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<div id="Layer1" style="position:absolute; width:711px; height:21px; z-index:1; top: 10px; background-color: #CCCCCC; layer-background-color: #CCCCCC; border: 1px none #000000; left: 26px"><b>|</b><font face="宋体" size="2"><a href="../text1/text1-0.htm">第一章</a></font><b>|</b><font face="宋体" size="2"><a href="../text2/text2-0.htm">第二章</a></font><b>|</b><font face="宋体" size="2"><a href="../text3/text3-0.htm">第三章</a></font><b>|</b><font face="宋体" size="2"><a href="../text4/text4-0.htm">第四章</a></font><b>|</b><font face="宋体" size="2"><a href="../text5/text5-0.htm">第五章</a></font><b>|</b><font face="宋体" size="2"><a href="../text6/text6-0.htm">第六章</a></font><b>|</b><font face="宋体" size="2"><a href="../text7/text7-0.htm">第七章</a></font><b>|</b><font face="宋体" size="2">第八章</font><b>|</b><font face="宋体" size="2"><a href="../text9/text9-0.htm">第九章</a></font><b>|</b><font face="宋体" size="2"><a href="../text10/text10-0.htm">第十章</a></font><b>|</b><font size="2" face="宋体"><a href="../textA/textA-0.htm">算法分析</a><b><font color="#000000">|</font></b>
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<b><font face="Arial, Helvetica, sans-serif" size="4" color="#000000">〖<font color="#FF0000">example</font>〗
X = <i>x<font size="2">1 </font>x<font size="2">2</font> </i> , Y = <i>x<font size="2">2</font>x<font size="2">1 </font></i>
C(<i>x<font size="2">1 </font></i> ) --- the internal representation for <i>x<font size="2">1 </font></i>
C(<i>x<font size="2">2</font></i> ) --- the internal representation for <i> x<font size="2">2</font></i>
X = <img src="image/26.gif" width="19" height="20" align="middle">C(</font></b><b><font face="Arial, Helvetica, sans-serif" size="4" color="#000000"><i>x<font size="2">1 </font></i></font></b><b><font face="Arial, Helvetica, sans-serif" size="4" color="#000000"> ) +C(<i>x<font size="2">2</font></i> )
Y = <img src="image/26.gif" width="19" height="20" align="middle">C(<i>x<font size="2">2</font></i> ) +C(<i>x<font size="2">1 </font></i> ) each character is represented by 6 bits
<font color="#FF0033"><i>p </i></font> -- a prime number dividing M
(f <font size="2">D</font> (X) - f <font size="2">D</font>(Y) ) % p
= (<img src="image/26.gif" width="19" height="20" align="middle"> C(<i>x<font size="2">1 </font></i> ) % p +C(<i>x<font size="2">2</font></i>) % p - <img src="image/26.gif" width="19" height="20" align="middle">C(<i>x<font size="2">2</font></i>) % p -C(<i>x<font size="2">1 </font></i> ) % p ) % p
if p = 3
(f <font size="2">D</font> (X) - f <font size="2">D</font> (Y) ) % p
= (64C(<i>x<font size="2">1 </font></i> ) % 3 +C(<i>x<font size="2">2</font></i> ) % 3 - 64C(<i>x<font size="2">2</font></i>) % 3 -C(<i>x<font size="2">1 </font></i> ) % 3 ) % 3
= C(<i>x<font size="2">1 </font></i> ) % 3 +C(<i>x<font size="2">2</font></i> ) % 3 - C( <i>x<font size="2">2</font></i>) % 3 -C(<i>x<font size="2">1 </font></i> ) % 3
= 0 % 3
---> permutations of the same set of characters are hashed
at a distance a factor of 3 part
<font color="#FF0000">Knuth :</font>
when M divides <img src="image/rk.gif" width="19" height="20" align="middle"> <img src="image/plus.gif" width="20" height="18" align="middle"> <img src="image/a.gif" width="15" height="12" align="middle"> where k and <img src="image/a.gif" width="15" height="12" align="middle"> are small number
and r is the radix of the character set, then X % M tends to
be a simple superposition of the characters in X.
<font color="#FF0000">Good choice:</font>
M a prime number such that M does not divide <img src="image/rk.gif" width="19" height="20" align="middle"> <img src="image/plus.gif" width="20" height="18" align="middle"> <img src="image/a.gif" width="15" height="12" align="middle"> for
small k and <img src="image/a.gif" width="15" height="12" align="middle">
experience :<font color="#FF0000"> M has no prime divisor less than 20 <i><font size="3" color="#000000"> (1,3,5,7,11,13,17,19)
</font></i></font></font></b></pre>
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