<p>/*在一条高速公路边上有V个村庄，用一条坐标轴来描述这条公路，每个村庄的坐标各不相同，<br />
* 且都是整数。两个村庄间的距离用他们的坐标值差的绝对值表示。现在要在这些村庄中选<br />
* 出P个建立邮局，邮局建立在村庄里，每个村庄使用离他最近的那个邮局。求一种建设方案，<br />
* 使得所有村庄到各自所使用的邮局的距离总和最小。<br />
*<br />
* 算法: 动态规划 */</p>

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</pre></td><td class="code"><pre class="java" style="font-family:monospace;"><span style="color: #000000; font-weight: bold;">import</span> <span style="color: #006699;">java.util.*</span><span style="color: #339933;">;</span>
<span style="color: #000000; font-weight: bold;">public</span> <span style="color: #000000; font-weight: bold;">class</span> Main <span style="color: #009900;">&#123;</span>
&nbsp;
<span style="color: #666666; font-style: italic;">/*Cost[j,i]表示安排前i个邮局给前j个村庄使用
   * D[i,j]表示在第i个到第j个村庄中建立一个邮局得到的最短距离总和。
   * D[a,b]可以利用关系式d[a,a]=0, D[a,b]=D[a,b-1]+x[b]-x[(a+b)/2]表示*/</span>
<span style="color: #000000; font-weight: bold;">public</span> <span style="color: #000000; font-weight: bold;">static</span> <span style="color: #000066; font-weight: bold;">void</span> main<span style="color: #009900;">&#40;</span><span style="color: #003399;">String</span><span style="color: #009900;">&#91;</span><span style="color: #009900;">&#93;</span> args<span style="color: #009900;">&#41;</span> <span style="color: #009900;">&#123;</span>
   <span style="color: #666666; font-style: italic;">// TODO Auto-generated method stub</span>
   Scanner cin <span style="color: #339933;">=</span> <span style="color: #000000; font-weight: bold;">new</span> Scanner<span style="color: #009900;">&#40;</span><span style="color: #003399;">System</span>.<span style="color: #006633;">in</span><span style="color: #009900;">&#41;</span><span style="color: #339933;">;</span>
   <span style="color: #000066; font-weight: bold;">int</span> n, m<span style="color: #339933;">;</span>
   n <span style="color: #339933;">=</span> cin.<span style="color: #006633;">nextInt</span><span style="color: #009900;">&#40;</span><span style="color: #009900;">&#41;</span><span style="color: #339933;">;</span>
   m <span style="color: #339933;">=</span> cin.<span style="color: #006633;">nextInt</span><span style="color: #009900;">&#40;</span><span style="color: #009900;">&#41;</span><span style="color: #339933;">;</span>
   <span style="color: #000066; font-weight: bold;">int</span><span style="color: #009900;">&#91;</span><span style="color: #009900;">&#93;</span> x <span style="color: #339933;">=</span> <span style="color: #000000; font-weight: bold;">new</span> <span style="color: #000066; font-weight: bold;">int</span><span style="color: #009900;">&#91;</span>n <span style="color: #339933;">+</span> <span style="color: #cc66cc;">1</span><span style="color: #009900;">&#93;</span><span style="color: #339933;">;</span>
   <span style="color: #000066; font-weight: bold;">int</span><span style="color: #009900;">&#91;</span><span style="color: #009900;">&#93;</span><span style="color: #009900;">&#91;</span><span style="color: #009900;">&#93;</span> d <span style="color: #339933;">=</span> <span style="color: #000000; font-weight: bold;">new</span> <span style="color: #000066; font-weight: bold;">int</span><span style="color: #009900;">&#91;</span>n <span style="color: #339933;">+</span> <span style="color: #cc66cc;">2</span><span style="color: #009900;">&#93;</span><span style="color: #009900;">&#91;</span>n <span style="color: #339933;">+</span> <span style="color: #cc66cc;">2</span><span style="color: #009900;">&#93;</span><span style="color: #339933;">;</span>
