PHP二叉树（三）：红黑树
来源：互联网 发布：单片机输入的是1和0吗 编辑：程序博客网 时间：2024/05/19 02:21
关于红黑树的原理网上的资源就挺多的，而且情况有点小复杂，所以在这里我就不再陈述了，直接上代码吧：
<code class="hljs xml has-numbering"><span class="php"><span class="hljs-comment"><span class="hljs-preprocessor"><?php</span>/** * author:zhongjin * time:2016/10/20 11:53 * description: 红黑树 */</span><span class="hljs-comment">//结点</span><span class="hljs-class"><span class="hljs-keyword">class</span> <span class="hljs-title">Node</span>{</span> <span class="hljs-keyword">public</span> <span class="hljs-variable">$key</span>; <span class="hljs-keyword">public</span> <span class="hljs-variable">$parent</span>; <span class="hljs-keyword">public</span> <span class="hljs-variable">$left</span>; <span class="hljs-keyword">public</span> <span class="hljs-variable">$right</span>; <span class="hljs-keyword">public</span> <span class="hljs-variable">$IsRed</span>; <span class="hljs-comment">//分辨红节点或黑节点</span> <span class="hljs-keyword">public</span> <span class="hljs-function"><span class="hljs-keyword">function</span> <span class="hljs-title">__construct</span><span class="hljs-params">(<span class="hljs-variable">$key</span>, <span class="hljs-variable">$IsRed</span> = TRUE)</span> {</span> <span class="hljs-variable">$this</span>->key = <span class="hljs-variable">$key</span>; <span class="hljs-variable">$this</span>-><span class="hljs-keyword">parent</span> = <span class="hljs-keyword">NULL</span>; <span class="hljs-variable">$this</span>->left = <span class="hljs-keyword">NULL</span>; <span class="hljs-variable">$this</span>->right = <span class="hljs-keyword">NULL</span>; <span class="hljs-comment">//插入结点默认是红色</span> <span class="hljs-variable">$this</span>->IsRed = <span class="hljs-variable">$IsRed</span>; }}<span class="hljs-comment">//红黑树</span><span class="hljs-class"><span class="hljs-keyword">class</span> <span class="hljs-title">Rbt</span>{</span> <span class="hljs-keyword">public</span> <span class="hljs-variable">$root</span>; <span class="hljs-comment">/** * 初始化树结构 *<span class="hljs-phpdoc"> @param</span> $arr 初始化树结构的数组 *<span class="hljs-phpdoc"> @return</span> null */</span> <span class="hljs-keyword">public</span> <span class="hljs-function"><span class="hljs-keyword">function</span> <span class="hljs-title">init</span><span class="hljs-params">(<span class="hljs-variable">$arr</span>)</span> {</span> <span class="hljs-comment">//根节点必须是黑色</span> <span class="hljs-variable">$this</span>->root = <span class="hljs-keyword">new</span> Node(<span class="hljs-variable">$arr</span>[<span class="hljs-number">0</span>], <span class="hljs-keyword">FALSE</span>); <span class="hljs-keyword">for</span> (<span class="hljs-variable">$i</span> = <span class="hljs-number">1</span>; <span class="hljs-variable">$i</span> < count(<span class="hljs-variable">$arr</span>); <span class="hljs-variable">$i</span>++) { <span class="hljs-variable">$this</span>->Insert(<span class="hljs-variable">$arr</span>[<span class="hljs-variable">$i</span>]); } } <span class="hljs-comment">/** * （对内）中序遍历 *<span class="hljs-phpdoc"> @param</span> $root （树或子树的）根节点 *<span class="hljs-phpdoc"> @return</span> null */</span> <span class="hljs-keyword">private</span> <span class="hljs-function"><span class="hljs-keyword">function</span> <span class="hljs-title">mid_order</span><span class="hljs-params">(<span class="hljs-variable">$root</span>)</span> {</span> <span class="hljs-keyword">if</span> (<span class="hljs-variable">$root</span> != <span class="hljs-keyword">NULL</span>) { <span class="hljs-variable">$this</span>->mid_order(<span class="hljs-variable">$root</span>->left); <span class="hljs-keyword">echo</span> <span class="hljs-variable">$root</span>->key . <span class="hljs-string">"-"</span> . (<span class="hljs-variable">$root</span>->IsRed ? <span class="hljs-string">'r'</span> : <span class="hljs-string">'b'</span>) . <span class="hljs-string">' '</span>; <span class="hljs-variable">$this</span>->mid_order(<span class="hljs-variable">$root</span>->right); } } <span class="hljs-comment">/** * （对外）中序遍历 *<span class="hljs-phpdoc"> @param</span> null *<span class="hljs-phpdoc"> @return</span> null */</span> <span class="hljs-keyword">public</span> <span class="hljs-function"><span class="hljs-keyword">function</span> <span class="hljs-title">MidOrder</span><span class="hljs-params">()</span> {</span> <span class="hljs-variable">$this</span>->mid_order(<span class="hljs-variable">$this</span>->root); } <span class="hljs-comment">/** * 查找树中是否存在$key对应的节点 *<span class="hljs-phpdoc"> @param</span> $key 待搜索数字 *<span class="hljs-phpdoc"> @return</span> $key对应的节点 */</span> <span class="hljs-function"><span class="hljs-keyword">function</span> <span class="hljs-title">search</span><span class="hljs-params">(<span class="hljs-variable">$key</span>)</span> {</span> <span