deploy

chapter_backtracking/permutations_problem/index.html

@@ -4455,7 +4455,7 @@
 <a id="__codelineno-18-17" name="__codelineno-18-17" href="#__codelineno-18-17"></a><span class="w">            </span><span class="p">(</span><span class="o">*</span><span class="nx">selected</span><span class="p">)[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="kc">true</span>
 <a id="__codelineno-18-18" name="__codelineno-18-18" href="#__codelineno-18-18"></a><span class="w">            </span><span class="o">*</span><span class="nx">state</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="o">*</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">)</span>
 <a id="__codelineno-18-19" name="__codelineno-18-19" href="#__codelineno-18-19"></a><span class="w">            </span><span class="c1">// 进行下一轮选择</span>
-<a id="__codelineno-18-20" name="__codelineno-18-20" href="#__codelineno-18-20"></a><span class="w">            </span><span class="nx">backtrackI</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choices</span><span class="p">,</span><span class="w"> </span><span class="nx">selected</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">)</span>
+<a id="__codelineno-18-20" name="__codelineno-18-20" href="#__codelineno-18-20"></a><span class="w">            </span><span class="nx">backtrackII</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choices</span><span class="p">,</span><span class="w"> </span><span class="nx">selected</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">)</span>
 <a id="__codelineno-18-21" name="__codelineno-18-21" href="#__codelineno-18-21"></a><span class="w">            </span><span class="c1">// 回退：撤销选择，恢复到之前的状态</span>
 <a id="__codelineno-18-22" name="__codelineno-18-22" href="#__codelineno-18-22"></a><span class="w">            </span><span class="p">(</span><span class="o">*</span><span class="nx">selected</span><span class="p">)[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="kc">false</span>
 <a id="__codelineno-18-23" name="__codelineno-18-23" href="#__codelineno-18-23"></a><span class="w">            </span><span class="o">*</span><span class="nx">state</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">state</span><span class="p">)[:</span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">state</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>

chapter_sorting/bucket_sort/index.html

@@ -4055,7 +4055,35 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">bucket_sort.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">bucket_sort</span><span class="p">}</span>
+<div class="highlight"><span class="filename">bucket_sort.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### 桶排序 ###</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">bucket_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w">  </span><span class="c1"># 初始化 k = n/2 个桶，预期向每个桶分配 2 个元素</span>
+<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w">  </span><span class="n">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">.</span><span class="n">length</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w">  </span><span class="n">buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">k</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">[]</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a>
+<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w">  </span><span class="c1"># 1. 将数组元素分配到各个桶中</span>
+<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w">  </span><span class="n">nums</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="k">do</span><span class="w"> </span><span class="o">|</span><span class="n">num</span><span class="o">|</span>
+<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w">    </span><span class="c1"># 输入数据范围为 [0, 1)，使用 num * k 映射到索引范围 [0, k-1]</span>
+<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w">    </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">num</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">k</span><span class="p">)</span><span class="o">.</span><span class="n">to_i</span>
+<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="w">    </span><span class="c1"># 将 num 添加进桶 i</span>
+<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="w">    </span><span class="n">buckets</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">num</span>
+<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a>
+<a id="__codelineno-12-15" name="__codelineno-12-15" href="#__codelineno-12-15"></a><span class="w">  </span><span class="c1"># 2. 对各个桶执行排序</span>
+<a id="__codelineno-12-16" name="__codelineno-12-16" href="#__codelineno-12-16"></a><span class="w">  </span><span class="n">buckets</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="k">do</span><span class="w"> </span><span class="o">|</span><span class="n">bucket</span><span class="o">|</span>
+<a id="__codelineno-12-17" name="__codelineno-12-17" href="#__codelineno-12-17"></a><span class="w">    </span><span class="c1"># 使用内置排序函数，也可以替换成其他排序算法</span>
+<a id="__codelineno-12-18" name="__codelineno-12-18" href="#__codelineno-12-18"></a><span class="w">    </span><span class="n">bucket</span><span class="o">.</span><span class="n">sort!</span>
+<a id="__codelineno-12-19" name="__codelineno-12-19" href="#__codelineno-12-19"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-20" name="__codelineno-12-20" href="#__codelineno-12-20"></a>
+<a id="__codelineno-12-21" name="__codelineno-12-21" href="#__codelineno-12-21"></a><span class="w">  </span><span class="c1"># 3. 遍历桶合并结果</span>
+<a id="__codelineno-12-22" name="__codelineno-12-22" href="#__codelineno-12-22"></a><span class="w">  </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-12-23" name="__codelineno-12-23" href="#__codelineno-12-23"></a><span class="w">  </span><span class="n">buckets</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="k">do</span><span class="w"> </span><span class="o">|</span><span class="n">bucket</span><span class="o">|</span>
+<a id="__codelineno-12-24" name="__codelineno-12-24" href="#__codelineno-12-24"></a><span class="w">    </span><span class="n">bucket</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="k">do</span><span class="w"> </span><span class="o">|</span><span class="n">num</span><span class="o">|</span>
+<a id="__codelineno-12-25" name="__codelineno-12-25" href="#__codelineno-12-25"></a><span class="w">      </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span>
+<a id="__codelineno-12-26" name="__codelineno-12-26" href="#__codelineno-12-26"></a><span class="w">      </span><span class="n">i</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-12-27" name="__codelineno-12-27" href="#__codelineno-12-27"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-12-28" name="__codelineno-12-28" href="#__codelineno-12-28"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-29" name="__codelineno-12-29" href="#__codelineno-12-29"></a><span class="k">end</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">

