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	<title>Sharpmark &#124; 刘炯的博客 &#187; 具体数学</title>
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		<title>具体数学 &#8211; 约瑟夫问题</title>
		<link>http://liujiong.com/blog/posts/concrete-mathematics-the-josephus-problem/</link>
		<comments>http://liujiong.com/blog/posts/concrete-mathematics-the-josephus-problem/#comments</comments>
		<pubDate>Tue, 17 Oct 2006 08:11:00 +0000</pubDate>
		<dc:creator>sharpmark</dc:creator>
				<category><![CDATA[个人作品集]]></category>
		<category><![CDATA[文摘笔记]]></category>
		<category><![CDATA[计算机科学]]></category>
		<category><![CDATA[latex]]></category>
		<category><![CDATA[具体数学]]></category>
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		<category><![CDATA[翻译]]></category>

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		<description><![CDATA[It seems a lot of stuff is attributed to Gauss&#8230; either he was really smart or he has great press agent. May be he just had a magnetic personality. 最近在看《具体数学 Concrete mathematics》，这是一本值得计算机相关专业任何... ]]></description>
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It seems a lot of stuff is attributed to Gauss&#8230;<br />
either he was really smart or he has great press agent.<br />
May be he just had a magnetic personality.</p></blockquote>
<p>最近在看《具体数学 Concrete mathematics》，这是一本值得计算机相关专业任何年级的同学阅读的书。<br />
第一章通过三个问题:The Tower of Hanoi; Lines in the Plane; The Josephus Problem. 前两个问题以前学习的深度已经够了，所以看了没有太大感觉，Josephus Problem的解决给了我很大的震撼。一个看似平常而无捷径的问题，通过用二进制表示，最终居然只要用一个循环移位就能解决。之后又扩展到 Josephus方程一般形式。其间，他的解题方法论很重要，以及其严谨的思路和发散的思维。<br />
现列出书中第一章使用的解题方法：</p>
<blockquote>
<ol>
<li> Look at small cases. This gives us insight into the problem and helps us in stages 2 and 3.</li>
<li>Find and prove a mathematical expression for the quantity of interest.</li>
<li>Find and prove a closed form for our mathematical expression.</li>
</ol>
</blockquote>
<p>已经翻译完成The Josephus Problem小节。对此感兴趣的<a href="http://sharpmark.googlecode.com/files/josephus.pdf">点此下载</a>(版本1.1.1，2007-12-23)。</p>
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