class="hljs-variable">$current</span> = <span class="hljs-variable">$this</span>->root; <span class="hljs-keyword">while</span> (<span class="hljs-variable">$current</span> != <span class="hljs-keyword">NULL</span>) { <span class="hljs-keyword">if</span> (<span class="hljs-variable">$current</span>->key == <span class="hljs-variable">$key</span>) { <span class="hljs-keyword">return</span> <span class="hljs-variable">$current</span>; } <span class="hljs-keyword">elseif</span> (<span class="hljs-variable">$current</span>->key > <span class="hljs-variable">$key</span>) { <span class="hljs-variable">$current</span> = <span class="hljs-variable">$current</span>->left; } <span class="hljs-keyword">else</span> { <span class="hljs-variable">$current</span> = <span class="hljs-variable">$current</span>->right; } } <span class="hljs-comment">//结点不存在</span> <span class="hljs-keyword">return</span> <span class="hljs-variable">$current</span>; } <span class="hljs-comment">/** * 将以$root为根节点的最小不平衡二叉树做右旋处理 *<span class="hljs-phpdoc"> @param</span> $root（树或子树）根节点 *<span class="hljs-phpdoc"> @return</span> null */</span> <span class="hljs-keyword">private</span> <span class="hljs-function"><span class="hljs-keyword">function</span> <span class="hljs-title">R_Rotate</span><span class="hljs-params">(<span class="hljs-variable">$root</span>)</span> {</span> <span class="hljs-variable">$L</span> = <span class="hljs-variable">$root</span>->left; <span class="hljs-keyword">if</span> (!is_null(<span class="hljs-variable">$root</span>-><span class="hljs-keyword">parent</span>)) { <span class="hljs-variable">$P</span> = <span class="hljs-variable">$root</span>-><span class="hljs-keyword">parent</span>; <span class="hljs-keyword">if</span>(<span class="hljs-variable">$root</span> == <span class="hljs-variable">$P</span>->left){ <span class="hljs-variable">$P</span>->left = <span class="hljs-variable">$L</span>; }<span class="hljs-keyword">else</span>{ <span class="hljs-variable">$P</span>->right = <span class="hljs-variable">$L</span>; } <span class="hljs-variable">$L</span>-><span class="hljs-keyword">parent</span> = <span class="hljs-variable">$P</span>; } <span class="hljs-keyword">else</span> { <span class="hljs-variable">$L</span>-><span class="hljs-keyword">parent</span> = <span class="hljs-keyword">NULL</span>; } <span class="hljs-variable">$root</span>-><span class="hljs-keyword">parent</span> = <span class="hljs-variable">$L</span>; <span class="hljs-variable">$root</span>->left = <span class="hljs-variable">$L</span>->right; <span class="hljs-variable">$L</span>->right = <span class="hljs-variable">$root</span>; <span class="hljs-comment">//这句必须啊！</span> <span class="hljs-keyword">if</span> (<span class="hljs-variable">$L</span>-><span class="hljs-keyword">parent</span> == <span class="hljs-keyword">NULL</span>) { <span class="hljs-variable">$this</span>->root = <span class="hljs-variable">$L</span>; } } <span class="hljs-comment">/** * 将以$root为根节点的最小不平衡二叉树做左旋处理 *<span class="hljs-phpdoc"> @param</span> $root（树或子树）根节点 *<span class="hljs-phpdoc"> @return</span> null */</span> <span class="hljs-keyword">private</span> <span class="hljs-function"><span class="hljs-keyword">function</span> <span class="hljs-title">L_Rotate</span><span class="hljs-params">(<span class="hljs-variable">$root</span>)</span> {</span> <span class="hljs-variable">$R</span> = <span class="hljs-variable">$root</span>->right; <span class="hljs-keyword">if</span> (!is_null(<span class="hljs-variable">$root</span>-><span class="hljs-keyword">parent</span>)) { <span class="hljs-variable">$P</span> = <span class="hljs-variable">$root</span>-><span class="hljs-keyword">parent</span>; <span class="hljs-keyword">if</span>(<span class="hljs-variable">$root</span> == <span class="hljs-variable">$P</span>->right){ <span class="hljs-variable">$P</span>->right = <span class="hljs-variable">$R</span>; }<span class="hljs-keyword">else</span>{ <span class="hljs-variable">$P</span>->left = <span class="hljs-variable">$R</span>; } <span class="hljs-variable">$R</span>-><span class="hljs-keyword">parent</span> = <span class="hljs-variable">$P</span>; } <span class="hljs-keyword">else</span> { <span class="hljs-variable">$R</span>-><span class="hljs-keyword">parent</span> = <span class="hljs-keyword">NULL</span>; } <span class="hljs-variable">$root</span>-><span class="hljs-keyword">parent</span> = <span class="hljs-variable">$R</span>; <span class="hljs-variable">$root</span>->right = <span class="hljs-variable">$R</span>->left; <span class="hljs-variable">$R</span>->left = <span class="hljs-variable">$root</span>; <span class="hljs-comment">//这句必须啊！