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	<title>潘锦的空间 &#187; pku1088</title>
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		<title>滑雪 pku1088 动态规划</title>
		<link>https://www.phppan.com/2009/08/pku1088/</link>
		<comments>https://www.phppan.com/2009/08/pku1088/#comments</comments>
		<pubDate>Tue, 25 Aug 2009 14:46:30 +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[pku1088]]></category>
		<category><![CDATA[动态规划]]></category>
		<category><![CDATA[滑雪]]></category>

		<guid isPermaLink="false">http://www.phppan.com/?p=118</guid>
		<description><![CDATA[【Description】 Michael喜欢滑雪百这并不奇怪， 因为滑雪的确很刺激。可是为了获得速度，滑的区 [&#8230;]]]></description>
				<content:encoded><![CDATA[<p>【Description】<br />
Michael喜欢滑雪百这并不奇怪， 因为滑雪的确很刺激。可是为了获得速度，滑的区域必须向下倾斜，而且当你滑到坡底，你不得不再次走上坡或者等待升降机来载你。Michael想知道载一个区域中最长底滑坡。区域由一个二维数组给出。数组的每个数字代表点的高度。下面是一个例子 </p>
<p> 1   2   3   4 5<br />
16 17 18 19 6<br />
15 24 25 20 7<br />
14 23 22 21 8<br />
13 12 11 10 9</p>
<p>一个人可以从某个点滑向上下左右相邻四个点之一，当且仅当高度减小。在上面的例子中，一条可滑行的滑坡为24-17-16-1。当然25-24-23-&#8230;-3-2-1更长。事实上，这是最长的一条。</p>
<p>【Input】<br />
输入的第一行表示区域的行数R和列数C(1 <= R,C <= 100)。下面是R行，每行有C个整数，代表高度h，0<=h<=10000。

