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	<title>潘锦的空间 &#187; 双子塔</title>
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		<title>双子塔</title>
		<link>https://www.phppan.com/2009/09/the-petronastowers/</link>
		<comments>https://www.phppan.com/2009/09/the-petronastowers/#comments</comments>
		<pubDate>Tue, 01 Sep 2009 23:33:15 +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[动态规划]]></category>
		<category><![CDATA[双子塔]]></category>

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		<description><![CDATA[【Description】 为了纪念9.11,大家决定重修双子塔. 材料是立方体的水晶{这么阔！}， 问对于给 [&#8230;]]]></description>
				<content:encoded><![CDATA[<p>【Description】<br />
为了纪念9.11,大家决定重修双子塔. 材料是立方体的水晶{这么阔！}， 问对于给定的水晶，可否修起等高的 双子塔(高度&lt;＝2000).</p>
<p>【Input】<br />
第一个数字N(100000以内)代表水晶的个数.<br />
接下来N行每行一个数(&lt;1000),代表水晶体的边长.</p>
<p>【Output】<br />
如果可以建成就输入高度，不能建则输出0.</p>
<p>【Sample Input】<br />
4<br />
11<br />
11<br />
11<br />
11</p>
<p>【Sample Output】<br />
22</p>
<p>【算法描述】</p>
<p>动态规划。<br />
由于这道题目已经给出了相等的高度不会大于2000，所有可以用装箱问题的模型来做这个道题。<br />
【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>
&nbsp;
<span style="color: #993333;">int</span> main<span style="color: #009900;">&#40;</span><span style="color: #009900;">&#41;</span>
<span style="color: #009900;">&#123;</span>
       <span style="color: #993333;">int</span> n<span style="color: #339933;">,</span> i<span style="color: #339933;">,</span> j<span style="color: #339933;">,</span> a<span style="color: #009900;">&#91;</span><span style="color: #0000dd;">3000</span><span style="color: #009900;">&#93;</span><span style="color: #339933;">;</span> <span style="color: #666666; font-style: italic;">//a[i]存储是可以搭建的塔高为i时的方法种数。</span>
     <span style="color: #993333;">int</span> b<span style="color: #009900;">&#91;</span><span style="color: #0000dd;">100001</span><span style="color: #009900;">&#93;</span><span style="color: #339933;">,</span> sum <span style="color: #339933;">=</span> <span style="color: #0000dd;">0</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;">,</span> <span style="color: #339933;">&amp;</span>n<span style="color: #009900;">&#41;</span><span style="color: #339933;">;</span>
&nbsp;
       <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>
       <span style="color: #009900;">&#123;</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;">,</span> <span style="color: #339933;">&amp;</span>b<span style="color: #009900;">&#91;</span>i<span style="color: #009900;">&#93;</span><span style="color: #009900;">&#41;</span><span style="color: #339933;">;</span>
              sum <span style="color: #339933;">+=</span> b<span style="color: #009900;">&#91;</span>i<span style="color: #009900;">&#93;</span><span style="color: #339933;">;</span>
       <span style="color: #009900;">&#125;</span>     
&nbsp;
       <span style="color: #000066;">memset</span><span style="color: #009900;">&#40;</span>a<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>a<span style="color: #009900;">&#41;</span><span style="color: #009900;">&#41;</span><span style="color: #339933;">;</span>
       sum <span style="color: #339933;">=</span> sum <span style="color: #339933;">/</span> <span style="color: #0000dd;">2</span><span style="color: #339933;">;</span>
       a<span style="color: #009900;">&#91;</span><span style="color: #0000dd;">0</span><span style="color: #009900;">&#93;</span> <span style="color: #339933;">=</span> <span style="color: #0000dd;">1</span><span style="color: #339933;">;</span>
&nbsp;
       <span style="color: #b1b100;">if</span> <span style="color: #009900;">&#40;</span>sum <span style="color: #339933;">&gt;</span> <span style="color: #0000dd;">2000</span><span style="color: #009900;">&#41;</span>
              sum <span style="color: #339933;">=</span> <span style="color: #0000dd;">2000</span><span style="color: #339933;">;</span>
&nbsp;
       <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><span style="color: #666666; font-style: italic;">//对于每个立方体</span>
       <span style="color: #009900;">&#123;</span>
              <span style="color: #b1b100;">for</span> <span style="color: #009900;">&#40;</span>j <span style="color: #339933;">=</span> sum <span style="color: #339933;">-</span> b<span style="color: #009900;">&#91;</span>i<span style="color: #009900;">&#93;</span><span style="color: #339933;">;</span> j <span style="color: #339933;">&gt;=</span> <span style="color: #0000dd;">0</span><span style="color: #339933;">;</span> j<span style="color: #339933;">--</span><span style="color: #009900;">&#41;</span><span style="color: #666666; font-style: italic;">//从后面往前面找已经存在的高度。</span>
              <span style="color: #009900;">&#123;</span>
                     <span style="color: #b1b100;">if</span> <span style="color: #009900;">&#40;</span>a<span style="color: #009900;">&#91;</span>j<span style="color: #009900;">&#93;</span> <span style="color: #339933;">&gt;=</span> <span style="color: #0000dd;">1</span><span style="color: #009900;">&#41;</span>
                            a<span style="color: #009900;">&#91;</span>j <span style="color: #339933;">+</span> b<span style="color: #009900;">&#91;</span>i<span style="color: #009900;">&#93;</span><span style="color: #009900;">&#93;</span><span style="color: #339933;">++;</span><span style="color: #666666; font-style: italic;">//这里是与装箱问题不同的地方。</span>
              <span style="color: #009900;">&#125;</span>
       <span style="color: #009900;">&#125;</span>
&nbsp;
       <span style="color: #b1b100;">for</span> <span style="color: #009900;">&#40;</span>i <span style="color: #339933;">=</span> sum<span style="color: #339933;">;</span> i <span style="color: #339933;">&gt;=</span> <span style="color: #0000dd;">0</span><span style="color: #339933;">;</span> i<span style="color: #339933;">--</span><span style="color: #009900;">&#41;</span> <span style="color: #666666; font-style: italic;">//找最大值</span>
              <span style="color: #b1b100;">if</span> <span style="color: #009900;">&#40;</span>a<span style="color: #009900;">&#91;</span>i<span style="color: #009900;">&#93;</span> <span style="color: #339933;">&gt;</span> <span style="color: #0000dd;">1</span><span style="color: #009900;">&#41;</span>
                     <span style="color: #000000; font-weight: bold;">break</span><span style="color: #339933;">;</span>
&nbsp;
       <span style="color: #b1b100;">if</span> <span style="color: #009900;">&#40;</span>i <span style="color: #339933;">&lt;=</span> <span style="color: #0000dd;">0</span><span style="color: #009900;">&#41;</span><span style="color: #666666; font-style: italic;">//特殊情况，比赛时就因为这里所以错了两次。切记切记！</span>
              <span style="color: #000066;">printf</span><span style="color: #009900;">&#40;</span><span style="color: #ff0000;">&quot;0<span style="color: #000099; font-weight: bold;">\n</span>&quot;</span><span style="color: #009900;">&#41;</span><span style="color: #339933;">;</span>
       <span style="color: #b1b100;">else</span>
           <span style="color: #000066;">printf</span><span style="color: #009900;">&#40;</span><span style="color: #ff0000;">&quot;%d<span style="color: #000099; font-weight: bold;">\n</span>&quot;</span><span style="color: #339933;">,</span> i<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>
&nbsp;
<span style="color: #009900;">&#125;</span></pre></td></tr></table></div>

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