</span> <span class="hljs-keyword">if</span> (<span class="hljs-variable">$R</span>-><span class="hljs-keyword">parent</span> == <span class="hljs-keyword">NULL</span>) { <span class="hljs-variable">$this</span>->root = <span class="hljs-variable">$R</span>; } } <span class="hljs-comment">/** * 查找树中的最小关键字 *<span class="hljs-phpdoc"> @param</span> $root 根节点 *<span class="hljs-phpdoc"> @return</span> 最小关键字对应的节点 */</span> <span class="hljs-function"><span class="hljs-keyword">function</span> <span class="hljs-title">search_min</span><span class="hljs-params">(<span class="hljs-variable">$root</span>)</span> {</span> <span class="hljs-variable">$current</span> = <span class="hljs-variable">$root</span>; <span class="hljs-keyword">while</span> (<span class="hljs-variable">$current</span>->left != <span class="hljs-keyword">NULL</span>) { <span class="hljs-variable">$current</span> = <span class="hljs-variable">$current</span>->left; } <span class="hljs-keyword">return</span> <span class="hljs-variable">$current</span>; } <span class="hljs-comment">/** * 查找树中的最大关键字 *<span class="hljs-phpdoc"> @param</span> $root 根节点 *<span class="hljs-phpdoc"> @return</span> 最大关键字对应的节点 */</span> <span class="hljs-function"><span class="hljs-keyword">function</span> <span class="hljs-title">search_max</span><span class="hljs-params">(<span class="hljs-variable">$root</span>)</span> {</span> <span class="hljs-variable">$current</span> = <span class="hljs-variable">$root</span>; <span class="hljs-keyword">while</span> (<span class="hljs-variable">$current</span>->right != <span class="hljs-keyword">NULL</span>) { <span class="hljs-variable">$current</span> = <span class="hljs-variable">$current</span>->right; } <span class="hljs-keyword">return</span> <span class="hljs-variable">$current</span>; } <span class="hljs-comment">/** * 查找某个$key在中序遍历时的直接前驱节点 *<span class="hljs-phpdoc"> @param</span> $x 待查找前驱节点的节点引用 *<span class="hljs-phpdoc"> @return</span> 前驱节点引用 */</span> <span class="hljs-function"><span class="hljs-keyword">function</span> <span class="hljs-title">predecessor</span><span class="hljs-params">(<span class="hljs-variable">$x</span>)</span> {</span> <span class="hljs-comment">//左子节点存在，直接返回左子节点的最右子节点</span> <span class="hljs-keyword">if</span> (<span class="hljs-variable">$x</span>->left != <span class="hljs-keyword">NULL</span>) { <span class="hljs-keyword">return</span> <span class="hljs-variable">$this</span>->search_max(<span class="hljs-variable">$x</span>->left); } <span class="hljs-comment">//否则查找其父节点，直到当前结点位于父节点的右边</span> <span class="hljs-variable">$p</span> = <span class="hljs-variable">$x</span>-><span class="hljs-keyword">parent</span>; <span class="hljs-comment">//如果x是p的左孩子，说明p是x的后继，我们需要找的是p是x的前驱</span> <span class="hljs-keyword">while</span> (<span class="hljs-variable">$p</span> != <span class="hljs-keyword">NULL</span> && <span class="hljs-variable">$x</span> == <span class="hljs-variable">$p</span>->left) { <span class="hljs-variable">$x</span> = <span class="hljs-variable">$p</span>; <span class="hljs-variable">$p</span> = <span class="hljs-variable">$p</span>-><span class="hljs-keyword">parent</span>; } <span class="hljs-keyword">return</span> <span class="hljs-variable">$p</span>; } <span class="hljs-comment">/** * 查找某个$key在中序遍历时的直接后继节点 *<span class="hljs-phpdoc"> @param</span> $x 待查找后继节点的节点引用 *<span class="hljs-phpdoc"> @return</span> 后继节点引用 */</span> <span class="hljs-function"><span class="hljs-keyword">function</span> <span class="hljs-title">successor</span><span class="hljs-params">(<span class="hljs-variable">$x</span>)</span> {</span> <span class="hljs-keyword">if</span> (<span class="hljs-variable">$x</span>->left != <span class="hljs-keyword">NULL</span>) { <span class="hljs-keyword">return</span> <span class="hljs-variable">$this</span>->search_min(<span class="hljs-variable">$x</span>->right); } <span class="hljs-variable">$p</span> = <span class="hljs-variable">$x</span>-><span class="hljs-keyword">parent</span>; <span class="hljs-keyword">while</span> (<span class="hljs-variable">$p</span> != <span class="hljs-keyword">NULL</span> && <span class="hljs-variable">$x</span> == <span class="hljs-variable">$p</span>->right) { <span class="hljs-variable">$x</span> = <span class="hljs-variable">$p</span>; <span class="hljs-variable">$p</span> = <span class="hljs-variable">$p</span>-><span class="hljs-keyword">parent</span>; } <span class="hljs-keyword">return</span> <span class="hljs-variable">$p</span>; } <span class="hljs-comment">/** * 将$key插入树中 *<span class="hljs-phpdoc"> @param</span> $key 待插入树的数字 *<span class="hljs-phpdoc"> @return</span> null */</span> <span class="hljs-keyword">public</span> <span class="hljs-function"><span class="hljs-keyword">function</span> <span class="hljs-title">Insert</span><span class="hljs-params">(<span class="hljs-variable">$key</span>)</span> {</span> <span class="hljs-keyword">if</span> (!is_null(<span class="hljs-variable">$this</span>->search(<span class="hljs-variable">$key</span>))) { <span class="hljs-keyword">throw</span> <span class="hljs-keyword">new</span> <span class="hljs-keyword">Exception</span>(<span class="hljs-string">'结点'</span> . <span class="hljs-variable">$key</span> . <span class="hljs-string">'已存在，不可插入！'