【Output】
输出最长区域的长度。

【Sample Input】

5 5
1 2 3 4 5
16 17 18 19 6
15 24 25 20 7
14 23 22 21 8
13 12 11 10 9


【Sample Output】
25


【Source】
SHTSC 2002



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</pre></td><td class="code"><pre class="java" style="font-family:monospace;"><span style="color: #000000; font-weight: bold;">package</span> <span style="color: #006699;">pku1088</span><span style="color: #339933;">;</span>
&nbsp;
<span style="color: #008000; font-style: italic; font-weight: bold;">/**深度搜索+备忘录方法 / 动态规划   参考了pku牛人的解题报告*/</span>
<span style="color: #000000; font-weight: bold;">import</span> <span style="color: #006699;">java.util.*</span><span style="color: #339933;">;</span>
&nbsp;
<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: #008000; font-style: italic; font-weight: bold;">/**
   * @param args
   */</span>
<span style="color: #000000; font-weight: bold;">private</span> <span style="color: #000000; font-weight: bold;">static</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> a <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><span style="color: #cc66cc;">101</span><span style="color: #009900;">&#93;</span><span style="color: #009900;">&#91;</span><span style="color: #cc66cc;">101</span><span style="color: #009900;">&#93;</span><span style="color: #339933;">;</span>
&nbsp;
<span style="color: #000000; font-weight: bold;">private</span> <span style="color: #000000; font-weight: bold;">static</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> b <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><span style="color: #cc66cc;">101</span><span style="color: #009900;">&#93;</span><span style="color: #009900;">&#91;</span><span style="color: #cc66cc;">101</span><span style="color: #009900;">&#93;</span><span style="color: #339933;">;</span><span style="color: #666666; font-style: italic;">// 备忘录</span>
&nbsp;
<span style="color: #000000; font-weight: bold;">private</span> <span style="color: #000000; font-weight: bold;">static</span> <span style="color: #000066; font-weight: bold;">boolean</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> flag <span style="color: #339933;">=</span> <span style="color: #000000; font-weight: bold;">new</span> <span style="color: #000066; font-weight: bold;">boolean</span><span style="color: #009900;">&#91;</span><span style="color: #cc66cc;">101</span><span style="color: #009900;">&#93;</span><span style="color: #009900;">&#91;</span><span style="color: #cc66cc;">101</span><span style="color: #009900;">&#93;</span><span style="color: #339933;">;</span>
&nbsp;
<span style="color: #000000; font-weight: bold;">private</span> <span style="color: #000000; font-weight: bold;">static</span> <span style="color: #000066; font-weight: bold;">int</span> r, c<span style="color: #339933;">;</span>
&nbsp;
<span style="color: #000000; font-weight: bold;">private</span> <span style="color: #000000; font-weight: bold;">static</span> <span style="color: #000066; font-weight: bold;">int</span><span style="color: #009900;">&#91;</span><span style="color: #009900;">&#93;</span> tempx <span style="color: #339933;">=</span> <span style="color: #009900;">&#123;</span> <span style="color: #cc66cc;">1</span>, <span style="color: #cc66cc;">0</span>, <span style="color: #339933;">-</span><span style="color: #cc66cc;">1</span>, <span style="color: #cc66cc;">0</span> <span style="color: #009900;">&#125;</span><span style="color: #339933;">;</span>
&nbsp;
<span style="color: #000000; font-weight: bold;">private</span> <span style="color: #000000; font-weight: bold;">static</span> <span style="color: #000066; font-weight: bold;">int</span><span style="color: #009900;">&#91;</span><span style="color: #009900;">&#93;</span> tempy <span style="color: #339933;">=</span> <span style="color: #009900;">&#123;</span> <span style="color: #cc66cc;">0</span>, <span style="color: #339933;">-</span><span style="color: #cc66cc;">1</span>, <span style="color: #cc66cc;">0</span>, <span style="color: #cc66cc;">1</span> <span style="color: #009900;">&#125;</span><span style="color: #339933;">;</span>
&nbsp;
<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;">int</span> trydo<span style="color: #009900;">&#40;</span><span style="color: #000066; font-weight: bold;">int</span> x, <span style="color: #000066; font-weight: bold;">int</span> y<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>flag<span style="color: #009900;">&#91;</span>x<span style="color: #009900;">&#93;</span><span style="color: #009900;">&#91;</span>y<span style="color: #009900;">&#93;</span><span style="color: #009900;">&#41;</span><span style="color: #666666; font-style: italic;">// 如果已经有了,直接输出,备忘录方法快就快在这里</span>
    <span style="color: #000000; font-weight: bold;">return</span> b<span style="color: #009900;">&#91;</span>x<span style="color: #009900;">&#93;</span><span style="color: #009900;">&#91;</span>y<span style="color: #009900;">&#93;</span><span style="color: #339933;">;</span>
   <span style="color: #000066; font-weight: bold;">int</span> max <span style="color: #339933;">=</span> <span style="color: #cc66cc;">1</span>, temp<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;">0</span><span style="color: #339933;">;</span> i <span style="color: #339933;">&lt;</span> <span style="color: #cc66cc;">4</span><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: #666666; font-style: italic;">// 四个方向</span>
    <span style="color: #000066; font-weight: bold;">int</span> xx <span style="color: #339933;">=</span> x <span style="color: #339933;">+</span> tempx<span style="color: #009900;">&#91;</span>i<span style="color: #009900;">&#93;</span><span style="color: #339933;">;</span>