chapter_sorting/heap_sort/index.html

@@ -4219,9 +4219,38 @@
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">heap_sort.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">sift_down</span><span class="p">}</span>
+<div class="highlight"><span class="filename">heap_sort.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### 堆的长度为 n ，从节点 i 开始，从顶至底堆化 ###</span>
-<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">sift_down</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">)</span>
-<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">heap_sort</span><span class="p">}</span>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w">  </span><span class="k">while</span><span class="w"> </span><span class="kp">true</span>
+<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w">    </span><span class="c1"># 判断节点 i, l, r 中值最大的节点，记为 ma</span>
+<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w">    </span><span class="n">l</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w">    </span><span class="n">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">2</span>
+<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w">    </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span>
+<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w">    </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">l</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">ma</span><span class="o">]</span>
+<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w">    </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">r</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">ma</span><span class="o">]</span>
+<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w">    </span><span class="c1"># 若节点 i 最大或索引 l, r 越界，则无须继续堆化，跳出</span>
+<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="w">    </span><span class="k">break</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">i</span>
+<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="w">    </span><span class="c1"># 交换两节点</span>
+<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a><span class="w">    </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">ma</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">ma</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span>
+<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a><span class="w">    </span><span class="c1"># 循环向下堆化</span>
+<a id="__codelineno-12-15" name="__codelineno-12-15" href="#__codelineno-12-15"></a><span class="w">    </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ma</span>
+<a id="__codelineno-12-16" name="__codelineno-12-16" href="#__codelineno-12-16"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-17" name="__codelineno-12-17" href="#__codelineno-12-17"></a><span class="k">end</span>
+<a id="__codelineno-12-18" name="__codelineno-12-18" href="#__codelineno-12-18"></a>
+<a id="__codelineno-12-19" name="__codelineno-12-19" href="#__codelineno-12-19"></a><span class="c1">### 堆排序 ###</span>
+<a id="__codelineno-12-20" name="__codelineno-12-20" href="#__codelineno-12-20"></a><span class="k">def</span><span class="w"> </span><span class="nf">heap_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
+<a id="__codelineno-12-21" name="__codelineno-12-21" href="#__codelineno-12-21"></a><span class="w">  </span><span class="c1"># 建堆操作：堆化除叶节点以外的其他所有节点</span>
+<a id="__codelineno-12-22" name="__codelineno-12-22" href="#__codelineno-12-22"></a><span class="w">  </span><span class="p">(</span><span class="n">nums</span><span class="o">.</span><span class="n">length</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="o">.</span><span class="n">downto</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="k">do</span><span class="w"> </span><span class="o">|</span><span class="n">i</span><span class="o">|</span>
+<a id="__codelineno-12-23" name="__codelineno-12-23" href="#__codelineno-12-23"></a><span class="w">    </span><span class="n">sift_down</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="o">.</span><span class="n">length</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">)</span>
+<a id="__codelineno-12-24" name="__codelineno-12-24" href="#__codelineno-12-24"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-25" name="__codelineno-12-25" href="#__codelineno-12-25"></a><span class="w">  </span><span class="c1"># 从堆中提取最大元素，循环 n-1 轮</span>
+<a id="__codelineno-12-26" name="__codelineno-12-26" href="#__codelineno-12-26"></a><span class="w">  </span><span class="p">(</span><span class="n">nums</span><span class="o">.</span><span class="n">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="o">.</span><span class="n">downto</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="k">do</span><span class="w"> </span><span class="o">|</span><span class="n">i</span><span class="o">|</span>
+<a id="__codelineno-12-27" name="__codelineno-12-27" href="#__codelineno-12-27"></a><span class="w">    </span><span class="c1"># 交换根节点与最右叶节点（交换首元素与尾元素）</span>
+<a id="__codelineno-12-28" name="__codelineno-12-28" href="#__codelineno-12-28"></a><span class="w">    </span><span class="n">nums</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span>
+<a id="__codelineno-12-29" name="__codelineno-12-29" href="#__codelineno-12-29"></a><span class="w">    </span><span class="c1"># 以根节点为起点，从顶至底进行堆化</span>
+<a id="__codelineno-12-30" name="__codelineno-12-30" href="#__codelineno-12-30"></a><span class="w">    </span><span class="n">sift_down</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-12-31" name="__codelineno-12-31" href="#__codelineno-12-31"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-32" name="__codelineno-12-32" href="#__codelineno-12-32"></a><span class="k">end</span>
 </code></pre></div>
 </div>
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chapter_sorting/merge_sort/index.html