</span>); } <span class="hljs-variable">$root</span> = <span class="hljs-variable">$this</span>->root; <span class="hljs-variable">$inode</span> = <span class="hljs-keyword">new</span> Node(<span class="hljs-variable">$key</span>); <span class="hljs-variable">$current</span> = <span class="hljs-variable">$root</span>; <span class="hljs-variable">$prenode</span> = <span class="hljs-keyword">NULL</span>; <span class="hljs-comment">//为$inode找到合适的插入位置</span> <span class="hljs-keyword">while</span> (<span class="hljs-variable">$current</span> != <span class="hljs-keyword">NULL</span>) { <span class="hljs-variable">$prenode</span> = <span class="hljs-variable">$current</span>; <span class="hljs-keyword">if</span> (<span class="hljs-variable">$current</span>->key > <span class="hljs-variable">$inode</span>->key) { <span class="hljs-variable">$current</span> = <span class="hljs-variable">$current</span>->left; } <span class="hljs-keyword">else</span> { <span class="hljs-variable">$current</span> = <span class="hljs-variable">$current</span>->right; } } <span class="hljs-variable">$inode</span>-><span class="hljs-keyword">parent</span> = <span class="hljs-variable">$prenode</span>; <span class="hljs-comment">//如果$prenode == NULL， 则证明树是空树</span> <span class="hljs-keyword">if</span> (<span class="hljs-variable">$prenode</span> == <span class="hljs-keyword">NULL</span>) { <span class="hljs-variable">$this</span>->root = <span class="hljs-variable">$inode</span>; } <span class="hljs-keyword">else</span> { <span class="hljs-keyword">if</span> (<span class="hljs-variable">$inode</span>->key < <span class="hljs-variable">$prenode</span>->key) { <span class="hljs-variable">$prenode</span>->left = <span class="hljs-variable">$inode</span>; } <span class="hljs-keyword">else</span> { <span class="hljs-variable">$prenode</span>->right = <span class="hljs-variable">$inode</span>; } } <span class="hljs-comment">//将它重新修正为一颗红黑树</span> <span class="hljs-variable">$this</span>->InsertFixUp(<span class="hljs-variable">$inode</span>); } <span class="hljs-comment">/** * 对插入节点的位置及往上的位置进行颜色调整 *<span class="hljs-phpdoc"> @param</span> $inode 插入的节点 *<span class="hljs-phpdoc"> @return</span> null */</span> <span class="hljs-keyword">private</span> <span class="hljs-function"><span class="hljs-keyword">function</span> <span class="hljs-title">InsertFixUp</span><span class="hljs-params">(<span class="hljs-variable">$inode</span>)</span> {</span> <span class="hljs-comment">//情况一：需要调整条件，父节点存在且父节点的颜色是红色</span> <span class="hljs-keyword">while</span> ((<span class="hljs-variable">$parent</span> = <span class="hljs-variable">$inode</span>-><span class="hljs-keyword">parent</span>) != <span class="hljs-keyword">NULL</span> && <span class="hljs-variable">$parent</span>->IsRed == <span class="hljs-keyword">TRUE</span>) { <span class="hljs-comment">//祖父结点：</span> <span class="hljs-variable">$gparent</span> = <span class="hljs-variable">$parent</span>-><span class="hljs-keyword">parent</span>; <span class="hljs-comment">//如果父节点是祖父结点的左子结点，下面的else与此相反</span> <span class="hljs-keyword">if</span> (<span class="hljs-variable">$parent</span> == <span class="hljs-variable">$gparent</span>->left) { <span class="hljs-comment">//叔叔结点</span> <span class="hljs-variable">$uncle</span> = <span class="hljs-variable">$gparent</span>->right; <span class="hljs-comment">//case1:叔叔结点也是红色</span> <span class="hljs-keyword">if</span> (<span class="hljs-variable">$uncle</span> != <span class="hljs-keyword">NULL</span> && <span class="hljs-variable">$uncle</span>->IsRed == <span class="hljs-keyword">TRUE</span>) { <span class="hljs-comment">//将父节点和叔叔结点都涂黑，将祖父结点涂红</span> <span class="hljs-variable">$parent</span>->IsRed = <span class="hljs-keyword">FALSE</span>; <span class="hljs-variable">$uncle</span>->IsRed = <span class="hljs-keyword">FALSE</span>; <span class="hljs-variable">$gparent</span>->IsRed = <span class="hljs-keyword">TRUE</span>; <span class="hljs-comment">//将新节点指向祖父节点（现在祖父结点变红，可以看作新节点存在）</span> <span class="hljs-variable">$inode</span> = <span class="hljs-variable">$gparent</span>; <span class="hljs-comment">//继续while循环，重新判断</span> <span class="hljs-keyword">continue</span>; <span class="hljs-comment">//经过这一步之后，组父节点作为新节点存在（跳到case2）</span> } <span class="hljs-comment">//case2:叔叔结点是黑色，且当前结点是右子节点</span> <span class="hljs-keyword">if</span> (<span class="hljs-variable">$inode</span> == <span class="hljs-variable">$parent</span>->right) { <span class="hljs-comment">//以父节点作为旋转结点做左旋转处理</span> <span class="hljs-variable">$this</span>->L_Rotate(<span class="hljs-variable">$parent</span>); <span class="hljs-comment">//在树中实际上已经转换，但是这里的变量的指向还没交换，</span> <span