📄
字号:
"Times New Roman";mso-hansi-font-family:"Times New Roman"">这可以保证红黑树的黑色高度不被破坏</span><span lang="EN-US">,</span><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";
mso-hansi-font-family:"Times New Roman"">但如果这个结点的父结点是红色，则破坏了红结点的子结点必须都是黑结点的要求，必须进行调整。</span></p>
<p class="MsoNormal" style="text-indent:17.95pt;mso-char-indent-count:1.71;
mso-char-indent-size:10.45pt"><span lang="EN-US"> <o:p>
</o:p>
</span></p>
<p class="MsoNormal" style="text-indent:17.95pt;mso-char-indent-count:1.71;
mso-char-indent-size:10.45pt"><span style="font-family:宋体;mso-ascii-font-family:
"Times New Roman";mso-hansi-font-family:"Times New Roman"">这里我们把问题分成三个可能性，（确切的说是六种可能性，但别外的三种与这三种是对称结构，所以只须讨论三种就可以）</span></p>
<p class="MsoNormal" style="text-indent:17.95pt;mso-char-indent-count:1.71;
mso-char-indent-size:10.45pt"><span lang="EN-US"> <o:p>
</o:p>
</span></p>
<p class="MsoNormal" style="text-indent:17.95pt;mso-char-indent-count:1.71;
mso-char-indent-size:10.45pt"><span lang="EN-US"> <o:p>
</o:p>
</span></p>
<p class="MsoNormal" style="text-indent:17.95pt;mso-char-indent-count:1.71;
mso-char-indent-size:10.45pt"><span style="font-family:宋体;mso-ascii-font-family:
"Times New Roman";mso-hansi-font-family:"Times New Roman"">下面是第一种可能性的源代码</span></p>
<p class="MsoNormal" style="text-indent:17.95pt;mso-char-indent-count:1.71;
mso-char-indent-size:10.45pt"><span lang="EN-US">while (ap[ak - 1]->color ==
RB_RED)//</span><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:
"Times New Roman"">这个地方就是控制只在调整的当前的父结点也是</span></p>
<p class="MsoNormal" style="text-indent:17.95pt;mso-char-indent-count:1.71;
mso-char-indent-size:10.45pt"><span lang="EN-US"><span style="mso-spacerun:
yes"> </span>//</span><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";
mso-hansi-font-family:"Times New Roman"">红色的时候才有必要再进行调整</span></p>
<p class="MsoNormal" style="text-indent:17.95pt;mso-char-indent-count:1.71;
mso-char-indent-size:10.45pt"><span lang="EN-US"><span style="mso-spacerun:
yes"> </span>if (ad[ak - 2] == 0) {//</span><span style="font-family:宋体;
mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"">如果现在调整的结点是它的爷爷结点的左子结点的话</span></p>
<p class="MsoNormal" style="text-indent:17.95pt;mso-char-indent-count:1.71;
mso-char-indent-size:10.45pt"><span lang="EN-US"><span style="mso-spacerun:
yes"> </span>y = ap[ak - 2]->link[1];//y</span><span style="font-family:
宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"">取现在调整结点的叔叔</span></p>
<p class="MsoNormal" style="text-indent:17.95pt;mso-char-indent-count:1.71;
mso-char-indent-size:10.45pt"><span lang="EN-US"><span style="mso-spacerun:
yes"> </span>if (y != NULL && y->color
== RB_RED) {//</span><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:
"Times New Roman"">如果它的（</span><span lang="EN-US">x</span><span style="font-family:
宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"">）叔叔是红色的话，那就</span></p>
<p class="MsoNormal" style="text-indent:17.95pt;mso-char-indent-count:1.71;
mso-char-indent-size:10.45pt"><span lang="EN-US">//</span><span style="font-family:
宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"">让</span><span lang="EN-US">x</span><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";
mso-hansi-font-family:"Times New Roman"">的父结点与它的叔叔的颜色变为黑色，</span><span lang="EN-US">x</span><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";
mso-hansi-font-family:"Times New Roman"">的爷爷的颜色变为红色</span></p>
<p class="MsoNormal" style="text-indent:17.95pt;mso-char-indent-count:1.71;
mso-char-indent-size:10.45pt"><span lang="EN-US">ap[--ak]->color =
y->color = RB_BLACK;</span></p>
<p class="MsoNormal" style="text-indent:17.95pt;mso-char-indent-count:1.71;
mso-char-indent-size:10.45pt"><span lang="EN-US">ap[--ak]->color = RB_RED;</span></p>
