deploy

chapter_tree/avl_tree/index.html

@@ -3682,7 +3682,7 @@
 <a id="__codelineno-69-3" name="__codelineno-69-3" href="#__codelineno-69-3"></a><span class="w">    </span><span class="nx">t</span><span class="p">.</span><span class="nx">root</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">insertHelper</span><span class="p">(</span><span class="nx">t</span><span class="p">.</span><span class="nx">root</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">)</span>
 <a id="__codelineno-69-4" name="__codelineno-69-4" href="#__codelineno-69-4"></a><span class="p">}</span>
 <a id="__codelineno-69-5" name="__codelineno-69-5" href="#__codelineno-69-5"></a>
-<a id="__codelineno-69-6" name="__codelineno-69-6" href="#__codelineno-69-6"></a><span class="cm">/* 递归插入节点（辅助方法） */</span>
+<a id="__codelineno-69-6" name="__codelineno-69-6" href="#__codelineno-69-6"></a><span class="cm">/* 递归插入节点（辅助函数） */</span>
 <a id="__codelineno-69-7" name="__codelineno-69-7" href="#__codelineno-69-7"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">t</span><span class="w"> </span><span class="o">*</span><span class="nx">aVLTree</span><span class="p">)</span><span class="w"> </span><span class="nx">insertHelper</span><span class="p">(</span><span class="nx">node</span><span class="w"> </span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="nx">TreeNode</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-69-8" name="__codelineno-69-8" href="#__codelineno-69-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-69-9" name="__codelineno-69-9" href="#__codelineno-69-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">NewTreeNode</span><span class="p">(</span><span class="nx">val</span><span class="p">)</span>
@@ -3758,7 +3758,7 @@
 <a id="__codelineno-72-3" name="__codelineno-72-3" href="#__codelineno-72-3"></a><span class="w">    </span><span class="n">tree</span><span class="o">-&gt;</span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">insertHelper</span><span class="p">(</span><span class="n">tree</span><span class="o">-&gt;</span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
 <a id="__codelineno-72-4" name="__codelineno-72-4" href="#__codelineno-72-4"></a><span class="p">}</span>
 <a id="__codelineno-72-5" name="__codelineno-72-5" href="#__codelineno-72-5"></a>
-<a id="__codelineno-72-6" name="__codelineno-72-6" href="#__codelineno-72-6"></a><span class="cm">/* 递归插入节点（辅助方法） */</span>
+<a id="__codelineno-72-6" name="__codelineno-72-6" href="#__codelineno-72-6"></a><span class="cm">/* 递归插入节点（辅助函数） */</span>
 <a id="__codelineno-72-7" name="__codelineno-72-7" href="#__codelineno-72-7"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="nf">insertHelper</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-72-8" name="__codelineno-72-8" href="#__codelineno-72-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-72-9" name="__codelineno-72-9" href="#__codelineno-72-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">newTreeNode</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
@@ -3836,8 +3836,8 @@
 </div>
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">avl_tree.zig</span><pre><span></span><code><a id="__codelineno-75-1" name="__codelineno-75-1" href="#__codelineno-75-1"></a><span class="c1">// 插入节点</span>
-<a id="__codelineno-75-2" name="__codelineno-75-2" href="#__codelineno-75-2"></a><span class="k">fn</span><span class="w"> </span><span class="n">insert</span><span class="p">(</span><span class="n">self</span><span class="o">:</span><span class="w"> </span><span class="o">*</span><span class="n">Self</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="o">:</span><span class="w"> </span><span class="n">T</span><span class="p">)</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-75-3" name="__codelineno-75-3" href="#__codelineno-75-3"></a><span class="w">    </span><span class="n">self</span><span class="p">.</span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">try</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">insertHelper</span><span class="p">(</span><span class="n">self</span><span class="p">.</span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-75-2" name="__codelineno-75-2" href="#__codelineno-75-2"></a><span class="k">fn</span><span class="w"> </span><span class="n">insert</span><span class="p">(</span><span class="n">self</span><span class="o">:</span><span class="w"> </span><span class="o">*</span><span class="n">Self</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="o">:</span><span class="w"> </span><span class="n">T</span><span class="p">)</span><span class="w"> </span><span class="o">!</span><span class="kt">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-75-3" name="__codelineno-75-3" href="#__codelineno-75-3"></a><span class="w">    </span><span class="n">self</span><span class="p">.</span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="k">try</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">insertHelper</span><span class="p">(</span><span class="n">self</span><span class="p">.</span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">)).</span><span class="o">?</span><span class="p">;</span>
