关于最少步复原的问题，需要论证

ggglgq

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原帖由 <I>咖啡味的茶</I> 于 2008-8-19 20:27 发表 <A href="http://bbs.mf8-china.com/redirect.php?goto=findpost&amp;pid=217951&amp;ptid=12817" target=_blank><IMG alt="" src="http://bbs.mf8-china.com/images/common/back.gif" border=0></A> </P>
<P>（我所述的是纯色<SPAN class=t_tag onclick=tagshow(event) href="tag.php?name=%C4%A7%B7%BD">魔方</SPAN>）我列出几个我认为是正确的命题，但是暂时没有给出证明，这里给大家看看： 1.你用K步可以<SPAN class=t_tag onclick=tagshow(event) href="tag.php?name=%BB%B9%D4%AD">还原</SPAN>一个给定的<SPAN class=t_tag onclick=tagshow(event) href="tag.php?name=%C4%A7%B7%BD">魔方</SPAN>（你已经知道方法）。如果做“原第N步，原第N+1步……，原第K步，原第一步，原第二……原第N-1步”可以<SPAN class=t_tag onclick=tagshow(event) href="tag.php?name=%BB%B9%D4%AD">还原</SPAN>给定的<SPAN class=t_tag onclick=tagshow(event) href="tag.php?name=%C4%A7%B7%BD">魔方</SPAN>的话，那么，最少<SPAN class=t_tag onclick=tagshow(event) href="tag.php?name=%BB%B9%D4%AD">还原</SPAN>这个<SPAN class=t_tag onclick=tagshow(event) href="tag.php?name=%C4%A7%B7%BD">魔方</SPAN>的步骤肯定小于K。 2.最少步骤<SPAN class=t_tag onclick=tagshow(event) href="tag.php?name=%BB%B9%D4%AD">还原</SPAN><SPAN class=t_tag onclick=tagshow(event) href="tag.php?name=%C4%A7%B7%BD">魔方</SPAN>，不一定只有一种复原方法。请大家来看一下。</P>
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<P>&nbsp; <BR>&nbsp; <BR>&nbsp; <BR>&nbsp;&nbsp;&nbsp; 一、第一步，第二步，……第N步……第K步，复原；<BR>&nbsp; <BR>&nbsp;&nbsp;&nbsp; 二、改一下“大次序”，原第N步，原第N＋1步，……原第K步，原第一步，原第二步，……原第N－1步，也复原；<BR>&nbsp; <BR>&nbsp;&nbsp;&nbsp; <FONT color=blue><STRONG>这是 <FONT size=6>定理</FONT>！ 也是循环变换理论的基石。 但光满足条件 一、二 却 不一定<BR>&nbsp; <BR></STRONG>是<STRONG>“循环变换”。<BR></STRONG></FONT>&nbsp; <BR>&nbsp; <BR>&nbsp;&nbsp;&nbsp; 三、那么，还原这个魔方的最少步骤数肯定小于K。<BR>&nbsp; <BR>&nbsp;&nbsp;&nbsp; <FONT color=blue><STRONG>不一定！</STRONG></FONT><BR>&nbsp; <BR>&nbsp; <BR>&nbsp; <BR>&nbsp;&nbsp;&nbsp; 2.最少步骤还原魔方，不一定只有一种复原方法。<BR>&nbsp; <BR>&nbsp; <BR>&nbsp;&nbsp;&nbsp; <FONT color=blue><STRONG>不错！</STRONG></FONT><BR>&nbsp; <BR>&nbsp; <BR>&nbsp; </P>

ggglgq

<P>&nbsp; <BR>&nbsp; <BR>&nbsp; <BR>&nbsp;&nbsp;&nbsp; 可能 earthengine 先生理解 我的 循环变换 有误。<BR>&nbsp; <BR>&nbsp;&nbsp;&nbsp; <BR>&nbsp; <BR>&nbsp;&nbsp;&nbsp; 当时楼主的帖子写得让人看不懂，我是按 乌木 先生 4 楼的写法这样理解的：<BR>&nbsp; <BR>&nbsp;&nbsp; <BR>&nbsp;&nbsp;&nbsp; 如果 对 <FONT color=blue><STRONG>还原的魔方</STRONG></FONT> 做<BR>&nbsp; <BR>&nbsp;&nbsp;&nbsp; 一、第一步，第二步，……第N步……第K步，复原；<BR>&nbsp; <BR>&nbsp;&nbsp;&nbsp; 那么 对 <FONT color=blue><STRONG>还原的魔方</STRONG></FONT> 再做<BR>&nbsp; <BR>&nbsp;&nbsp;&nbsp; 二、改一下“大次序”，原第N步，原第N＋1步，……原第K步，原第一步，原第二步，……原第N－1步，也复原；<BR>&nbsp;&nbsp; <BR>&nbsp; <BR>&nbsp;&nbsp;<FONT color=blue><STRONG>&nbsp; 如果楼主是这个意思，那这是群论中的一个简单定理了</STRONG></FONT>！<BR>&nbsp; <BR>&nbsp; <BR>&nbsp;&nbsp;&nbsp; <BR>&nbsp; <BR>&nbsp; </P>

ggglgq

&nbsp;&nbsp;&nbsp; <BR>&nbsp; <BR>&nbsp; <BR>&nbsp; <BR>&nbsp;&nbsp;&nbsp; 还是举例说明吧：<BR>&nbsp; <BR>&nbsp;&nbsp;&nbsp; 比如：对 正六面体三阶<FONT color=blue><STRONG>还原</STRONG></FONT>的魔方 做变换<BR>&nbsp; <BR>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; F' L'F R F'L F L U L'U'R'U L U'L' <BR>&nbsp; <BR>&nbsp;&nbsp;&nbsp; 使得正六面体三阶魔方还原。<BR>&nbsp; <BR>&nbsp;&nbsp;&nbsp; 那么 对 正六面体三阶<FONT color=blue><STRONG>还原</STRONG></FONT>的魔方 做变换<BR>&nbsp; <BR>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; L'F R F'L F L U L'U'R'U L U'L' F' <BR>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <BR>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; F R F'L F L U L'U'R'U L U'L' F' L'&nbsp; <BR>&nbsp;&nbsp; <BR>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; ...............................<BR>&nbsp; <BR>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <BR>&nbsp;&nbsp;&nbsp;&nbsp; 必然也都使得正六面体三阶魔方<FONT color=blue><STRONG>还原</STRONG></FONT>。 您可以自己试试。我就不发 Java 了。<BR>&nbsp; <BR>&nbsp; <BR>&nbsp; <BR>&nbsp;