<p class="MsoNormal" style="text-indent:17.95pt;mso-char-indent-count:1.71;
mso-char-indent-size:10.45pt"><span lang="EN-US"> <o:p>
</o:p>
</span></p>
<p class="MsoNormal" style="text-indent:17.95pt;mso-char-indent-count:1.71;
mso-char-indent-size:10.45pt"><span style="font-family:宋体;mso-ascii-font-family:
"Times New Roman";mso-hansi-font-family:"Times New Roman"">这一段代码的示意图如下</span></p>
<p class="MsoNormal" style="text-indent:17.95pt;mso-char-indent-count:1.71;
mso-char-indent-size:10.45pt"><span style="font-family:宋体;mso-ascii-font-family:
"Times New Roman";mso-hansi-font-family:"Times New Roman"">图中的</span><span lang="EN-US">x</span><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";
mso-hansi-font-family:"Times New Roman"">指向两个结点是表明</span><span lang="EN-US">x</span><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:
"Times New Roman"">可以是其中任一个结点</span></p>
<p class="MsoNormal" style="text-indent:17.95pt;mso-char-indent-count:1.71;
mso-char-indent-size:10.45pt"><span lang="EN-US"> <o:p>
</o:p>
</span></p>
<p class="MsoNormal" style="text-indent:17.95pt;mso-char-indent-count:1.71;
mso-char-indent-size:10.45pt"><span style="font-family:宋体;mso-ascii-font-family:
"Times New Roman";mso-hansi-font-family:"Times New Roman"">在这里请记住，经过这一次的变换后当前的结点已经变成原来结点的爷爷。</span></p>
<p class="MsoNormal" style="text-indent:17.95pt;mso-char-indent-count:1.71;
mso-char-indent-size:10.45pt"><span lang="EN-US"> <o:p>
</o:p>
</span></p>
<p class="MsoNormal" style="text-indent:17.95pt;mso-char-indent-count:1.71;
mso-char-indent-size:10.45pt"><span lang="EN-US"> <o:p>
</o:p>
</span></p>
<p class="MsoNormal" style="text-indent:17.95pt;mso-char-indent-count:1.71;
mso-char-indent-size:10.45pt"><span lang="EN-US"><!--[if gte vml 1]><v:shape
id="_x0000_i1026" type="#_x0000_t75" style='width:414.75pt;height:200.25pt'>
<v:imagedata src="file:///E:/DOCUME~1/ADMINI~1.000/LOCALS~1/Temp/msoclip1/01/clip_image003.png"
o:title="addcase1"/>
</v:shape><![endif]-->
<img src="红黑2.jpg" v:shapes="_x0000_i1026" width="553" height="267"></span></p>
<p class="MsoNormal" style="text-indent:17.95pt;mso-char-indent-count:1.71;
mso-char-indent-size:10.45pt"><span lang="EN-US"> <o:p>
</o:p>
</span></p>
<p class="MsoNormal" style="text-indent:17.95pt;mso-char-indent-count:1.71;
mso-char-indent-size:10.45pt"><span style="font-family:宋体;mso-ascii-font-family:
"Times New Roman";mso-hansi-font-family:"Times New Roman"">第二种可能性的源代码：</span></p>
<p class="MsoNormal" style="text-indent:17.95pt;mso-char-indent-count:1.71;
mso-char-indent-size:10.45pt"><span lang="EN-US"><span style="mso-spacerun:
yes"> </span>else {</span></p>
<p class="MsoNormal" style="text-indent:17.95pt;mso-char-indent-count:1.71;
mso-char-indent-size:10.45pt"><span lang="EN-US">if (ad[ak - 1] == 1) {//</span><span style="font-family:宋体;mso-ascii-font-family:
"Times New Roman";mso-hansi-font-family:"Times New Roman"">如果当前结点是其父结点的右子结点</span><span lang="EN-US">,</span><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";
mso-hansi-font-family:"Times New Roman"">则进行一次左旋，具体的实</span></p>
<p class="MsoNormal" style="text-indent:17.95pt;mso-char-indent-count:1.71;
mso-char-indent-size:10.45pt"><span lang="EN-US">//</span><span style="font-family:
宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"">现请看下面的那个图，这样第二种可能就变成了第三种可能</span></p>
<p class="MsoNormal" style="text-indent:17.95pt;mso-char-indent-count:1.71;
mso-char-indent-size:10.45pt"><span lang="EN-US"><span style="mso-spacerun: yes">
</span>x = ap[ak - 1];//x</span><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:
"Times New Roman"">把当前结点变为它的父结点，就是下图左图中的</span><span lang="EN-US">p(x)</span></p>
<p class="MsoNormal" style="text-indent:17.95pt;mso-char-indent-count:1.71;
