📄 ds9.4.2.htm
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<title>数 据 结 构</title>
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<p align="center"><span style="mso-bidi-font-size: 10.0pt; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA"><b><font color="#FFFF00" size="6"><span lang="EN-US" style="mso-bidi-font-size: 10.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">9.4.2
</span><span style="mso-bidi-font-size: 10.0pt; font-family: 宋体; mso-ascii-font-family: Times New Roman; mso-hansi-font-family: Times New Roman; mso-bidi-font-family: Times New Roman; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">常用的哈希函数</span></font></b></span></p>
<p class="MsoNormal"><b><span style="mso-bidi-font-size: 10.0pt; font-family: 黑体"><font size="5" color="#FFFF00">一<span lang="EN-US">.
直接定<o:p>
址法</span></font><span lang="EN-US"><font size="5" color="#FFFFFF"></o:p>
</font></span></span></b></p>
<p class="MsoNormal"><b><font size="5" color="#FFFFFF"><span lang="EN-US"><span style="mso-spacerun: yes">
</span>Hash(key)=a</span><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:
"Times New Roman"">·</span><span lang="EN-US">key+b<span style="mso-spacerun:
yes"> </span>(a</span><span style="font-family:宋体;mso-ascii-font-family:
"Times New Roman";mso-hansi-font-family:"Times New Roman"">、</span><span lang="EN-US">b</span><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";
mso-hansi-font-family:"Times New Roman"">为常数</span><span lang="EN-US">)</span></font></b></p>
<p class="MsoNormal"><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";
mso-hansi-font-family:"Times New Roman""><b><font size="5" color="#FFFFFF">
即取关键码的某个线性函数值为哈希地址，这类函数是一一对应函数，不会产生冲突，但要求地址集合与关键码集合大小相同，因此，对于较大的关键码集合不适用。</font></b></span></p>
<p class="MsoNormal"><b><font size="5" color="#FFFFFF"><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";
mso-hansi-font-family:"Times New Roman"">【例</span><span lang="EN-US">9.7</span><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:
"Times New Roman"">】关键码集合为</span><span lang="EN-US">{100</span><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:
"Times New Roman"">，</span><span lang="EN-US">300</span><span style="font-family:
宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"">，</span><span lang="EN-US">500</span><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";
mso-hansi-font-family:"Times New Roman"">，</span><span lang="EN-US">700</span><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:
"Times New Roman"">，</span><span lang="EN-US">800</span><span style="font-family:
宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"">，</span><span lang="EN-US">900}</span><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";
mso-hansi-font-family:"Times New Roman"">，选取哈希函数为</span></font></b></p>
<b><font size="5" color="#FFFFFF"><span lang="EN-US" style="mso-bidi-font-size: 10.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA"><span style="mso-spacerun: yes">
</span>Hash(key)=key/100</span><span style="mso-bidi-font-size: 10.0pt; font-family: 宋体; mso-ascii-font-family: Times New Roman; mso-hansi-font-family: Times New Roman; mso-bidi-font-family: Times New Roman; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">，则存放如下：</span></font></b>
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<td width="36" height="30" valign="middle" align="center"><!--mstheme--><font face="宋体"><font size="5" color="#FFFFFF"><b>0</b></font><!--mstheme--></font></td>
<td width="56" height="30" valign="middle" align="center"><!--mstheme--><font face="宋体"><font size="5" color="#FFFFFF"><b>1</b></font><!--mstheme--></font></td>
<td width="43" height="30" valign="middle" align="center"><!--mstheme--><font face="宋体"><font size="5" color="#FFFFFF"><b>2</b></font><!--mstheme--></font></td>
<td width="41" height="30" valign="middle" align="center"><!--mstheme--><font face="宋体"><font size="5" color="#FFFFFF"><b>3</b></font><!--mstheme--></font></td>
<td width="48" height="30" valign="middle" align="center"><!--mstheme--><font face="宋体"><font size="5" color="#FFFFFF"><b>4</b></font><!--mstheme--></font></td>