    <span style="color: #000066; font-weight: bold;">int</span> yy <span style="color: #339933;">=</span> y <span style="color: #339933;">+</span> tempy<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;">if</span> <span style="color: #009900;">&#40;</span>xx <span style="color: #339933;">&gt;=</span> <span style="color: #cc66cc;">0</span> <span style="color: #339933;">&amp;&amp;</span> xx <span style="color: #339933;">&lt;</span> r <span style="color: #339933;">&amp;&amp;</span> yy <span style="color: #339933;">&gt;=</span> <span style="color: #cc66cc;">0</span> <span style="color: #339933;">&amp;&amp;</span> yy <span style="color: #339933;">&lt;</span> c<span style="color: #009900;">&#41;</span> <span style="color: #009900;">&#123;</span><span style="color: #666666; font-style: italic;">// 判断是否出界                                                           </span>
     <span style="color: #000000; font-weight: bold;">if</span> <span style="color: #009900;">&#40;</span>a<span style="color: #009900;">&#91;</span>xx<span style="color: #009900;">&#93;</span><span style="color: #009900;">&#91;</span>yy<span style="color: #009900;">&#93;</span> <span style="color: #339933;">&lt;</span> a<span style="color: #009900;">&#91;</span>x<span style="color: #009900;">&#93;</span><span style="color: #009900;">&#91;</span>y<span style="color: #009900;">&#93;</span><span style="color: #009900;">&#41;</span> <span style="color: #009900;">&#123;</span><span style="color: #666666; font-style: italic;">// 如果要到的点到本点低</span>
      temp <span style="color: #339933;">=</span> trydo<span style="color: #009900;">&#40;</span>xx, yy<span style="color: #009900;">&#41;</span><span style="color: #339933;">;</span><span style="color: #666666; font-style: italic;">// 走下一个点</span>
      <span style="color: #000000; font-weight: bold;">if</span> <span style="color: #009900;">&#40;</span>temp <span style="color: #339933;">+</span> <span style="color: #cc66cc;">1</span> <span style="color: #339933;">&gt;</span> max<span style="color: #009900;">&#41;</span><span style="color: #666666; font-style: italic;">//</span>
       max <span style="color: #339933;">=</span> temp <span style="color: #339933;">+</span> <span style="color: #cc66cc;">1</span><span style="color: #339933;">;</span>
     <span style="color: #009900;">&#125;</span>
    <span style="color: #009900;">&#125;</span>
   <span style="color: #009900;">&#125;</span>
   flag<span style="color: #009900;">&#91;</span>x<span style="color: #009900;">&#93;</span><span style="color: #009900;">&#91;</span>y<span style="color: #009900;">&#93;</span> <span style="color: #339933;">=</span> <span style="color: #000066; font-weight: bold;">true</span><span style="color: #339933;">;</span><span style="color: #666666; font-style: italic;">// 已经走过</span>
   b<span style="color: #009900;">&#91;</span>x<span style="color: #009900;">&#93;</span><span style="color: #009900;">&#91;</span>y<span style="color: #009900;">&#93;</span> <span style="color: #339933;">=</span> max<span style="color: #339933;">;</span><span style="color: #666666; font-style: italic;">// 存入备忘录</span>
   <span style="color: #000000; font-weight: bold;">return</span> max<span style="color: #339933;">;</span>
&nbsp;
<span style="color: #009900;">&#125;</span>
&nbsp;
<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>
   r <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>
   c <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;">0</span><span style="color: #339933;">;</span> i <span style="color: #339933;">&lt;</span> r<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;">0</span><span style="color: #339933;">;</span> j <span style="color: #339933;">&lt;</span> c<span style="color: #339933;">;</span> j<span style="color: #339933;">++</span><span style="color: #009900;">&#41;</span> <span style="color: #009900;">&#123;</span>
     a<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> cin.<span style="color: #006633;">nextInt</span><span style="color: #009900;">&#40;</span><span style="color: #009900;">&#41;</span><span style="color: #339933;">;</span>
     b<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>
     flag<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: #000066; font-weight: bold;">false</span><span style="color: #339933;">;</span>
    <span style="color: #009900;">&#125;</span>
   <span style="color: #009900;">&#125;</span>
   <span style="color: #000066; font-weight: bold;">int</span> max <span style="color: #339933;">=</span> <span style="color: #cc66cc;">0</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;">0</span><span style="color: #339933;">;</span> i <span style="color: #339933;">&lt;</span> r<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: #666666; font-style: italic;">// 生成每个点的最大</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;">0</span><span style="color: #339933;">;</span> j <span style="color: #339933;">&lt;</span> c<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>trydo<span style="color: #009900;">&#40;</span>i, j<span style="color: #009900;">&#41;</span> <span style="color: #339933;">&gt;</span> max<span style="color: #009900;">&#41;</span>
      max <span style="color: #339933;">=</span> trydo<span style="color: #009900;">&#40;</span>i, j<span style="color: #009900;">&#41;</span><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>max<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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