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2023-03-12 18:46:10 +08:00
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@@ -1916,9 +1916,9 @@
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="cm">/* AVL 树结点类 */</span>
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="kd">class</span> <span class="nc">TreeNode</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a><span class="w"> </span><span class="kd">public</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="c1">// 结点值</span>
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">height</span><span class="p">;</span><span class="w"> </span><span class="c1">// 结点高度</span>
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">left</span><span class="p">;</span><span class="w"> </span><span class="c1">// 左子结点</span>
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a><span class="w"> </span><span class="kd">public</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="c1">// 结点值</span>
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">height</span><span class="p">;</span><span class="w"> </span><span class="c1">// 结点高度</span>
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">left</span><span class="p">;</span><span class="w"> </span><span class="c1">// 左子结点</span>
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">right</span><span class="p">;</span><span class="w"> </span><span class="c1">// 右子结点</span>
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="nf">TreeNode</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">x</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">x</span><span class="p">;</span><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a><span class="p">}</span>
@@ -1927,10 +1927,10 @@
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* AVL 树结点类 */</span>
<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="k">struct</span><span class="w"> </span><span class="nc">TreeNode</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><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="c1">// 结点值</span>
<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">height</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// 结点高度</span>
<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">left</span><span class="p">{};</span><span class="w"> </span><span class="c1">// 左子结点</span>
<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">right</span><span class="p">{};</span><span class="w"> </span><span class="c1">// 右子结点</span>
<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><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="c1">// 结点值</span>
<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">height</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// 结点高度</span>
<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">left</span><span class="p">{};</span><span class="w"> </span><span class="c1">// 左子结点</span>
<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">right</span><span class="p">{};</span><span class="w"> </span><span class="c1">// 右子结点</span>
<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w"> </span><span class="n">TreeNode</span><span class="p">()</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">default</span><span class="p">;</span>
<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w"> </span><span class="k">explicit</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">x</span><span class="p">)</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">x</span><span class="p">){}</span>
<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="p">};</span>
@@ -1939,11 +1939,11 @@
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="sd">&quot;&quot;&quot; AVL 树结点类 &quot;&quot;&quot;</span>
<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="k">class</span> <span class="nc">TreeNode</span><span class="p">:</span>
<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></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="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">left</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">right</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a> <span class="bp">self</span><span class="o">.</span><span class="n">val</span> <span class="o">=</span> <span class="n">val</span> <span class="c1"># 结点值</span>
<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a> <span class="bp">self</span><span class="o">.</span><span class="n">height</span> <span class="o">=</span> <span class="mi">0</span> <span class="c1"># 结点高度</span>
<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a> <span class="bp">self</span><span class="o">.</span><span class="n">left</span> <span class="o">=</span> <span class="n">left</span> <span class="c1"># 左子结点引用</span>
<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a> <span class="bp">self</span><span class="o">.</span><span class="n">right</span> <span class="o">=</span> <span class="n">right</span> <span class="c1"># 右子结点引用</span>
<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></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-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></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"># 结点值</span>
<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></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"># 结点高度</span>
<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></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"># 左子结点引用</span>
<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></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"># 右子结点引用</span>
</code></pre></div>
</div>
<div class="tabbed-block">
@@ -2339,7 +2339,7 @@
</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">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">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-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>
@@ -2501,7 +2501,7 @@
</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">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">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-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>
@@ -2735,7 +2735,7 @@
</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">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">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-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>
@@ -3027,8 +3027,8 @@
<div class="tabbed-block">
<div class="highlight"><span class="filename">avl_tree.py</span><pre><span></span><code><a id="__codelineno-62-1" name="__codelineno-62-1" href="#__codelineno-62-1"></a><span class="k">def</span> <span class="nf">insert</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="o">-&gt;</span> <span class="n">TreeNode</span><span class="p">:</span>
<a id="__codelineno-62-2" name="__codelineno-62-2" href="#__codelineno-62-2"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot; 插入结点 &quot;&quot;&quot;</span>
<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-62-3" 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-62-7" 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>
@@ -3329,10 +3329,10 @@
</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>
<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>
<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="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="n">root</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-72-7" 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>