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@@ -2070,14 +2070,14 @@
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">avl_tree.py</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="k">def</span> <span class="nf">height</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">node</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">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
<div class="highlight"><span class="filename">avl_tree.py</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="k">def</span> <span class="nf">height</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">node</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot; 获取结点高度 &quot;&quot;&quot;</span>
<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a> <span class="c1"># 空结点高度为 -1 ，叶结点高度为 0</span>
<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a> <span class="k">if</span> <span class="n">node</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a> <span class="k">return</span> <span class="n">node</span><span class="o">.</span><span class="n">height</span>
<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a> <span class="k">return</span> <span class="o">-</span><span class="mi">1</span>
<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a>
<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="k">def</span> <span class="nf">__update_height</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">node</span><span class="p">:</span> <span class="n">Optional</span><span class="p">[</span><span class="n">TreeNode</span><span class="p">]):</span>
<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="k">def</span> <span class="nf">__update_height</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">node</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">):</span>
<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot; 更新结点高度 &quot;&quot;&quot;</span>
<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a> <span class="c1"># 结点高度等于最高子树高度 + 1</span>
<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a> <span class="n">node</span><span class="o">.</span><span class="n">height</span> <span class="o">=</span> <span class="nb">max</span><span class="p">([</span><span class="bp">self</span><span class="o">.</span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="p">),</span> <span class="bp">self</span><span class="o">.</span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="p">)])</span> <span class="o">+</span> <span class="mi">1</span>
@@ -2212,7 +2212,7 @@
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">avl_tree.py</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="k">def</span> <span class="nf">balance_factor</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">node</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">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
<div class="highlight"><span class="filename">avl_tree.py</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="k">def</span> <span class="nf">balance_factor</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">node</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot; 获取平衡因子 &quot;&quot;&quot;</span>
<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a> <span class="c1"># 空结点平衡因子为 0</span>
<a id="__codelineno-22-4" name="__codelineno-22-4" href="#__codelineno-22-4"></a> <span class="k">if</span> <span class="n">node</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
@@ -2355,7 +2355,7 @@
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">avl_tree.py</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="k">def</span> <span class="nf">__right_rotate</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">node</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">-&gt;</span> <span class="n">Optional</span><span class="p">[</span><span class="n">TreeNode</span><span class="p">]:</span>
<div class="highlight"><span class="filename">avl_tree.py</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="k">def</span> <span class="nf">__right_rotate</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">node</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">:</span>
<a id="__codelineno-32-2" name="__codelineno-32-2" href="#__codelineno-32-2"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot; 右旋操作 &quot;&quot;&quot;</span>
<a id="__codelineno-32-3" name="__codelineno-32-3" href="#__codelineno-32-3"></a> <span class="n">child</span> <span class="o">=</span> <span class="n">node</span><span class="o">.</span><span class="n">left</span>
<a id="__codelineno-32-4" name="__codelineno-32-4" href="#__codelineno-32-4"></a> <span class="n">grand_child</span> <span class="o">=</span> <span class="n">child</span><span class="o">.</span><span class="n">right</span>
@@ -2517,7 +2517,7 @@
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">avl_tree.py</span><pre><span></span><code><a id="__codelineno-42-1" name="__codelineno-42-1" href="#__codelineno-42-1"></a><span class="k">def</span> <span class="nf">__left_rotate</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">node</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">-&gt;</span> <span class="n">Optional</span><span class="p">[</span><span class="n">TreeNode</span><span class="p">]:</span>
<div class="highlight"><span class="filename">avl_tree.py</span><pre><span></span><code><a id="__codelineno-42-1" name="__codelineno-42-1" href="#__codelineno-42-1"></a><span class="k">def</span> <span class="nf">__left_rotate</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">node</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">:</span>
<a id="__codelineno-42-2" name="__codelineno-42-2" href="#__codelineno-42-2"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot; 左旋操作 &quot;&quot;&quot;</span>
<a id="__codelineno-42-3" name="__codelineno-42-3" href="#__codelineno-42-3"></a> <span class="n">child</span> <span class="o">=</span> <span class="n">node</span><span class="o">.</span><span class="n">right</span>
<a id="__codelineno-42-4" name="__codelineno-42-4" href="#__codelineno-42-4"></a> <span class="n">grand_child</span> <span class="o">=</span> <span class="n">child</span><span class="o">.</span><span class="n">left</span>
@@ -2751,7 +2751,7 @@
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">avl_tree.py</span><pre><span></span><code><a id="__codelineno-52-1" name="__codelineno-52-1" href="#__codelineno-52-1"></a><span class="k">def</span> <span class="nf">__rotate</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">node</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">-&gt;</span> <span class="n">Optional</span><span class="p">[</span><span class="n">TreeNode</span><span class="p">]:</span>