 <a id="__codelineno-75-4" name="__codelineno-75-4" href="#__codelineno-75-4"></a><span class="p">}</span>
 <a id="__codelineno-75-5" name="__codelineno-75-5" href="#__codelineno-75-5"></a>
 <a id="__codelineno-75-6" name="__codelineno-75-6" href="#__codelineno-75-6"></a><span class="c1">// 递归插入节点（辅助方法）</span>
@@ -4025,7 +4025,7 @@
 <a id="__codelineno-80-3" name="__codelineno-80-3" href="#__codelineno-80-3"></a><span class="w">    </span><span class="nx">t</span><span class="p">.</span><span class="nx">root</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">removeHelper</span><span class="p">(</span><span class="nx">t</span><span class="p">.</span><span class="nx">root</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">)</span>
 <a id="__codelineno-80-4" name="__codelineno-80-4" href="#__codelineno-80-4"></a><span class="p">}</span>
 <a id="__codelineno-80-5" name="__codelineno-80-5" href="#__codelineno-80-5"></a>
-<a id="__codelineno-80-6" name="__codelineno-80-6" href="#__codelineno-80-6"></a><span class="cm">/* 递归删除节点（辅助方法） */</span>
+<a id="__codelineno-80-6" name="__codelineno-80-6" href="#__codelineno-80-6"></a><span class="cm">/* 递归删除节点（辅助函数） */</span>
 <a id="__codelineno-80-7" name="__codelineno-80-7" href="#__codelineno-80-7"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">t</span><span class="w"> </span><span class="o">*</span><span class="nx">aVLTree</span><span class="p">)</span><span class="w"> </span><span class="nx">removeHelper</span><span class="p">(</span><span class="nx">node</span><span class="w"> </span><span class="o">*</span><span class="nx">TreeNode</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="nx">TreeNode</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-80-8" name="__codelineno-80-8" href="#__codelineno-80-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-80-9" name="__codelineno-80-9" href="#__codelineno-80-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="kc">nil</span>
@@ -4154,7 +4154,7 @@
 <a id="__codelineno-83-4" name="__codelineno-83-4" href="#__codelineno-83-4"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">removeHelper</span><span class="p">(</span><span class="n">tree</span><span class="o">-&gt;</span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
 <a id="__codelineno-83-5" name="__codelineno-83-5" href="#__codelineno-83-5"></a><span class="p">}</span>
 <a id="__codelineno-83-6" name="__codelineno-83-6" href="#__codelineno-83-6"></a>
-<a id="__codelineno-83-7" name="__codelineno-83-7" href="#__codelineno-83-7"></a><span class="cm">/* 递归删除节点（辅助方法） */</span>
+<a id="__codelineno-83-7" name="__codelineno-83-7" href="#__codelineno-83-7"></a><span class="cm">/* 递归删除节点（辅助函数） */</span>
 <a id="__codelineno-83-8" name="__codelineno-83-8" href="#__codelineno-83-8"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="nf">removeHelper</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-83-9" name="__codelineno-83-9" href="#__codelineno-83-9"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">child</span><span class="p">,</span><span class="w"> </span><span class="o">*</span><span class="n">grandChild</span><span class="p">;</span>
 <a id="__codelineno-83-10" name="__codelineno-83-10" href="#__codelineno-83-10"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
@@ -4289,7 +4289,7 @@
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">avl_tree.zig</span><pre><span></span><code><a id="__codelineno-86-1" name="__codelineno-86-1" href="#__codelineno-86-1"></a><span class="c1">// 删除节点</span>
 <a id="__codelineno-86-2" name="__codelineno-86-2" href="#__codelineno-86-2"></a><span class="k">fn</span><span class="w"> </span><span class="n">remove</span><span class="p">(</span><span class="n">self</span><span class="o">:</span><span class="w"> </span><span class="o">*</span><span class="n">Self</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="o">:</span><span class="w"> </span><span class="n">T</span><span class="p">)</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-86-3" name="__codelineno-86-3" href="#__codelineno-86-3"></a><span class="w">   </span><span class="n">self</span><span class="p">.</span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">removeHelper</span><span class="p">(</span><span class="n">self</span><span class="p">.</span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-86-3" name="__codelineno-86-3" href="#__codelineno-86-3"></a><span class="w">   </span><span class="n">self</span><span class="p">.</span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">removeHelper</span><span class="p">(</span><span class="n">self</span><span class="p">.</span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">).</span><span class="o">?</span><span class="p">;</span>
 <a id="__codelineno-86-4" name="__codelineno-86-4" href="#__codelineno-86-4"></a><span class="p">}</span>
 <a id="__codelineno-86-5" name="__codelineno-86-5" href="#__codelineno-86-5"></a>
 <a id="__codelineno-86-6" name="__codelineno-86-6" href="#__codelineno-86-6"></a><span class="c1">// 递归删除节点（辅助方法）</span>

