ds9.3.2.htm

这是清华大学所用的数据结构的电子版教材

<p align="left"><font size="5" color="#FFFFFF"><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><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">&nbsp;&nbsp;   
如图</span><span style="font-family: Times New Roman; mso-fareast-font-family: 宋体" lang="EN-US">(a)</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">为插入前的子树，根结点</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">a</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">的左子树比右子树高度高<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">1</span>，待插入结点<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>将插入到结点<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">b</span>的右子树上，并使结点<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">b</span>的右子树高度增<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">1</span>，从而使结点<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">a</span>的平衡因子的绝对值大于<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">1</span>，导致结点<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">a</span>为根的子树平衡被破坏，如图</span><span style="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-fareast-font-family: 宋体" lang="EN-US">a1</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 style="mso-fareast-font-family: 宋体" lang="EN-US">b1</span>所示。</span></b></span></font></p>
<p align="center"><img border="0" src="ds9.3.80.gif" width="175" height="133"></p>
<p align="center"><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"><font size="5" color="#FFFF00">图(a)</font></span></b></p>
<p align="left"><span style="font-family:宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;
mso-hansi-font-family:&quot;Times New Roman&quot;"><b><font size="5" color="#FFFF00">【调整策略】</font></b></span></p>
<p class="MsoNormal"><b><font size="5" color="#FFFFFF"><span style="mso-spacerun: yes" lang="EN-US">&nbsp;&nbsp;&nbsp;   
</span><span style="font-family:宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;mso-hansi-font-family:
&quot;Times New Roman&quot;">沿插入路径检查三个点</span><span lang="EN-US">a</span><span style="font-family:宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;mso-hansi-font-family:
&quot;Times New Roman&quot;">、</span><span lang="EN-US">b</span><span style="font-family:
宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;mso-hansi-font-family:&quot;Times New Roman&quot;">、</span><span lang="EN-US">c</span><span style="font-family:宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;
mso-hansi-font-family:&quot;Times New Roman&quot;">，若它们呈“</span><span lang="EN-US">&lt;</span><span style="font-family:宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;mso-hansi-font-family:
&quot;Times New Roman&quot;">”字形，需要进行先左后右双向旋转：</span></font></b></p>
<p class="MsoNormal"><span lang="EN-US"><span style="mso-spacerun: yes"><font size="5" color="#FFFFFF"><b>&nbsp;</b></font></span><font size="5" color="#FFFFFF"><b>1.   
</b></font></span><font size="5" color="#FFFFFF"><b><span style="font-family:宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;mso-hansi-font-family:
&quot;Times New Roman&quot;">首先，对结点</span><span lang="EN-US">b</span><span style="font-family:宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;mso-hansi-font-family:
&quot;Times New Roman&quot;">为根的子树，以结点</span><span lang="EN-US">c</span><span style="font-family:宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;mso-hansi-font-family:
&quot;Times New Roman&quot;">为轴，向左逆时针旋转，结点</span><span lang="EN-US">c</span><span style="font-family:宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;mso-hansi-font-family:
&quot;Times New Roman&quot;">成为该子树的新根，如图</span><span lang="EN-US">(a2</span><span style="font-family:宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;mso-hansi-font-family:
&quot;Times New Roman&quot;">、</span><span lang="EN-US">b2)</span><span style="font-family:
宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;mso-hansi-font-family:&quot;Times New Roman&quot;">；</span></b></font></p>
<p class="MsoNormal"><span lang="EN-US"><span style="mso-spacerun: yes"><font size="5" color="#FFFFFF"><b>&nbsp;</b></font></span><font size="5" color="#FFFFFF"><b>2.   
</b></font></span><font size="5" color="#FFFFFF"><b><span style="font-family:宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;mso-hansi-font-family:
&quot;Times New Roman&quot;;letter-spacing:-.1pt">由于旋转后，待插入结点</span><span lang="EN-US" style="letter-spacing:-.1pt">x</span><span style="font-family:宋体;mso-ascii-font-family:
&quot;Times New Roman&quot;;mso-hansi-font-family:&quot;Times New Roman&quot;;letter-spacing:-.1pt">相当于插入到结点</span><span lang="EN-US" style="letter-spacing:-.1pt">b</span><span style="font-family:宋体;
mso-ascii-font-family:&quot;Times New Roman&quot;;mso-hansi-font-family:&quot;Times New Roman&quot;;
letter-spacing:-.1pt">为根的子树上，这样</span><span lang="EN-US" style="letter-spacing:
-.1pt">a</span><span style="font-family:宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;
mso-hansi-font-family:&quot;Times New Roman&quot;;letter-spacing:-.1pt">、</span><span lang="EN-US" style="letter-spacing:-.1pt">c</span><span style="font-family:宋体;
mso-ascii-font-family:&quot;Times New Roman&quot;;mso-hansi-font-family:&quot;Times New Roman&quot;;
letter-spacing:-.1pt">、</span><span lang="EN-US" style="letter-spacing:-.1pt">b</span><span style="font-family:宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;mso-hansi-font-family:
&quot;Times New Roman&quot;;letter-spacing:-.1pt">三点处于“</span><span lang="EN-US" style="letter-spacing:-.1pt">/</span><span style="font-family:宋体;mso-ascii-font-family:
&quot;Times New Roman&quot;;mso-hansi-font-family:&quot;Times New Roman&quot;;letter-spacing:-.1pt">”直线上的同一个方向，则要作右单旋转，即以结点</span><span lang="EN-US" style="letter-spacing:-.1pt">c</span><span style="font-family:宋体;
mso-ascii-font-family:&quot;Times New Roman&quot;;mso-hansi-font-family:&quot;Times New Roman&quot;;
letter-spacing:-.1pt">为轴顺时针旋转，如图</span><span lang="EN-US" style="letter-spacing:
-.1pt">(</span><span style="letter-spacing: -.1pt" lang="EN-US">a3</span><span style="font-family:宋体;mso-ascii-font-family:&quot;Times New Roman&quot;;
mso-hansi-font-family:&quot;Times New Roman&quot;;letter-spacing:-.1pt">、</span><span lang="EN-US" style="letter-spacing:-.1pt">b3)</span><span style="font-family:宋体;
mso-ascii-font-family:&quot;Times New Roman&quot;;mso-hansi-font-family:&quot;Times New Roman&quot;;
letter-spacing:-.1pt">。</span></b></font></p>
<p align="center"><img border="0" src="ds9.3.81.gif" width="533" height="172"></p>
<p align="center"><b><font size="5" color="#FFFF00"><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"><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">a1.</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">插入后，调整前</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"><span style="mso-spacerun: yes; 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">&nbsp;