<div class="highlight"><span class="filename">avl_tree.py</span><pre><span></span><code><a id="__codelineno-52-1" name="__codelineno-52-1" href="#__codelineno-52-1"></a><span class="k">def</span> <span class="nf">__rotate</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">node</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">:</span>
<a id="__codelineno-52-2" name="__codelineno-52-2" href="#__codelineno-52-2"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot; 执行旋转操作，使该子树重新恢复平衡 &quot;&quot;&quot;</span>
<a id="__codelineno-52-3" name="__codelineno-52-3" href="#__codelineno-52-3"></a> <span class="c1"># 获取结点 node 的平衡因子</span>
<a id="__codelineno-52-4" name="__codelineno-52-4" href="#__codelineno-52-4"></a> <span class="n">balance_factor</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">balance_factor</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
@@ -3047,7 +3047,7 @@
<a id="__codelineno-62-3" name="__codelineno-62-3" href="#__codelineno-62-3"></a> <span class="bp">self</span><span class="o">.</span><span class="n">__root</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">__insert_helper</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__root</span><span class="p">,</span> <span class="n">val</span><span class="p">)</span>
<a id="__codelineno-62-4" name="__codelineno-62-4" href="#__codelineno-62-4"></a> <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">__root</span>
<a id="__codelineno-62-5" name="__codelineno-62-5" href="#__codelineno-62-5"></a>
<a id="__codelineno-62-6" name="__codelineno-62-6" href="#__codelineno-62-6"></a><span class="k">def</span> <span class="nf">__insert_helper</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">node</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="n">val</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">TreeNode</span><span class="p">:</span>
<a id="__codelineno-62-6" name="__codelineno-62-6" href="#__codelineno-62-6"></a><span class="k">def</span> <span class="nf">__insert_helper</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">node</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">TreeNode</span><span class="p">:</span>
<a id="__codelineno-62-7" name="__codelineno-62-7" href="#__codelineno-62-7"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot; 递归插入结点（辅助方法）&quot;&quot;&quot;</span>
<a id="__codelineno-62-8" name="__codelineno-62-8" href="#__codelineno-62-8"></a> <span class="k">if</span> <span class="n">node</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<a id="__codelineno-62-9" name="__codelineno-62-9" href="#__codelineno-62-9"></a> <span class="k">return</span> <span class="n">TreeNode</span><span class="p">(</span><span class="n">val</span><span class="p">)</span>
@@ -3349,12 +3349,12 @@
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">avl_tree.py</span><pre><span></span><code><a id="__codelineno-72-1" name="__codelineno-72-1" href="#__codelineno-72-1"></a><span class="k">def</span> <span class="nf">remove</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> <span class="o">-&gt;</span> <span class="n">Optional</span><span class="p">[</span><span class="n">TreeNode</span><span class="p">]:</span>
<div class="highlight"><span class="filename">avl_tree.py</span><pre><span></span><code><a id="__codelineno-72-1" name="__codelineno-72-1" href="#__codelineno-72-1"></a><span class="k">def</span> <span class="nf">remove</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> <span class="o">-&gt;</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">:</span>
<a id="__codelineno-72-2" name="__codelineno-72-2" href="#__codelineno-72-2"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot; 删除结点 &quot;&quot;&quot;</span>
<a id="__codelineno-72-3" name="__codelineno-72-3" href="#__codelineno-72-3"></a> <span class="bp">self</span><span class="o">.</span><span class="n">__root</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">__remove_helper</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__root</span><span class="p">,</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="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">__root</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="k">def</span> <span class="nf">__remove_helper</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">node</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="n">val</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">Optional</span><span class="p">[</span><span class="n">TreeNode</span><span class="p">]:</span>
<a id="__codelineno-72-6" name="__codelineno-72-6" href="#__codelineno-72-6"></a><span class="k">def</span> <span class="nf">__remove_helper</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">node</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">:</span>
<a id="__codelineno-72-7" name="__codelineno-72-7" href="#__codelineno-72-7"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot; 递归删除结点（辅助方法） &quot;&quot;&quot;</span>
<a id="__codelineno-72-8" name="__codelineno-72-8" href="#__codelineno-72-8"></a> <span class="k">if</span> <span class="n">node</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<a id="__codelineno-72-9" name="__codelineno-72-9" href="#__codelineno-72-9"></a> <span class="k">return</span> <span class="kc">None</span>
@@ -3381,7 +3381,7 @@
<a id="__codelineno-72-30" name="__codelineno-72-30" href="#__codelineno-72-30"></a> <span class="c1"># 2. 执行旋转操作，使该子树重新恢复平衡</span>
<a id="__codelineno-72-31" name="__codelineno-72-31" href="#__codelineno-72-31"></a> <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">__rotate</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
<a id="__codelineno-72-32" name="__codelineno-72-32" href="#__codelineno-72-32"></a>
<a id="__codelineno-72-33" name="__codelineno-72-33" href="#__codelineno-72-33"></a><span class="k">def</span> <span class="nf">__get_inorder_next</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">node</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">-&gt;</span> <span class="n">Optional</span><span class="p">[</span><span class="n">TreeNode</span><span class="p">]:</span>
<a id="__codelineno-72-33" name="__codelineno-72-33" href="#__codelineno-72-33"></a><span class="k">def</span> <span class="nf">__get_inorder_next</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">node</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">:</span>
<a id="__codelineno-72-34" name="__codelineno-72-34" href="#__codelineno-72-34"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot; 获取中序遍历中的下一个结点（仅适用于 root 有左子结点的情况） &quot;&quot;&quot;</span>
<a id="__codelineno-72-35" name="__codelineno-72-35" href="#__codelineno-72-35"></a> <span class="k">if</span> <span class="n">node</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<a id="__codelineno-72-36" name="__codelineno-72-36" href="#__codelineno-72-36"></a> <span class="k">return</span> <span class="kc">None</span>