<td width="44" height="30" valign="middle" align="center"><!--mstheme--><font face="宋体"><font size="5" color="#FFFFFF"><b>5</b></font><!--mstheme--></font></td>
<td width="47" height="30" valign="middle" align="center"><!--mstheme--><font face="宋体"><font size="5" color="#FFFFFF"><b>6</b></font><!--mstheme--></font></td>
<td width="55" height="30" valign="middle" align="center"><!--mstheme--><font face="宋体"><font size="5" color="#FFFFFF"><b>7</b></font><!--mstheme--></font></td>
<td width="48" height="30" valign="middle" align="center"><!--mstheme--><font face="宋体"><font size="5" color="#FFFFFF"><b>8</b></font><!--mstheme--></font></td>
<td width="49" height="30" valign="middle" align="center"><!--mstheme--><font face="宋体"><font size="5" color="#FFFFFF"><b>9</b></font><!--mstheme--></font></td>
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<td width="36" height="31" valign="middle" align="center"><!--mstheme--><font face="宋体"><font size="5" color="#FFFFFF"><b>100</b></font><!--mstheme--></font></td>
<td width="56" height="31" valign="middle" align="center"><!--mstheme--><font face="宋体"><!--mstheme--></font></td>
<td width="43" height="31" valign="middle" align="center"><!--mstheme--><font face="宋体"><!--mstheme--></font></td>
<td width="41" height="31" valign="middle" align="center"><!--mstheme--><font face="宋体"><font size="5" color="#FFFFFF"><b>300</b></font><!--mstheme--></font></td>
<td width="48" height="31" valign="middle" align="center"><!--mstheme--><font face="宋体"><!--mstheme--></font></td>
<td width="44" height="31" valign="middle" align="center"><!--mstheme--><font face="宋体"><font size="5" color="#FFFFFF"><b>500</b></font><!--mstheme--></font></td>
<td width="47" height="31" valign="middle" align="center"><!--mstheme--><font face="宋体"><!--mstheme--></font></td>
<td width="55" height="31" valign="middle" align="center"><!--mstheme--><font face="宋体"><font size="5" color="#FFFFFF"><b>700</b></font><!--mstheme--></font></td>
<td width="48" height="31" valign="middle" align="center"><!--mstheme--><font face="宋体"><font size="5" color="#FFFFFF"><b>800</b></font><!--mstheme--></font></td>
<td width="49" height="31" valign="middle" align="center"><!--mstheme--><font face="宋体"><font size="5" color="#FFFFFF"><b>900</b></font><!--mstheme--></font></td>
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<p class="MsoNormal"><b><span style="mso-bidi-font-size: 10.0pt; font-family: 黑体"><font size="5" color="#FFFF00">二<span lang="EN-US">.
除留余数法</span></font><span lang="EN-US"><font color="#FFFFFF" size="5"><o:p>
</o:p>
</font></span></span></b></p>
<p class="MsoNormal"><b><font color="#FFFFFF" size="5"><span lang="EN-US"><span style="mso-spacerun: yes">
</span>Hash(key)=key<span style="mso-spacerun: yes"> </span>mod<span style="mso-spacerun: yes">
</span>p<span style="mso-spacerun: yes"> </span>(p</span><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";
mso-hansi-font-family:"Times New Roman"">是一个整数</span><span lang="EN-US">)</span></font></b></p>
<font color="#FFFFFF" size="5"><b><span style="mso-bidi-font-size: 10.0pt; font-family: 宋体; mso-ascii-font-family: Times New Roman; mso-hansi-font-family: Times New Roman; mso-bidi-font-family: Times New Roman; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">
即取关键码除以</span><span lang="EN-US" style="mso-bidi-font-size: 10.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">p</span><span style="mso-bidi-font-size: 10.0pt; font-family: 宋体; mso-ascii-font-family: Times New Roman; mso-hansi-font-family: Times New Roman; mso-bidi-font-family: Times New Roman; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">的余数作为哈希地址。使用除留余数法，选取合适的</span><span lang="EN-US" style="mso-bidi-font-size: 10.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">p</span><span style="mso-bidi-font-size: 10.0pt; font-family: 宋体; mso-ascii-font-family: Times New Roman; mso-hansi-font-family: Times New Roman; mso-bidi-font-family: Times New Roman; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">很重要，若哈希表表长为</span><span lang="EN-US" style="mso-bidi-font-size: 10.