   <span style="color: #000066; font-weight: bold;">int</span><span style="color: #009900;">&#91;</span><span style="color: #009900;">&#93;</span><span style="color: #009900;">&#91;</span><span style="color: #009900;">&#93;</span> cost <span style="color: #339933;">=</span> <span style="color: #000000; font-weight: bold;">new</span> <span style="color: #000066; font-weight: bold;">int</span><span style="color: #009900;">&#91;</span>n <span style="color: #339933;">+</span> <span style="color: #cc66cc;">2</span><span style="color: #009900;">&#93;</span><span style="color: #009900;">&#91;</span>n <span style="color: #339933;">+</span> <span style="color: #cc66cc;">2</span><span style="color: #009900;">&#93;</span><span style="color: #339933;">;</span>
   <span style="color: #000000; font-weight: bold;">for</span> <span style="color: #009900;">&#40;</span><span style="color: #000066; font-weight: bold;">int</span> i <span style="color: #339933;">=</span> <span style="color: #cc66cc;">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>
    x<span style="color: #009900;">&#91;</span>i<span style="color: #009900;">&#93;</span> <span style="color: #339933;">=</span> cin.<span style="color: #006633;">nextInt</span><span style="color: #009900;">&#40;</span><span style="color: #009900;">&#41;</span><span style="color: #339933;">;</span>
   <span style="color: #000000; font-weight: bold;">for</span> <span style="color: #009900;">&#40;</span><span style="color: #000066; font-weight: bold;">int</span> i <span style="color: #339933;">=</span> <span style="color: #cc66cc;">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><span style="color: #009900;">&#123;</span> 
    <span style="color: #000000; font-weight: bold;">for</span> <span style="color: #009900;">&#40;</span><span style="color: #000066; font-weight: bold;">int</span> j <span style="color: #339933;">=</span> <span style="color: #cc66cc;">1</span><span style="color: #339933;">;</span> j <span style="color: #339933;">&lt;=</span> n<span style="color: #339933;">;</span> j<span style="color: #339933;">++</span><span style="color: #009900;">&#41;</span><span style="color: #009900;">&#123;</span>
     <span style="color: #000000; font-weight: bold;">if</span> <span style="color: #009900;">&#40;</span>i <span style="color: #339933;">&gt;=</span> j<span style="color: #009900;">&#41;</span>
      d<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: #cc66cc;">0</span><span style="color: #339933;">;</span>
     <span style="color: #000000; font-weight: bold;">else</span>
      d<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> d<span style="color: #009900;">&#91;</span>i<span style="color: #009900;">&#93;</span><span style="color: #009900;">&#91;</span>j <span style="color: #339933;">-</span> <span style="color: #cc66cc;">1</span><span style="color: #009900;">&#93;</span> <span style="color: #339933;">+</span> x<span style="color: #009900;">&#91;</span>j<span style="color: #009900;">&#93;</span> <span style="color: #339933;">-</span> x<span style="color: #009900;">&#91;</span><span style="color: #009900;">&#40;</span>i <span style="color: #339933;">+</span> j<span style="color: #009900;">&#41;</span> <span style="color: #339933;">/</span> <span style="color: #cc66cc;">2</span><span style="color: #009900;">&#93;</span><span style="color: #339933;">;</span> 
    <span style="color: #009900;">&#125;</span>
   <span style="color: #009900;">&#125;</span>
   <span style="color: #000000; font-weight: bold;">for</span> <span style="color: #009900;">&#40;</span><span style="color: #000066; font-weight: bold;">int</span> i <span style="color: #339933;">=</span> <span style="color: #cc66cc;">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>