chapter_tree/binary_search_tree/index.html

@@ -2790,19 +2790,18 @@
 <p>与查找节点相同，插入节点使用 <span class="arithmatex">\(O(\log n)\)</span> 时间。</p>
 <h3 id="_3">删除节点<a class="headerlink" href="#_3" title="Permanent link">&para;</a></h3>
 <p>与插入节点类似，我们需要在删除操作后维持二叉搜索树的“左子树 &lt; 根节点 &lt; 右子树”的性质。首先，我们需要在二叉树中执行查找操作，获取待删除节点。接下来，根据待删除节点的子节点数量，删除操作需分为三种情况：</p>
-<p>当待删除节点的子节点数量 <span class="arithmatex">\(= 0\)</span> 时，表示待删除节点是叶节点，可以直接删除。</p>
+<p>当待删除节点的度为 <span class="arithmatex">\(0\)</span> 时，表示待删除节点是叶节点，可以直接删除。</p>
 <p><img alt="在二叉搜索树中删除节点（度为 0）" src="../binary_search_tree.assets/bst_remove_case1.png" /></p>
 <p align="center"> Fig. 在二叉搜索树中删除节点（度为 0） </p>
 
-<p>当待删除节点的子节点数量 <span class="arithmatex">\(= 1\)</span> 时，将待删除节点替换为其子节点即可。</p>
+<p>当待删除节点的度为 <span class="arithmatex">\(1\)</span> 时，将待删除节点替换为其子节点即可。</p>
 <p><img alt="在二叉搜索树中删除节点（度为 1）" src="../binary_search_tree.assets/bst_remove_case2.png" /></p>
 <p align="center"> Fig. 在二叉搜索树中删除节点（度为 1） </p>
 