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">m</span><span style="mso-bidi-font-size: 10.0pt; font-family: 宋体; mso-ascii-font-family: Times New Roman; mso-hansi-font-family: Times New Roman; mso-bidi-font-family: Times New Roman; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">，则要求</span><span lang="EN-US" style="mso-bidi-font-size: 10.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">p</span><span style="mso-bidi-font-size: 10.0pt; font-family: 宋体; mso-ascii-font-family: Times New Roman; mso-hansi-font-family: Times New Roman; mso-bidi-font-family: Times New Roman; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">≤</span><span lang="EN-US" style="mso-bidi-font-size: 10.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">m</span><span style="mso-bidi-font-size: 10.0pt; font-family: 宋体; mso-ascii-font-family: Times New Roman; mso-hansi-font-family: Times New Roman; mso-bidi-font-family: Times New Roman; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">，且接近</span><span lang="EN-US" style="mso-bidi-font-size: 10.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">m</span><span style="mso-bidi-font-size: 10.0pt; font-family: 宋体; mso-ascii-font-family: Times New Roman; mso-hansi-font-family: Times New Roman; mso-bidi-font-family: Times New Roman; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">或等于</span><span lang="EN-US" style="mso-bidi-font-size: 10.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">m</span><span style="mso-bidi-font-size: 10.0pt; font-family: 宋体; mso-ascii-font-family: Times New Roman; mso-hansi-font-family: Times New Roman; mso-bidi-font-family: Times New Roman; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">。</span><span lang="EN-US" style="mso-bidi-font-size: 10.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">p</span><span style="mso-bidi-font-size: 10.0pt; font-family: 宋体; mso-ascii-font-family: Times New Roman; mso-hansi-font-family: Times New Roman; mso-bidi-font-family: Times New Roman; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">一般选取质数，也可以是不包含小于</span><span lang="EN-US" style="mso-bidi-font-size: 10.0pt; font-family: Times New Roman; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">20</span><span style="mso-bidi-font-size: 10.0pt; font-family: 宋体; mso-ascii-font-family: Times New Roman; mso-hansi-font-family: Times New Roman; mso-bidi-font-family: Times New Roman; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">质因子的合数。</span></b></font>
<p class="MsoNormal"><b><span style="mso-bidi-font-size: 10.0pt; font-family: 黑体"><font size="5" color="#FFFF00">三</font></span><span lang="EN-US" style="mso-bidi-font-size: 10.0pt; font-family: 黑体"><font size="5" color="#FFFF00">.
数字分析法</font><font color="#FFFFFF" size="5"><o:p>
</o:p>
</font></span></b></p>
<p class="MsoNormal"><font color="#FFFFFF" size="5"><b><span style="mso-spacerun: yes" lang="EN-US">
</span><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:
"Times New Roman"">设关键码集合中，每个关键码均由</span><span lang="EN-US">m</span><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:
"Times New Roman"">位组成，每位上可能有</span><span lang="EN-US">r</span><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:
"Times New Roman"">种不同的符号。</span></b></font></p>
<p class="MsoNormal"><b><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";
mso-hansi-font-family:"Times New Roman""><font size="5" color="#FFFF00">【例</font></span><font size="5" color="#FFFF00"><span lang="EN-US">9.8</span><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:
"Times New Roman"">】</span></font><font color="#FFFFFF" size="5"><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:
"Times New Roman"">若关键码是</span><span lang="EN-US">4</span><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:
"Times New Roman"">位十进制数，则每位上可能有十个不同的数符</span><span lang="EN-US">0</span><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:
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