@@ -4284,9 +4284,53 @@
 </code></pre></div>
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 <div class="tabbed-block">
-<div class="highlight"><span class="filename">merge_sort.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">merge</span><span class="p">}</span>
+<div class="highlight"><span class="filename">merge_sort.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### 合并左子数组和右子数组 ###</span>
-<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">merge</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">)</span>
-<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">merge_sort</span><span class="p">}</span>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w">  </span><span class="c1"># 左子数组区间为 [left, mid], 右子数组区间为 [mid+1, right]</span>
+<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w">  </span><span class="c1"># 创建一个临时数组 tmp，用于存放合并后的结果</span>
+<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w">  </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">right</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w">  </span><span class="c1"># 初始化左子数组和右子数组的起始索引</span>
+<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w">  </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">,</span><span class="w"> </span><span class="n">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w">  </span><span class="c1"># 当左右子数组都还有元素时，进行比较并将较小的元素复制到临时数组中</span>
+<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w">  </span><span class="k">while</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">right</span>
+<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span>
+<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="w">      </span><span class="n">tmp</span><span class="o">[</span><span class="n">k</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span>
+<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="w">      </span><span class="n">i</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a><span class="w">    </span><span class="k">else</span>
+<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a><span class="w">      </span><span class="n">tmp</span><span class="o">[</span><span class="n">k</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span>
+<a id="__codelineno-12-15" name="__codelineno-12-15" href="#__codelineno-12-15"></a><span class="w">      </span><span class="n">j</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-12-16" name="__codelineno-12-16" href="#__codelineno-12-16"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-12-17" name="__codelineno-12-17" href="#__codelineno-12-17"></a><span class="w">    </span><span class="n">k</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-12-18" name="__codelineno-12-18" href="#__codelineno-12-18"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-19" name="__codelineno-12-19" href="#__codelineno-12-19"></a><span class="w">  </span><span class="c1"># 将左子数组和右子数组的剩余元素复制到临时数组中</span>
+<a id="__codelineno-12-20" name="__codelineno-12-20" href="#__codelineno-12-20"></a><span class="w">  </span><span class="k">while</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">mid</span>
+<a id="__codelineno-12-21" name="__codelineno-12-21" href="#__codelineno-12-21"></a><span class="w">    </span><span class="n">tmp</span><span class="o">[</span><span class="n">k</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span>
+<a id="__codelineno-12-22" name="__codelineno-12-22" href="#__codelineno-12-22"></a><span class="w">    </span><span class="n">i</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-12-23" name="__codelineno-12-23" href="#__codelineno-12-23"></a><span class="w">    </span><span class="n">k</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-12-24" name="__codelineno-12-24" href="#__codelineno-12-24"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-25" name="__codelineno-12-25" href="#__codelineno-12-25"></a><span class="w">  </span><span class="k">while</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">right</span>