class="hljs-comment">//将父节点和字节调换一下，为下面右旋做准备</span> <span class="hljs-variable">$temp</span> = <span class="hljs-variable">$parent</span>; <span class="hljs-variable">$parent</span> = <span class="hljs-variable">$inode</span>; <span class="hljs-variable">$inode</span> = <span class="hljs-variable">$temp</span>; } <span class="hljs-comment">//case3:叔叔结点是黑色，而且当前结点是父节点的左子节点</span> <span class="hljs-variable">$parent</span>->IsRed = <span class="hljs-keyword">FALSE</span>; <span class="hljs-variable">$gparent</span>->IsRed = <span class="hljs-keyword">TRUE</span>; <span class="hljs-variable">$this</span>->R_Rotate(<span class="hljs-variable">$gparent</span>); } <span class="hljs-comment">//如果父节点是祖父结点的右子结点，与上面完全相反</span> <span class="hljs-keyword">else</span> { <span class="hljs-comment">//叔叔结点</span> <span class="hljs-variable">$uncle</span> = <span class="hljs-variable">$gparent</span>->left; <span class="hljs-comment">//case1:叔叔结点也是红色</span> <span class="hljs-keyword">if</span> (<span class="hljs-variable">$uncle</span> != <span class="hljs-keyword">NULL</span> && <span class="hljs-variable">$uncle</span>->IsRed == <span class="hljs-keyword">TRUE</span>) { <span class="hljs-comment">//将父节点和叔叔结点都涂黑，将祖父结点涂红</span> <span class="hljs-variable">$parent</span>->IsRed = <span class="hljs-keyword">FALSE</span>; <span class="hljs-variable">$uncle</span>->IsRed = <span class="hljs-keyword">FALSE</span>; <span class="hljs-variable">$gparent</span>->IsRed = <span class="hljs-keyword">TRUE</span>; <span class="hljs-comment">//将新节点指向祖父节点（现在祖父结点变红，可以看作新节点存在）</span> <span class="hljs-variable">$inode</span> = <span class="hljs-variable">$gparent</span>; <span class="hljs-comment">//继续while循环，重新判断</span> <span class="hljs-keyword">continue</span>; <span class="hljs-comment">//经过这一步之后，组父节点作为新节点存在（跳到case2）</span> } <span class="hljs-comment">//case2:叔叔结点是黑色，且当前结点是左子节点</span> <span class="hljs-keyword">if</span> (<span class="hljs-variable">$inode</span> == <span class="hljs-variable">$parent</span>->left) { <span class="hljs-comment">//以父节点作为旋转结点做右旋转处理</span> <span class="hljs-variable">$this</span>->R_Rotate(<span class="hljs-variable">$parent</span>); <span class="hljs-comment">//在树中实际上已经转换，但是这里的变量的指向还没交换，</span> <span class="hljs-comment">//将父节点和字节调换一下，为下面右旋做准备</span> <span class="hljs-variable">$temp</span> = <span class="hljs-variable">$parent</span>; <span class="hljs-variable">$parent</span> = <span class="hljs-variable">$inode</span>; <span class="hljs-variable">$inode</span> = <span class="hljs-variable">$temp</span>; } <span class="hljs-comment">//case3:叔叔结点是黑色，而且当前结点是父节点的右子节点</span> <span class="hljs-variable">$parent</span>->IsRed = <span class="hljs-keyword">FALSE</span>; <span class="hljs-variable">$gparent</span>->IsRed = <span class="hljs-keyword">TRUE</span>; <span class="hljs-variable">$this</span>->L_Rotate(<span class="hljs-variable">$gparent</span>); } } <span class="hljs-comment">//情况二：原树是根节点（父节点为空），则只需将根节点涂黑</span> <span class="hljs-keyword">if</span> (<span class="hljs-variable">$inode</span> == <span class="hljs-variable">$this</span>->root) { <span class="hljs-variable">$this</span>->root->IsRed = <span class="hljs-keyword">FALSE</span>; <span class="hljs-keyword">return</span>; } <span class="hljs-comment">//情况三：插入节点的父节点是黑色，则什么也不用做</span> <span class="hljs-keyword">if</span> (<span class="hljs-variable">$inode</span>-><span class="hljs-keyword">parent</span> != <span class="hljs-keyword">NULL</span> && <span class="hljs-variable">$inode</span>-><span class="hljs-keyword">parent</span>->IsRed == <span class="hljs-keyword">FALSE</span>) { <span class="hljs-keyword">return</span>; } } <span class="hljs-comment">/** * （对外）删除指定节点 *<span class="hljs-phpdoc"> @param</span> $key 删除节点的key值 *<span class="hljs-phpdoc"> @return</span> null */</span> <span class="hljs-function"><span class="hljs-keyword">function</span> <span class="hljs-title">Delete</span><span class="hljs-params">(<span class="hljs-variable">$key</span>)</span> {</span> <span class="hljs-keyword">if</span> (is_null(<span class="hljs-variable">$this</span>->search(<span class="hljs-variable">$key</span>))) { <span class="hljs-keyword">throw</span> <span class="hljs-keyword">new</span> <span class="hljs-keyword">Exception</span>(<span class="hljs-string">'结点'</span> . <span class="hljs-variable">$key</span> . <span class="hljs-string">"不存在，删除失败！"