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2026-07-12 23:36:06 +00:00 · 2023-09-21 20:44:52 +08:00
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@@ -3645,6 +3670,13 @@
  


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 <h1 id="75-avl">7.5 &nbsp; AVL 树 *<a class="headerlink" href="#75-avl" title="Permanent link">&para;</a></h1>
 <p>在二叉搜索树章节中，我们提到了在多次插入和删除操作后，二叉搜索树可能退化为链表。这种情况下，所有操作的时间复杂度将从 <span class="arithmatex">\(O(\log n)\)</span> 恶化为 <span class="arithmatex">\(O(n)\)</span> 。</p>
 <p>如图 7-24 所示，经过两次删除节点操作，这个二叉搜索树便会退化为链表。</p>
@@ -3666,10 +3698,10 @@
 <div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">class</span> <span class="nc">TreeNode</span><span class="p">:</span>
 <a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;AVL 树节点类&quot;&quot;&quot;</span>
 <a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
-<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">val</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">val</span>                    <span class="c1"># 节点值</span>
-<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">height</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">0</span>                   <span class="c1"># 节点高度</span>
-<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">left</span><span class="p">:</span> <span class="n">Optional</span><span class="p">[</span><span class="n">TreeNode</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span>   <span class="c1"># 左子节点引用</span>
-<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">right</span><span class="p">:</span> <span class="n">Optional</span><span class="p">[</span><span class="n">TreeNode</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span>  <span class="c1"># 右子节点引用</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">val</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">val</span>                 <span class="c1"># 节点值</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">height</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">0</span>                <span class="c1"># 节点高度</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">left</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span>   <span class="c1"># 左子节点引用</span>
+<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">right</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span>  <span class="c1"># 右子节点引用</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
@@ -5907,11 +5939,73 @@
 <li>红黑树在许多应用中比 AVL 树更受欢迎。这是因为红黑树的平衡条件相对宽松，在红黑树中插入与删除节点所需的旋转操作相对较少，其节点增删操作的平均效率更高。</li>
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