EMC的一道面试题

kaola103

有1000桶酒，其中1桶有毒。而一旦吃了，毒性会在1周后发作。现在我们用小老鼠做实验，要在1周内找出那桶毒酒，问最少需要多少老鼠。<br/>选项是9只、10只、32只、999只、以上都不是。

madio

<p>信息论的问题，利用信息熵就可以解决！</p>

testabc

没遇见国这样的问题，看看先

chj1983wd

用编码法, 请教了高手的.<br/><div id="dictdiv" style="margin: 5px; background: yellow none repeat scroll 0% 50%; position: absolute; left: 0pt; top: 0pt; z-index: 1000; font-family: arial; font-size: 13px; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; -moz-border-radius-topleft: 5px; -moz-border-radius-topright: 5px; -moz-border-radius-bottomright: 5px; -moz-border-radius-bottomleft: 5px; opacity: 0.9; display: none;"></div><div id="dictaudio"></div>

chj1983wd

<span lang="en-us"><font size="2" face="宋体">一只老鼠喝酒后又两种状态：死（</font></span><span lang="en-us"></span><span lang="en-us"><font size="2" face="Arial">0</font></span><span lang="en-us"></span><span lang="en-us"><font size="2" face="宋体">）和</font></span><span lang="en-us"></span><span lang="en-us"></span><span lang="en-us"></span><span lang="en-us">
, D# t$ S% ]+ q8 C                <font size="2" face="宋体">活</font></span><span lang="en-us"></span><span lang="en-us"><font size="2" face="Arial">(1). </font></span>
        <p align="justify" dir="ltr"><span lang="en-us"></span><span lang="en-us"><font size="2" face="宋体">所以</font></span><span lang="en-us"></span><span lang="en-us"><font size="2" face="Arial">10</font></span><span lang="en-us"></span><span lang="en-us"><font size="2" face="宋体">只老鼠就能表示</font></span><span lang="en-us"></span><span lang="en-us"><font size="2" face="Arial">2</font></span><span lang="en-us"></span><span lang="en-us"><font size="2" face="宋体">的</font></span><span lang="en-us"></span><span lang="en-us"><font size="2" face="Arial">10</font></span><span lang="en-us"></span><span lang="en-us"><font size="2" face="宋体">次方个状态（即</font></span><span lang="en-us"></span><span lang="en-us"><font size="2" face="Arial">1024</font></span><span lang="en-us"></span><span lang="en-us"><font size="2" face="宋体">个）。</font></span><span lang="en-us"></span><span lang="en-us"></span></p>
        <p align="justify" dir="ltr"><span lang="en-us"><font size="2" face="Arial">2^0</font></span><span lang="en-us"></span><span lang="en-us"><font size="2" face="宋体">表示</font></span><span lang="en-us"></span><span lang="en-us"><font size="2" face="Arial">2</font></span><span lang="en-us"></span><span lang="en-us"><font size="2" face="宋体">的零次方。</font></span><span lang="en-us"></span><span lang="en-us"><font size="2" face="Arial">2^8</font></span><span lang="en-us"></span><span lang="en-us"><font size="2" face="宋体">表示</font></span><span lang="en-us"></span><span lang="en-us"><font size="2" face="Arial">2</font></span><span lang="en-us"></span><span lang="en-us"><font size="2" face="宋体">的</font></span><span lang="en-us"></span><span lang="en-us"><font size="2" face="Arial">8</font></span><span lang="en-us"></span><span lang="en-us"><font size="2" face="宋体">次方。</font></span><span lang="en-us"></span><span lang="en-us"></span></p>
        <p align="justify" dir="ltr"><span lang="en-us"></span><span lang="en-us"><font size="2" face="宋体">设有</font></span><span lang="en-us"></span><span lang="en-us"><font size="2" face="Arial">10</font></span><span lang="en-us"></span><span lang="en-us"><font size="2" face="宋体">只老鼠编号分别为</font></span><span lang="en-us"></span><span lang="en-us"><font size="2" face="Arial">2^0</font></span><span lang="en-us"></span><span lang="en-us"><font size="2" face="宋体">，</font></span><span lang="en-us"></span><span lang="en-us"><font size="2" face="Arial">2^1</font></span><span lang="en-us"></span><span lang="en-us"><font size="2" face="宋体">，</font></span><span lang="en-us"></span><span lang="en-us"><font size="2" face="Arial"> 2^2</font></span><span lang="en-us"></span><span lang="en-us"><font size="2" face="宋体">，</font></span><span lang="en-us"></span><span lang="en-us"><font size="2" face="Arial"> 2^3</font></span><span lang="en-us"></span><span lang="en-us"><font size="2" face="宋体">，</font></span><span lang="en-us"></span><span lang="en-us"><font size="2" face="Arial"> 2^4</font></span><span lang="en-us"></span><span lang="en-us"><font size="2" face="宋体">，</font></span><span