</span>); } <span class="hljs-variable">$dnode</span> = <span class="hljs-variable">$this</span>->search(<span class="hljs-variable">$key</span>); <span class="hljs-keyword">if</span> (<span class="hljs-variable">$dnode</span>->left == <span class="hljs-keyword">NULL</span> || <span class="hljs-variable">$dnode</span>->right == <span class="hljs-keyword">NULL</span>) { <span class="hljs-comment">#如果待删除结点无子节点或只有一个子节点，则c = dnode</span> <span class="hljs-variable">$c</span> = <span class="hljs-variable">$dnode</span>; } <span class="hljs-keyword">else</span> { <span class="hljs-comment">#如果待删除结点有两个子节点，c置为dnode的直接后继，以待最后将待删除结点的值换为其后继的值</span> <span class="hljs-variable">$c</span> = <span class="hljs-variable">$this</span>->successor(<span class="hljs-variable">$dnode</span>); } <span class="hljs-comment">//为了后面颜色处理做准备</span> <span class="hljs-variable">$parent</span> = <span class="hljs-variable">$c</span>-><span class="hljs-keyword">parent</span>; <span class="hljs-comment">//无论前面情况如何，到最后c只剩下一边子结点</span> <span class="hljs-keyword">if</span> (<span class="hljs-variable">$c</span>->left != <span class="hljs-keyword">NULL</span>) { <span class="hljs-comment">//这里不会出现，除非选择的是删除结点的前驱</span> <span class="hljs-variable">$s</span> = <span class="hljs-variable">$c</span>->left; } <span class="hljs-keyword">else</span> { <span class="hljs-variable">$s</span> = <span class="hljs-variable">$c</span>->right; } <span class="hljs-keyword">if</span> (<span class="hljs-variable">$s</span> != <span class="hljs-keyword">NULL</span>) { <span class="hljs-comment">#将c的子节点的父母结点置为c的父母结点，此处c只可能有1个子节点，因为如果c有两个子节点，则c不可能是dnode的直接后继</span> <span class="hljs-variable">$s</span>-><span class="hljs-keyword">parent</span> = <span class="hljs-variable">$c</span>-><span class="hljs-keyword">parent</span>; } <span class="hljs-keyword">if</span> (<span class="hljs-variable">$c</span>-><span class="hljs-keyword">parent</span> == <span class="hljs-keyword">NULL</span>) { <span class="hljs-comment">#如果c的父母为空，说明c=dnode是根节点，删除根节点后直接将根节点置为根节点的子节点，此处dnode是根节点，且拥有两个子节点，则c是dnode的后继结点，c的父母就不会为空，就不会进入这个if</span> <span class="hljs-variable">$this</span>->root = <span class="hljs-variable">$s</span>; } <span class="hljs-keyword">else</span> <span class="hljs-keyword">if</span> (<span class="hljs-variable">$c</span> == <span class="hljs-variable">$c</span>-><span class="hljs-keyword">parent</span>->left) { <span class="hljs-comment">#如果c是其父节点的左右子节点，则将c父母的左右子节点置为c的左右子节点</span> <span class="hljs-variable">$c</span>-><span class="hljs-keyword">parent</span>->left = <span class="hljs-variable">$s</span>; } <span class="hljs-keyword">else</span> { <span class="hljs-variable">$c</span>-><span class="hljs-keyword">parent</span>->right = <span class="hljs-variable">$s</span>; } <span class="hljs-variable">$dnode</span>->key = <span class="hljs-variable">$c</span>->key; <span class="hljs-variable">$node</span> = <span class="hljs-variable">$s</span>; <span class="hljs-comment">//c的结点颜色是黑色，那么会影响路径上的黑色结点的数量，必须进行调整</span> <span class="hljs-keyword">if</span> (<span class="hljs-variable">$c</span>->IsRed == <span class="hljs-keyword">FALSE</span>) { <span class="hljs-variable">$this</span>->DeleteFixUp(<span class="hljs-variable">$node</span>,<span class="hljs-variable">$parent</span>); } } <span class="hljs-comment">/** * 删除节点后对接点周围的其他节点进行调整 *<span class="hljs-phpdoc"> @param</span> $key 删除节点的子节点和父节点 *<span class="hljs-phpdoc"> @return</span> null */</span> <span class="hljs-keyword">private</span> <span class="hljs-function"><span class="hljs-keyword">function</span> <span class="hljs-title">DeleteFixUp</span><span class="hljs-params">(<span class="hljs-variable">$node</span>,<span class="hljs-variable">$parent</span>)</span> {</span> <span class="hljs-comment">//如果待删结点的子节点为红色，直接将子节点涂黑</span> <span class="hljs-keyword">if</span> (<span class="hljs-variable">$node</span> != <span class="hljs-keyword">NULL</span> && <span class="hljs-variable">$node</span>->IsRed == <span class="hljs-keyword">TRUE</span>) { <span class="hljs-variable">$node</span>->IsRed = <span class="hljs-keyword">FALSE</span>; <span class="hljs-keyword">return</span>; } <span class="hljs-comment">//如果是根节点，那就直接将根节点置为黑色即可</span> <span class="hljs-keyword">while</span> ((<span class="hljs-variable">$node</span> == <span class="hljs-keyword">NULL</span> || <span class="hljs-variable">$node</span>->IsRed == <span class="hljs-keyword">FALSE</span>) && (<span class="hljs-variable">$node</span> != <span class="hljs-variable">$this</span>->root)) { <span class="hljs-comment">//node是父节点的左子节点，下面else与这里相反</span> <span class="hljs-keyword">if</span> (<span class="hljs-variable">$node</span> == <span class="hljs-variable">$parent</span>->left) { <span class="hljs-variable">$brother</span> = <span class="hljs-variable">$parent</span>->right; <span class="hljs-comment">//case1:兄弟结点颜色是红色（父节点和兄弟孩子结点都是黑色）</span> <span class="hljs-comment">//将父节点涂红，将兄弟结点涂黑，然后对父节点进行左旋处理（经过这一步，情况转换为兄弟结点颜色为黑色的情况）</span> <span class="hljs-keyword">if</span> (<span class="hljs-variable">$brother</span>->IsRed == <span class="hljs-keyword">TRUE</span>) { <span class="hljs-variable">$brother</span>->IsRed = <span class="hljs-keyword">FALSE</span>; <span class="hljs-variable">$parent</span>->IsRed = <span class="hljs-keyword">TRUE</span>; <span class="hljs-variable">$this</span>->L_Rotate(<span class="hljs-variable">$parent</span>); <span class="hljs-comment">//将情况转化为其他的情况</span> <span class="hljs-variable">$brother</span> = <span class="hljs-variable">$parent</span>->right; <span class="hljs-comment">//在左旋处理后，$parent->right指向的是原来兄弟结点的左子节点</span> } <span class="hljs-comment">//以下是兄弟结点为黑色的情况</span> <span class="hljs-comment">//case2:兄弟结点是黑色，且兄弟结点的两个子节点都是黑色</span> <span class="hljs-comment">//将兄弟结点涂红，将当前结点指向其父节点，将其父节点指向当前结点的祖父结点。