-<p>当待删除节点的子节点数量 <span class="arithmatex">\(= 2\)</span> 时，删除操作分为三步：</p>
+<p>当待删除节点的度为 <span class="arithmatex">\(2\)</span> 时，我们无法直接删除它，而需要使用一个节点替换该节点。由于要保持二叉搜索树“左 <span class="arithmatex">\(&lt;\)</span> 根 <span class="arithmatex">\(&lt;\)</span> 右”的性质，因此这个节点可以是右子树的最小节点或左子树的最大节点。假设我们选择右子树的最小节点（或者称为中序遍历的下个节点），则删除操作为：</p>
 <ol>
 <li>找到待删除节点在“中序遍历序列”中的下一个节点，记为 <code>tmp</code> ；</li>
-<li>在树中递归删除节点 <code>tmp</code> ；</li>
-<li>用 <code>tmp</code> 的值覆盖待删除节点的值；</li>
+<li>将 <code>tmp</code> 的值覆盖待删除节点的值，并在树中递归删除节点 <code>tmp</code> ；</li>
 </ol>
 <div class="tabbed-set tabbed-alternate" data-tabs="4:4"><input checked="checked" id="__tabbed_4_1" name="__tabbed_4" type="radio" /><input id="__tabbed_4_2" name="__tabbed_4" type="radio" /><input id="__tabbed_4_3" name="__tabbed_4" type="radio" /><input id="__tabbed_4_4" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1">&lt;1&gt;</label><label for="__tabbed_4_2">&lt;2&gt;</label><label for="__tabbed_4_3">&lt;3&gt;</label><label for="__tabbed_4_4">&lt;4&gt;</label></div>
 <div class="tabbed-content">
@@ -3316,7 +3315,7 @@
 </div>
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">binary_search_tree.zig</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="c1">// 删除节点</span>
-<a id="__codelineno-31-2" name="__codelineno-31-2" href="#__codelineno-31-2"></a><span class="k">fn</span><span class="w"> </span><span class="n">remove</span><span class="p">(</span><span class="n">self</span><span class="o">:</span><span class="w"> </span><span class="o">*</span><span class="n">Self</span><span class="p">,</span><span class="w"> </span><span class="n">num</span><span class="o">:</span><span class="w"> </span><span class="n">T</span><span class="p">)</span><span class="w"> </span><span class="o">!</span><span class="kt">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-2" name="__codelineno-31-2" href="#__codelineno-31-2"></a><span class="k">fn</span><span class="w"> </span><span class="n">remove</span><span class="p">(</span><span class="n">self</span><span class="o">:</span><span class="w"> </span><span class="o">*</span><span class="n">Self</span><span class="p">,</span><span class="w"> </span><span class="n">num</span><span class="o">:</span><span class="w"> </span><span class="n">T</span><span class="p">)</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-31-3" name="__codelineno-31-3" href="#__codelineno-31-3"></a><span class="w">    </span><span class="c1">// 若树为空，直接提前返回</span>
 <a id="__codelineno-31-4" name="__codelineno-31-4" href="#__codelineno-31-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">self</span><span class="p">.</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span>
 <a id="__codelineno-31-5" name="__codelineno-31-5" href="#__codelineno-31-5"></a><span class="w">    </span><span class="kr">var</span><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">root</span><span class="p">;</span>
@@ -3353,11 +3352,11 @@
 <a id="__codelineno-31-36" name="__codelineno-31-36" href="#__codelineno-31-36"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">tmp</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-31-37" name="__codelineno-31-37" href="#__codelineno-31-37"></a><span class="w">            </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">left</span><span class="p">;</span>
 <a id="__codelineno-31-38" name="__codelineno-31-38" href="#__codelineno-31-38"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-31-39" name="__codelineno-31-39" href="#__codelineno-31-39"></a><span class="w">        </span><span class="kr">var</span><span class="w"> </span><span class="n">tmpVal</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-31-39" name="__codelineno-31-39" href="#__codelineno-31-39"></a><span class="w">        </span><span class="kr">var</span><span class="w"> </span><span class="n">tmp_val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">val</span><span class="p">;</span>
 <a id="__codelineno-31-40" name="__codelineno-31-40" href="#__codelineno-31-40"></a><span class="w">        </span><span class="c1">// 递归删除节点 tmp</span>
-<a id="__codelineno-31-41" name="__codelineno-31-41" href="#__codelineno-31-41"></a><span class="w">        </span><span class="n">_</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">remove</span><span class="p">(</span><span class="n">tmp</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-31-41" name="__codelineno-31-41" href="#__codelineno-31-41"></a><span class="w">        </span><span class="n">self</span><span class="p">.</span><span class="n">remove</span><span class="p">(</span><span class="n">tmp</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">val</span><span class="p">);</span>
 <a id="__codelineno-31-42" name="__codelineno-31-42" href="#__codelineno-31-42"></a><span class="w">        </span><span class="c1">// 用 tmp 覆盖 cur</span>
-<a id="__codelineno-31-43" name="__codelineno-31-43" href="#__codelineno-31-43"></a><span class="w">        </span><span class="n">cur</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmpVal</span><span class="p">;</span>
+<a id="__codelineno-31-43" name="__codelineno-31-43" href="#__codelineno-31-43"></a><span class="w">        </span><span class="n">cur</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp_val</span><span class="p">;</span>
 <a id="__codelineno-31-44" name="__codelineno-31-44" href="#__codelineno-31-44"></a><span class="w">    </span><span class="p">}</span>
 <a id="__codelineno-31-45" name="__codelineno-31-45" href="#__codelineno-31-45"></a><span class="p">}</span>
 </code></pre></div>

chapter_tree/summary/index.html

@@ -1179,10 +1179,41 @@
         
       
       