lang="en-us"></span><span lang="en-us"><font size="2" face="Arial"> 2^5</font></span><span lang="en-us"></span><span lang="en-us"><font size="2" face="宋体">，</font></span><span lang="en-us"></span><span lang="en-us"><font size="2" face="Arial"> 2^6</font></span><span lang="en-us"></span><span lang="en-us"><font size="2" face="宋体">，</font></span><span lang="en-us"></span><span lang="en-us"><font size="2" face="Arial"> 2^7</font></span><span lang="en-us"></span><span lang="en-us"><font size="2" face="宋体">，</font></span><span lang="en-us"></span><span lang="en-us"><font size="2" face="Arial"> 2^8</font></span><span lang="en-us"></span><span lang="en-us"><font size="2" face="宋体">，</font></span><span lang="en-us"></span><span lang="en-us"><font size="2" face="Arial"> 2^9</font></span><span lang="en-us"></span><span lang="en-us">
& ~6 x# m3 y: p1 n0 @                        <font size="2" face="宋体">。</font></span><span lang="en-us"></span><span lang="en-us"></span></p>
        <p align="justify" dir="ltr"><span lang="en-us"></span><span lang="en-us"><font size="2" face="宋体">有</font></span><span lang="en-us"></span><span lang="en-us"><font size="2" face="Arial">1000</font></span><span lang="en-us"></span><span lang="en-us"><font size="2" face="宋体">桶酒编号为</font></span><span lang="en-us"></span><span lang="en-us"><font size="2" face="Arial">1</font></span><span lang="en-us"></span><span lang="en-us"><font size="2" face="宋体">，</font></span><span lang="en-us"></span><span lang="en-us"><font size="2" face="Arial">2</font></span><span lang="en-us"></span><span lang="en-us"><font size="2" face="宋体">，</font></span><span lang="en-us"></span><span lang="en-us"><font size="2" face="Arial">3</font></span><span lang="en-us"></span><span lang="en-us">
) b! P5 W8 k. v  A  t# `. @- S' Z* I( r                        <font size="2" face="宋体">。。。。一直到</font></span><span lang="en-us"></span><span lang="en-us"><font size="2" face="Arial"> 1000</font></span><span lang="en-us"></span><span lang="en-us">
& r! O) D% u% ~5 ^9 w                        <font size="2" face="宋体">。</font></span><span lang="en-us"></span><span lang="en-us"></span></p>
8 y! @' F# ^1 N9 V        <p align="justify" dir="ltr"><span lang="en-us"></span><span lang="en-us"><font size="2" face="宋体">任何一桶酒的编号都能分解为</font></span><span lang="en-us"></span><span lang="en-us"><font size="2" face="Arial">2</font></span><span lang="en-us"></span><span lang="en-us"><font size="2" face="宋体">的幂指数之和的形式，而且唯一。</font></span><span lang="en-us"></span><span lang="en-us"></span></p>
        <p align="justify" dir="ltr"><span lang="en-us"></span><span lang="en-us"><font size="2" face="宋体">比如：第九桶酒</font></span><span lang="en-us"></span><span lang="en-us"><font size="2" face="Arial"> 9= 2^0 + 2^3 </font></span><span lang="en-us"></span><span lang="en-us">
& a  p/ b: g4 E                        <font size="2" face="宋体">（那么我们就让编号为</font></span><span lang="en-us"></span><span lang="en-us"><font size="2" face="Arial">2^0</font></span><span lang="en-us"></span><span lang="en-us">
; d' ~: c( V4 R+ u! ]                        <font size="2" face="宋体">和</font></span><span lang="en-us"></span><span lang="en-us"><font size="2" face="Arial"> 2^3</font></span><span lang="en-us"></span><span lang="en-us">
                        <font size="2" face="宋体">的这</font><font size="2" face="宋体">两只老鼠去喝这桶酒）</font></span><span lang="en-us"></span><span lang="en-us"></span></p>
        <p align="justify" dir="ltr"><span lang="en-us"></span><span lang="en-us"></span></p>
/ J3 X! h, W0 j* Q; I) t        <span lang="en-us"></span><span lang="en-us"><font size="2" face="宋体">最后只要看那几只老鼠死了就知道是那桶酒有问题。<wbr></wbr>（只要把死了的老鼠编号加起来就是酒桶的编号）<br/><br/>S:感谢</font></span>FOYang指教 <br/><div id="dictdiv" style="margin: 5px; background: yellow none repeat scroll 0%; position: absolute; left: 0pt; top: 0pt; z-index: 1000; font-family: arial; font-size: 13px; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; -moz-border-radius-topleft: 5px; -moz-border-radius-topright: 5px; -moz-border-radius-bottomright: 5px; -moz-border-radius-bottomleft: 5px; opacity: 0.9; display: none;"></div><div id="dictaudio"></div>