</span> <span class="hljs-keyword">if</span> ((<span class="hljs-variable">$brother</span>->left == <span class="hljs-keyword">NULL</span> || <span class="hljs-variable">$brother</span>->left->IsRed == <span class="hljs-keyword">FALSE</span>) && (<span class="hljs-variable">$brother</span>->right == <span class="hljs-keyword">NULL</span> || <span class="hljs-variable">$brother</span>->right->IsRed == <span class="hljs-keyword">FALSE</span>)) { <span class="hljs-variable">$brother</span>->IsRed = <span class="hljs-keyword">TRUE</span>; <span class="hljs-variable">$node</span> = <span class="hljs-variable">$parent</span>; <span class="hljs-variable">$parent</span> = <span class="hljs-variable">$node</span>-><span class="hljs-keyword">parent</span>; } <span class="hljs-keyword">else</span> { <span class="hljs-comment">//case3:兄弟结点是黑色，兄弟结点的左子节点是红色，右子节点为黑色</span> <span class="hljs-comment">//将兄弟结点涂红，将兄弟节点的左子节点涂黑，然后对兄弟结点做右旋处理（经过这一步，情况转换为兄弟结点颜色为黑色，右子节点为红色的情况）</span> <span class="hljs-keyword">if</span> (<span class="hljs-variable">$brother</span>->right == <span class="hljs-keyword">NULL</span> || <span class="hljs-variable">$brother</span>->right->IsRed == <span class="hljs-keyword">FALSE</span>) { <span class="hljs-variable">$brother</span>->IsRed = <span class="hljs-keyword">TRUE</span>; <span class="hljs-variable">$brother</span>->left->IsRed = <span class="hljs-keyword">FALSE</span>; <span class="hljs-variable">$this</span>->R_Rotate(<span class="hljs-variable">$brother</span>); <span class="hljs-comment">//将情况转换为其他情况</span> <span class="hljs-variable">$brother</span> = <span class="hljs-variable">$parent</span>->right; } <span class="hljs-comment">//case4:兄弟结点是黑色，且兄弟结点的右子节点为红色，左子节点为任意颜色</span> <span class="hljs-comment">//将兄弟节点涂成父节点的颜色，再把父节点涂黑，将兄弟结点的右子节点涂黑，然后对父节点做左旋处理</span> <span class="hljs-variable">$brother</span>->IsRed = <span class="hljs-variable">$parent</span>->IsRed; <span class="hljs-variable">$parent</span>->IsRed = <span class="hljs-keyword">FALSE</span>; <span class="hljs-variable">$brother</span>->right->IsRed = <span class="hljs-keyword">FALSE</span>; <span class="hljs-variable">$this</span>->L_Rotate(<span class="hljs-variable">$parent</span>); <span class="hljs-comment">//到了第四种情况，已经是最基本的情况了，可以直接退出了</span> <span class="hljs-variable">$node</span> = <span class="hljs-variable">$this</span>->root; <span class="hljs-keyword">break</span>; } } <span class="hljs-comment">//node是父节点的右子节点</span> <span class="hljs-keyword">else</span> { <span class="hljs-variable">$brother</span> = <span class="hljs-variable">$parent</span>->left; <span class="hljs-comment">//case1:兄弟结点颜色是红色（父节点和兄弟孩子结点都是黑色）</span> <span class="hljs-comment">//将父节点涂红，将兄弟结点涂黑，然后对父节点进行右旋处理（经过这一步，情况转换为兄弟结点颜色为黑色的情况）</span> <span class="hljs-keyword">if</span> (<span class="hljs-variable">$brother</span>->IsRed == <span class="hljs-keyword">TRUE</span>) { <span class="hljs-variable">$brother</span>->IsRed = <span class="hljs-keyword">FALSE</span>; <span class="hljs-variable">$parent</span>->IsRed = <span class="hljs-keyword">TRUE</span>; <span class="hljs-variable">$this</span>->R_Rotate(<span class="hljs-variable">$parent</span>); <span class="hljs-comment">//将情况转化为其他的情况</span> <span class="hljs-variable">$brother</span> = <span class="hljs-variable">$parent</span>->left; <span class="hljs-comment">//在右旋处理后，$parent->left指向的是原来兄弟结点的右子节点</span> } <span class="hljs-comment">//以下是兄弟结点为黑色的情况</span> <span class="hljs-comment">//case2:兄弟结点是黑色，且兄弟结点的两个子节点都是黑色</span> <span class="hljs-comment">//将兄弟结点涂红，将当前结点指向其父节点，将其父节点指向当前结点的祖父结点。</span> <span class="hljs-keyword">if</span> ((<span class="hljs-variable">$brother</span>->left == <span class="hljs-keyword">NULL</span> || <span class="hljs-variable">$brother</span>->left->IsRed == <span class="hljs-keyword">FALSE</span>) && (<span class="hljs-variable">$brother</span>->right == <span class="hljs-keyword">NULL</span> || <span class="hljs-variable">$brother</span>->right->IsRed == <span class="hljs-keyword">FALSE</span>)) { <span class="hljs-variable">$brother</span>->IsRed = <span class="hljs-keyword">TRUE</span>; <span class="hljs-variable">$node</span> = <span class="hljs-variable">$parent</span>; <span class="hljs-variable">$parent</span> = <span class="hljs-variable">$node</span>-><span class="hljs-keyword">parent</span>; } <span class="hljs-keyword">else</span> { <span