📄 ds6.4.1.htm
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<td width="33%" align="center"><!--mstheme--><font face="宋体"><font size="4" color="#FFFFFF"><b>4</b></font><!--mstheme--></font></td>
<td width="33%" align="center"><!--mstheme--><font face="宋体"><font size="4" color="#FFFFFF"><b>E</b></font><!--mstheme--></font></td>
<td width="34%" align="center"><!--mstheme--><font face="宋体"><font size="4" color="#FFFFFF"><b>1</b></font><!--mstheme--></font></td>
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<td width="33%" align="center"><!--mstheme--><font face="宋体"><font size="4" color="#FFFFFF"><b>5</b></font><!--mstheme--></font></td>
<td width="33%" align="center"><!--mstheme--><font face="宋体"><font size="4" color="#FFFFFF"><b>F</b></font><!--mstheme--></font></td>
<td width="34%" align="center"><!--mstheme--><font face="宋体"><font size="4" color="#FFFFFF"><b>1</b></font><!--mstheme--></font></td>
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<td width="33%" align="center"><!--mstheme--><font face="宋体"><font size="4" color="#FFFFFF"><b>6</b></font><!--mstheme--></font></td>
<td width="33%" align="center"><!--mstheme--><font face="宋体"><font size="4" color="#FFFFFF"><b>G</b></font><!--mstheme--></font></td>
<td width="34%" align="center"><!--mstheme--><font face="宋体"><font size="4" color="#FFFFFF"><b>2</b></font><!--mstheme--></font></td>
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<td width="33%" align="center"><!--mstheme--><font face="宋体"><font size="4" color="#FFFFFF"><b>7</b></font><!--mstheme--></font></td>
<td width="33%" align="center"><!--mstheme--><font face="宋体"><font size="4" color="#FFFFFF"><b>H</b></font><!--mstheme--></font></td>
<td width="34%" align="center"><!--mstheme--><font face="宋体"><font size="4" color="#FFFFFF"><b>4</b></font><!--mstheme--></font></td>
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<td width="33%" align="center"><!--mstheme--><font face="宋体"><font size="4" color="#FFFFFF"><b>8</b></font><!--mstheme--></font></td>
<td width="33%" align="center"><!--mstheme--><font face="宋体"><font size="4" color="#FFFFFF"><b>I</b></font><!--mstheme--></font></td>
<td width="34%" align="center"><!--mstheme--><font face="宋体"><font size="4" color="#FFFFFF"><b>4</b></font><!--mstheme--></font></td>
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<p><b><span style="mso-spacerun: yes; 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" lang="EN-US"><font color="#FFFFFF" size="5">
</font></span><font color="#FFFFFF" size="5"><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">树的双亲表示法对于实现</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">Parent</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">t</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">x</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">）操作和</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">Root</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">x</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">）操作很方便，但若求某结点的孩子结点，即实现</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">Child</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">t</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">x</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">i</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">）操作时，则需要查询整个数组。此外，这种存储方式不能反映各兄弟结点之间的关系，所以实现</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">RightSibling</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">t</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">x</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">）操作也比较困难。在实际中，如果需要实现这些操作，可在结点结构中增设存放第一个孩子的域和存放第一个右兄弟的域，就能较方便地实现上述操作了。</span></font></b></p>
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<h5><!--mstheme--><font face="宋体" color="#6666FF"><font size="5" color="#FFFFFF"><b><span lang="EN-US" style="mso-bidi-font-size: 10.0pt; mso-fareast-font-family: 黑体">2</span><span style="mso-bidi-font-size: 10.0pt; font-family: 黑体; mso-ascii-font-family: Times New Roman">．孩子表示法</span><span lang="EN-US" style="mso-bidi-font-size: 10.0pt; mso-fareast-font-family: 黑体"><o:p>
</o:p>
</span></b></font><!--mstheme--></font></h5>
<!--mstheme--><font face="宋体">
<p class="MsoNormal" style="margin-left:21.0pt"><font size="5" color="#FFFFFF"><b><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">1</span><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";
mso-hansi-font-family:"Times New Roman"">）多重链表法</span></b></font></p>