mso-char-indent-size:10.45pt"><span lang="EN-US"><span style="mso-spacerun: yes">
</span>y = x->link[1];//y</span><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:
"Times New Roman"">为下图左图中的</span><span lang="EN-US">x</span></p>
<p class="MsoNormal" style="text-indent:17.95pt;mso-char-indent-count:1.71;
mso-char-indent-size:10.45pt"><span lang="EN-US"><span style="mso-spacerun: yes">
</span>x->link[1] = y->link[0];//</span><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:
"Times New Roman"">当前结点的</span><span lang="EN-US">x</span><span style="font-family:
宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"">的右结点变为</span><span lang="EN-US">y</span><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";
mso-hansi-font-family:"Times New Roman"">的左结点</span></p>
<p class="MsoNormal" style="text-indent:17.95pt;mso-char-indent-count:1.71;
mso-char-indent-size:10.45pt"><span lang="EN-US"><span style="mso-spacerun: yes">
</span>y->link[0] = x;//y </span><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:
"Times New Roman"">的左子结点也就是</span><span lang="EN-US">x</span></p>
<p class="MsoNormal" style="text-indent:17.95pt;mso-char-indent-count:1.71;
mso-char-indent-size:10.45pt"><span lang="EN-US"><span style="mso-spacerun: yes">
</span>ap[ak - 2]->link[0] = y;//y</span><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:
"Times New Roman"">成为新的当前结点的父结点，就是下图右图中的</span><span lang="EN-US">x</span><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:
"Times New Roman"">的父结点</span></p>
<p class="MsoNormal" style="text-indent:17.95pt;mso-char-indent-count:1.71;
mso-char-indent-size:10.45pt"><span lang="EN-US">//</span><span style="font-family:
宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"">这上面的四个等式就是一个左旋</span></p>
<p class="MsoNormal" style="text-indent:17.95pt;mso-char-indent-count:1.71;
mso-char-indent-size:10.45pt"><span lang="EN-US">}</span></p>
<p class="MsoNormal" style="text-indent:17.95pt;mso-char-indent-count:1.71;
mso-char-indent-size:10.45pt"><span lang="EN-US"> <o:p>
</o:p>
</span></p>
<p class="MsoNormal" style="text-indent:17.95pt;mso-char-indent-count:1.71;
mso-char-indent-size:10.45pt"><span lang="EN-US"> <o:p>
</o:p>
</span></p>
<p class="MsoNormal" style="text-indent:17.95pt;mso-char-indent-count:1.71;
mso-char-indent-size:10.45pt"><span lang="EN-US"><!--[if gte vml 1]><v:shape
id="_x0000_i1027" type="#_x0000_t75" style='width:414.75pt;height:200.25pt'>
<v:imagedata src="file:///E:/DOCUME~1/ADMINI~1.000/LOCALS~1/Temp/msoclip1/01/clip_image005.png"
o:title="addcase2"/>
</v:shape><![endif]-->
<img src="红黑3.jpg" v:shapes="_x0000_i1027" width="553" height="267"></span></p>
<p class="MsoNormal" style="text-indent:17.95pt;mso-char-indent-count:1.71;
mso-char-indent-size:10.45pt"><span style="font-family:宋体;mso-ascii-font-family:
"Times New Roman";mso-hansi-font-family:"Times New Roman"">在这里特别注意的是经过这一次的变换后，当前的结点</span><span lang="EN-US">x(</span><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";
mso-hansi-font-family:"Times New Roman"">在右图中的</span><span lang="EN-US">x)</span><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:
"Times New Roman"">已经变成未变换时的</span><span lang="EN-US">p(x)(</span><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:
"Times New Roman"">在左图中的</span><span lang="EN-US">p(x))</span><span style="font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:
"Times New Roman"">而这个结点是原来自己子结点的子结点了</span></p>
<p class="MsoNormal" style="text-indent:17.95pt;mso-char-indent-count:1.71;
mso-char-indent-size:10.45pt"><span lang="EN-US"> <o:p>
</o:p>
</span></p>
<p class="MsoNormal" style="text-indent:17.95pt;mso-char-indent-count:1.71;
mso-char-indent-size:10.45pt"><span lang="EN-US"> <o:p>
</o:p>
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