class="hljs-comment">//case3:兄弟结点是黑色，兄弟结点的右子节点是红色，左子节点为黑色</span> <span class="hljs-comment">//将兄弟结点涂红，将兄弟节点的左子节点涂黑，然后对兄弟结点做左旋处理（经过这一步，情况转换为兄弟结点颜色为黑色，右子节点为红色的情况）</span> <span class="hljs-keyword">if</span> (<span class="hljs-variable">$brother</span>->left == <span class="hljs-keyword">NULL</span> || <span class="hljs-variable">$brother</span>->left->IsRed == <span class="hljs-keyword">FALSE</span>) { <span class="hljs-variable">$brother</span>->IsRed = <span class="hljs-keyword">TRUE</span>; <span class="hljs-variable">$brother</span>->right = <span class="hljs-keyword">FALSE</span>; <span class="hljs-variable">$this</span>->L_Rotate(<span class="hljs-variable">$brother</span>); <span class="hljs-comment">//将情况转换为其他情况</span> <span class="hljs-variable">$brother</span> = <span class="hljs-variable">$parent</span>->left; } <span class="hljs-comment">//case4:兄弟结点是黑色，且兄弟结点的左子节点为红色，右子节点为任意颜色</span> <span class="hljs-comment">//将兄弟节点涂成父节点的颜色，再把父节点涂黑，将兄弟结点的右子节点涂黑，然后对父节点左左旋处理</span> <span class="hljs-variable">$brother</span>->IsRed = <span class="hljs-variable">$parent</span>->IsRed; <span class="hljs-variable">$parent</span>->IsRed = <span class="hljs-keyword">FALSE</span>; <span class="hljs-variable">$brother</span>->left->IsRed = <span class="hljs-keyword">FALSE</span>; <span class="hljs-variable">$this</span>->R_Rotate(<span class="hljs-variable">$parent</span>); <span class="hljs-variable">$node</span> = <span class="hljs-variable">$this</span>->root; <span class="hljs-keyword">break</span>; } } } <span class="hljs-keyword">if</span> (<span class="hljs-variable">$node</span> != <span class="hljs-keyword">NULL</span>) { <span class="hljs-variable">$this</span>->root->IsRed = <span class="hljs-keyword">FALSE</span>; } } <span class="hljs-comment">/** * （对内）获取树的深度 *<span class="hljs-phpdoc"> @param</span> $root 根节点 *<span class="hljs-phpdoc"> @return</span> 树的深度 */</span> <span class="hljs-keyword">private</span> <span class="hljs-function"><span class="hljs-keyword">function</span> <span class="hljs-title">getdepth</span><span class="hljs-params">(<span class="hljs-variable">$root</span>)</span> {</span> <span class="hljs-keyword">if</span> (<span class="hljs-variable">$root</span> == <span class="hljs-keyword">NULL</span>) { <span class="hljs-keyword">return</span> <span class="hljs-number">0</span>; } <span class="hljs-variable">$dl</span> = <span class="hljs-variable">$this</span>->getdepth(<span class="hljs-variable">$root</span>->left); <span class="hljs-variable">$dr</span> = <span class="hljs-variable">$this</span>->getdepth(<span class="hljs-variable">$root</span>->right); <span class="hljs-keyword">return</span> (<span class="hljs-variable">$dl</span> > <span class="hljs-variable">$dr</span> ? <span class="hljs-variable">$dl</span> : <span class="hljs-variable">$dr</span>) + <span class="hljs-number">1</span>; } <span class="hljs-comment">/** * （对外）获取树的深度 *<span class="hljs-phpdoc"> @param</span> null *<span class="hljs-phpdoc"> @return</span> null */</span> <span class="hljs-keyword">public</span> <span class="hljs-function"><span class="hljs-keyword">function</span> <span class="hljs-title">Depth</span><span class="hljs-params">()</span> {</span> <span class="hljs-keyword">return</span> <span class="hljs-variable">$this</span>->getdepth(<span class="hljs-variable">$this</span>->root); }}</span></code><ul class="pre-numbering" 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><li>426</li><li>427</li><li>428</li><li>429</li><li>430</li><li>431</li><li>432</li><li>433</li><li>434</li><li>435</li><li>436</li><li>437</li><li>438</li><li>439</li><li>440</li><li>441</li><li>442</li><li>443</li><li>444</li><li>445</li><li>446</li><li>447</li><li>448</li><li>449</li><li>450</li><li>451</li><li>452</li><li>453</li><li>454</li><li>455</li><li>456</li><li>457</li><li>458</li><li>459</li><li>460</li><li>461</li><li>462</li><li>463</li><li>464</li><li>465</li><li>466</li><li>467</li><li>468</li><li>469</li><li>470</li><li>471</li><li>472</li><li>473</li><li>474</li><li>475</li><li>476</li><li>477</li><li>478</li><li>479</li><li>480</li><li>481</li><li>482</li><li>483</li><li>484</li><li>485</li><li>486</li><li>487</li><li>488</li><li>489</li><li>490</li><li>491</li><li>492</li><li>493</li><li>494</li><li>495</li><li>496</li><li>497</li><li>498</li><li>499</li><li>500</li><li>501</li><li>502</li><li>503</li><li>504</li><li>505</li><li>506</li><li>507</li><li>508</li><li>509</li><li>510</li><li>511</li><li>512</li><li>513</li><li>514</li><li>515</li><li>516</li><li>517</li><li>518</li><li>519</li><li>520</li><li>521</li><li>522</li><li>523</li><li>524</li><li>525</li><li>526</li><li>527</li><li>528</li><li>529</li></ul>调试的时候你们可以调用中序遍历来做，我在上一篇博客中提供了PHP实现的二叉树图形化，有了视觉上的帮助就能更好的帮助我们进行调试，详细大家可以访问我的上一篇博客：《利用PHP实现二叉树的图形显示》 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