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          7.6. &nbsp; 小结
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
       <a href="./" class="md-nav__link md-nav__link--active">
         7.6. &nbsp; 小结
       </a>
       
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目录">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目录
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#761-q-a" class="md-nav__link">
+    7.6.1. &nbsp; Q &amp; A
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
     </li>
   
 
@@ -2051,6 +2082,21 @@
     
   
   
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目录
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#761-q-a" class="md-nav__link">
+    7.6.1. &nbsp; Q &amp; A
+  </a>
+  
+</li>
+      
+    </ul>
+  
 </nav>
                   </div>
                 </div>
@@ -2086,6 +2132,27 @@
 <li>AVL 树，也称为平衡二叉搜索树，它通过旋转操作，确保在不断插入和删除节点后，树仍然保持平衡。</li>
 <li>AVL 树的旋转操作包括右旋、左旋、先右旋再左旋、先左旋再右旋。在插入或删除节点后，AVL 树会从底向顶执行旋转操作，使树重新恢复平衡。</li>
 </ul>
+<h2 id="761-q-a">7.6.1. &nbsp; Q &amp; A<a class="headerlink" href="#761-q-a" title="Permanent link">&para;</a></h2>
+<div class="admonition question">
+<p class="admonition-title">对于只有一个节点的二叉树，树的高度和根节点的深度都是 <span class="arithmatex">\(0\)</span> 吗？</p>
+<p>是的，因为高度和深度通常定义为“走过边的数量”。</p>
+</div>
+<div class="admonition question">
+<p class="admonition-title">二叉树中的插入与删除一般都是由一套操作配合完成的，这里的“一套操作”指什么呢？可以理解为资源的子节点的资源释放吗？</p>
+<p>拿二叉搜索树来举例，删除节点操作要分为三种情况处理，其中每种情况都需要进行多个步骤的节点操作。</p>
+</div>
+<div class="admonition question">
+<p class="admonition-title">为什么 DFS 遍历二叉树有前、中、后三种顺序，分别有什么用呢？</p>
+<p>DFS 的前、中、后序遍历和访问数组的顺序类似，是遍历二叉树的基本方法，利用这三种遍历方法，我们可以得到一个特定顺序的遍历结果。例如在二叉搜索树中，由于结点大小满足 <code>左子结点值 &lt; 根结点值 &lt; 右子结点值</code> ，因此我们只要按照 <code>左-&gt;根-&gt;右</code> 的优先级遍历树，就可以获得有序的节点序列。</p>
+</div>
+<div class="admonition question">
+<p class="admonition-title">右旋操作是处理失衡节点 <code>node</code> , <code>child</code> , <code>grand_child</code> 之间的关系，那 <code>node</code> 的父节点和 <code>node</code> 原来的连接不需要维护吗？右旋操作后岂不是断掉了？</p>
+<p>我们需要从递归的视角来看这个问题。右旋操作 <code>right_rotate(root)</code> 传入的是子树的根节点，最终 <code>return child</code> 返回旋转之后的子树的根节点。子树的根节点和其父节点的连接是在该函数返回后完成的，不属于右旋操作的维护范围。</p>
+</div>
+<div class="admonition question">
+<p class="admonition-title">在 C++ 中，函数被划分到 <code>private</code> 和 <code>public</code> 中，这方面有什么考量吗？为什么要将 <code>height()</code> 函数和 <code>updateHeight()</code> 函数分别放在 <code>public</code> 和 <code>private</code> 中呢？</p>
+<p>主要看方法的使用范围，如果方法只在类内部使用，那么就设计为 <code>private</code> 。例如，用户单独调用 <code>updateHeight()</code> 是没有意义的，它只是插入、删除操作中的一步。而 <code>height()</code> 是访问结点高度，类似于 <code>vector.size()</code> ，因此设置成 <code>public</code> 以便使用。</p>
+</div>