<p class="MsoNormal"><font size="5" color="#FFFFFF"><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"">由于树中每个结点都有零个或多个孩子结点，因此，可以令每个结点包括一个结点信息域和多个指针域，每个指针域指向该结点的一个孩子结点，通过各个指针域值反映出树中各结点之间的逻辑关系。在这种表示法中，树中每个结点有多个指针域，形成了多条链表，所以这种方法又常称为多重链表法。</span></b></font></p>
<p class="MsoNormal" style="margin-left:21.0pt"><span style="font-family:宋体;
mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman""><font size="5" color="#FFFFFF"><b>在一棵树中，各结点的度数各异，因此结点的指针域个数的设置有两种方法：</b></font></span></p>
<p class="MsoNormal"><font size="5" color="#FFFFFF"><b><span style="mso-spacerun: yes" lang="EN-US">
</span><span style="font-family:宋体;mso-hansi-font-family:"Times New Roman"">①
</span><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:
"Times New Roman"">每个结点指针域的个数等于该结点的度数；</span></b></font></p>
<p class="MsoNormal" style="margin-left:21.0pt"><font size="5" color="#FFFFFF"><b><span style="font-family:宋体;
mso-hansi-font-family:"Times New Roman"">② </span><span style="font-family:
宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"">每个结点指针域的个数等于树的度数。</span></b></font></p>
<p class="MsoNormal" style="text-indent:21.0pt"><font size="5" color="#FFFFFF"><b><span style="font-family:宋体;
mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"">对于方法</span><span style="font-family:宋体;mso-hansi-font-family:"Times New Roman"">①</span><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:
"Times New Roman"">，它虽然在一定程度上节约了存储空间，但由于树中各结点是不同构的，各种操作不容易实现，所以这种方法很少采用；方法</span><span style="font-family:宋体;mso-hansi-font-family:"Times New Roman"">②</span><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:
"Times New Roman"">中各结点是同构的，各种操作相对容易实现，但为此付出的代价是存储空间的浪费。下图</span><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";
mso-hansi-font-family:"Times New Roman"">是图</span><span lang="EN-US">7.1(a)</span><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:
"Times New Roman"">所示的树采用这种方法的存储结构示意图。显然，方法</span><span style="font-family:
宋体;mso-hansi-font-family:"Times New Roman"">②</span><span style="font-family:
宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"">适用于各结点的度数相差不大的情况。</span></b></font></p>
<p class="MsoNormal" style="margin-left:21.0pt"><span style="font-family:宋体;
mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman""><font size="5" color="#FFFFFF"><b>树中结点的存储表示可描述为：</b></font></span></p>
<p class="MsoNormal" style="margin-top: 0; margin-bottom: 0"><font size="5" color="#FFFFFF"><b><span lang="EN-US"><span style="mso-spacerun: yes">
</span>#define MAXSON <</span><span style="font-family:宋体;mso-ascii-font-family:
"Times New Roman";mso-hansi-font-family:"Times New Roman"">树的度数</span><span lang="EN-US">></span></b></font></p>
<p class="MsoNormal" style="margin-top: 0; margin-bottom: 0"><span lang="EN-US"><span style="mso-spacerun: yes"><font color="#FFFFFF"><b><font size="5">
</font></b></font></span><font color="#FFFFFF"><b><font size="5">typedef struct
TreeNode {</font></b></font></span></p>
<p class="MsoNormal" style="margin-top: 0; margin-bottom: 0"><span lang="EN-US"><span style="mso-spacerun: yes"><font color="#FFFFFF"><b><font size="5">
</font></b></font></span><font color="#FFFFFF"><b><font size="5">elemtype data;</font></b></font></span></p>
<p class="MsoNormal" style="margin-top: 0; margin-bottom: 0"><span lang="EN-US"><span style="mso-spacerun: yes"><font color="#FFFFFF"><b><font size="5">
</font></b></font></span><font color="#FFFFFF"><b><font size="5">struct TreeNode<span style="mso-spacerun: yes">
</span>*son[MAXSON];</font></b></font></span></p>
<p class="MsoNormal" style="margin-top: 0; margin-bottom: 0"><span lang="EN-US"><span style="mso-spacerun: yes"><font color="#FFFFFF"><b><font size="5">
</font></b></font></span><font color="#FFFFFF"><b><font size="5">}NodeType;</font></b></font></span></p>
<font size="5" color="#FFFFFF"><b><span style="mso-spacerun: yes; 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" lang="EN-US">
</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">对于任意一棵树</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">t</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">，可以定义：</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">NodeType<span style="mso-spacerun: yes">
</span>*t;</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">使变量</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">t</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">为指向树的根结点的指针。</span></b></font>
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