+<a id="__codelineno-12-26" name="__codelineno-12-26" href="#__codelineno-12-26"></a><span class="w">    </span><span class="n">tmp</span><span class="o">[</span><span class="n">k</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span>
+<a id="__codelineno-12-27" name="__codelineno-12-27" href="#__codelineno-12-27"></a><span class="w">    </span><span class="n">j</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-12-28" name="__codelineno-12-28" href="#__codelineno-12-28"></a><span class="w">    </span><span class="n">k</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
+<a id="__codelineno-12-29" name="__codelineno-12-29" href="#__codelineno-12-29"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-30" name="__codelineno-12-30" href="#__codelineno-12-30"></a><span class="w">  </span><span class="c1"># 将临时数组 tmp 中的元素复制回原数组 nums 的对应区间</span>
+<a id="__codelineno-12-31" name="__codelineno-12-31" href="#__codelineno-12-31"></a><span class="w">  </span><span class="p">(</span><span class="mi">0</span><span class="o">...</span><span class="n">tmp</span><span class="o">.</span><span class="n">length</span><span class="p">)</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="k">do</span><span class="w"> </span><span class="o">|</span><span class="n">k</span><span class="o">|</span>
+<a id="__codelineno-12-32" name="__codelineno-12-32" href="#__codelineno-12-32"></a><span class="w">    </span><span class="n">nums</span><span class="o">[</span><span class="n">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">k</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="o">[</span><span class="n">k</span><span class="o">]</span>
+<a id="__codelineno-12-33" name="__codelineno-12-33" href="#__codelineno-12-33"></a><span class="w">  </span><span class="k">end</span>
+<a id="__codelineno-12-34" name="__codelineno-12-34" href="#__codelineno-12-34"></a><span class="k">end</span>
+<a id="__codelineno-12-35" name="__codelineno-12-35" href="#__codelineno-12-35"></a>
+<a id="__codelineno-12-36" name="__codelineno-12-36" href="#__codelineno-12-36"></a><span class="c1">### 归并排序 ###</span>
+<a id="__codelineno-12-37" name="__codelineno-12-37" href="#__codelineno-12-37"></a><span class="k">def</span><span class="w"> </span><span class="nf">merge_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">)</span>
+<a id="__codelineno-12-38" name="__codelineno-12-38" href="#__codelineno-12-38"></a><span class="w">  </span><span class="c1"># 终止条件</span>
+<a id="__codelineno-12-39" name="__codelineno-12-39" href="#__codelineno-12-39"></a><span class="w">  </span><span class="c1"># 当子数组长度为 1 时终止递归</span>
+<a id="__codelineno-12-40" name="__codelineno-12-40" href="#__codelineno-12-40"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">right</span>
+<a id="__codelineno-12-41" name="__codelineno-12-41" href="#__codelineno-12-41"></a><span class="w">  </span><span class="c1"># 划分阶段</span>
+<a id="__codelineno-12-42" name="__codelineno-12-42" href="#__codelineno-12-42"></a><span class="w">  </span><span class="n">mid</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="c1"># 计算中点</span>
+<a id="__codelineno-12-43" name="__codelineno-12-43" href="#__codelineno-12-43"></a><span class="w">  </span><span class="n">merge_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="p">)</span><span class="w"> </span><span class="c1"># 递归左子数组</span>
+<a id="__codelineno-12-44" name="__codelineno-12-44" href="#__codelineno-12-44"></a><span class="w">  </span><span class="n">merge_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="c1"># 递归右子数组</span>
+<a id="__codelineno-12-45" name="__codelineno-12-45" href="#__codelineno-12-45"></a><span class="w">  </span><span class="c1"># 合并阶段</span>
+<a id="__codelineno-12-46" name="__codelineno-12-46" href="#__codelineno-12-46"></a><span class="w">  </span><span class="n">merge</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">)</span>
+<a id="__codelineno-12-47" name="__codelineno-12-47" href="#__codelineno-12-47"></a><span class="k">end</span>
 </code></pre></div>
 </div>
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