    cost<span style="color: #009900;">&#91;</span>i<span style="color: #009900;">&#93;</span><span style="color: #009900;">&#91;</span><span style="color: #cc66cc;">1</span><span style="color: #009900;">&#93;</span> <span style="color: #339933;">=</span> d<span style="color: #009900;">&#91;</span><span style="color: #cc66cc;">1</span><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: #000000; font-weight: bold;">for</span> <span style="color: #009900;">&#40;</span><span style="color: #000066; font-weight: bold;">int</span> i <span style="color: #339933;">=</span> <span style="color: #cc66cc;">2</span><span style="color: #339933;">;</span> i <span style="color: #339933;">&lt;=</span> m<span style="color: #339933;">;</span> i<span style="color: #339933;">++</span> <span style="color: #009900;">&#41;</span><span style="color: #009900;">&#123;</span> 
    <span style="color: #000000; font-weight: bold;">for</span> <span style="color: #009900;">&#40;</span><span style="color: #000066; font-weight: bold;">int</span> j <span style="color: #339933;">=</span> i <span style="color: #339933;">+</span> <span style="color: #cc66cc;">1</span><span style="color: #339933;">;</span> j <span style="color: #339933;">&lt;=</span> n<span style="color: #339933;">;</span> j<span style="color: #339933;">++</span><span style="color: #009900;">&#41;</span><span style="color: #009900;">&#123;</span>
     <span style="color: #000066; font-weight: bold;">int</span> tmp <span style="color: #339933;">=</span> <span style="color: #003399;">Integer</span>.<span style="color: #006633;">MAX_VALUE</span><span style="color: #339933;">;</span>
     <span style="color: #000000; font-weight: bold;">for</span> <span style="color: #009900;">&#40;</span><span style="color: #000066; font-weight: bold;">int</span> k <span style="color: #339933;">=</span> i <span style="color: #339933;">-</span> <span style="color: #cc66cc;">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>
      <span style="color: #000000; font-weight: bold;">if</span> <span style="color: #009900;">&#40;</span> tmp <span style="color: #339933;">&gt;</span> cost<span style="color: #009900;">&#91;</span>k<span style="color: #009900;">&#93;</span><span style="color: #009900;">&#91;</span>i <span style="color: #339933;">-</span> <span style="color: #cc66cc;">1</span><span style="color: #009900;">&#93;</span> <span style="color: #339933;">+</span> d<span style="color: #009900;">&#91;</span>k <span style="color: #339933;">+</span> <span style="color: #cc66cc;">1</span><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>
       tmp <span style="color: #339933;">=</span> cost<span style="color: #009900;">&#91;</span>k<span style="color: #009900;">&#93;</span><span style="color: #009900;">&#91;</span>i <span style="color: #339933;">-</span> <span style="color: #cc66cc;">1</span><span style="color: #009900;">&#93;</span> <span style="color: #339933;">+</span> d<span style="color: #009900;">&#91;</span>k <span style="color: #339933;">+</span> <span style="color: #cc66cc;">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> <span style="color: #666666; font-style: italic;">// Cost[n,m] = min{Cost[i,m-1]+D[i+1,n]}，i=m-1,m,…,n-1。</span>
     <span style="color: #009900;">&#125;</span>
     cost<span style="color: #009900;">&#91;</span>j<span style="color: #009900;">&#93;</span><span style="color: #009900;">&#91;</span>i<span style="color: #009900;">&#93;</span> <span style="color: #339933;">=</span> tmp<span style="color: #339933;">;</span>
    <span style="color: #009900;">&#125;</span>
   <span style="color: #009900;">&#125;</span>
   <span style="color: #003399;">System</span>.<span style="color: #006633;">out</span>.<span style="color: #006633;">println</span><span style="color: #009900;">&#40;</span>cost<span style="color: #009900;">&#91;</span>n<span style="color: #009900;">&#93;</span><span style="color: #009900;">&#91;</span>m<span style="color: #009900;">&#93;</span><span style="color: #009900;">&#41;</span><span style="color: #339933;">;</span>
<span style="color: #009900;">&#125;</span>
&nbsp;
<span style="color: #009900;">&#125;</span></pre></td></tr></table></div>

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