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chapter_sorting/merge_sort/index.html

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@@ -4536,7 +4536,7 @@
 <li><strong>归并排序</strong>：先递归左子数组，再递归右子数组，最后处理合并。</li>
 </ul>
 <p>归并排序的实现如以下代码所示。请注意，<code>nums</code> 的待合并区间为 <code>[left, right]</code> ，而 <code>tmp</code> 的对应区间为 <code>[0, right - left]</code> 。</p>
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 <div class="highlight"><span class="filename">merge_sort.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></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="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">left</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">mid</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">right</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
@@ -5130,58 +5130,6 @@
 <a id="__codelineno-12-47" name="__codelineno-12-47" href="#__codelineno-12-47"></a><span class="k">end</span>
 </code></pre></div>
 </div>
-<div class="tabbed-block">
-<div class="highlight"><span class="filename">merge_sort.zig</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="c1">// 合并左子数组和右子数组</span>
-<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="c1">// 左子数组区间 [left, mid]</span>
-<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a><span class="c1">// 右子数组区间 [mid + 1, right]</span>
-<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a><span class="k">fn</span><span class="w"> </span><span class="n">merge</span><span class="p">(</span><span class="n">nums</span><span class="o">:</span><span class="w"> </span><span class="p">[]</span><span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="o">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="o">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="o">:</span><span class="w"> </span><span class="kt">usize</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-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a><span class="w">    </span><span class="c1">// 初始化辅助数组</span>
-<a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a><span class="w">    </span><span class="kr">var</span><span class="w"> </span><span class="n">mem_arena</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">std</span><span class="p">.</span><span class="n">heap</span><span class="p">.</span><span class="n">ArenaAllocator</span><span class="p">.</span><span class="n">init</span><span class="p">(</span><span class="n">std</span><span class="p">.</span><span class="n">heap</span><span class="p">.</span><span class="n">page_allocator</span><span class="p">);</span>
-<a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a><span class="w">    </span><span class="k">defer</span><span class="w"> </span><span class="n">mem_arena</span><span class="p">.</span><span class="n">deinit</span><span class="p">();</span>
-<a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a><span class="w">    </span><span class="kr">const</span><span class="w"> </span><span class="n">mem_allocator</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mem_arena</span><span class="p">.</span><span class="n">allocator</span><span class="p">();</span>
-<a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a><span class="w">    </span><span class="kr">var</span><span class="w"> </span><span class="n">tmp</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">mem_allocator</span><span class="p">.</span><span class="n">alloc</span><span class="p">(</span><span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">left</span><span class="p">);</span>
-<a id="__codelineno-13-10" name="__codelineno-13-10" href="#__codelineno-13-10"></a><span class="w">    </span><span class="n">std</span><span class="p">.</span><span class="n">mem</span><span class="p">.</span><span class="n">copy</span><span class="p">(</span><span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="n">tmp</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="p">..</span><span class="n">right</span><span class="o">+</span><span class="mi">1</span><span class="p">]);</span>
-<a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a><span class="w">    </span><span class="c1">// 左子数组的起始索引和结束索引</span>
-<a id="__codelineno-13-12" name="__codelineno-13-12" href="#__codelineno-13-12"></a><span class="w">    </span><span class="kr">var</span><span class="w"> </span><span class="n">leftStart</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="n">left</span><span class="p">;</span>
-<a id="__codelineno-13-13" name="__codelineno-13-13" href="#__codelineno-13-13"></a><span class="w">    </span><span class="kr">var</span><span class="w"> </span><span class="n">leftEnd</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">left</span><span class="p">;</span>
-<a id="__codelineno-13-14" name="__codelineno-13-14" href="#__codelineno-13-14"></a><span class="w">    </span><span class="c1">// 右子数组的起始索引和结束索引</span>
-<a id="__codelineno-13-15" name="__codelineno-13-15" href="#__codelineno-13-15"></a><span class="w">    </span><span class="kr">var</span><span class="w"> </span><span class="n">rightStart</span><span class="w"> </span><span class="o">=</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="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">left</span><span class="p">;</span>
-<a id="__codelineno-13-16" name="__codelineno-13-16" href="#__codelineno-13-16"></a><span class="w">    </span><span class="kr">var</span><span class="w"> </span><span class="n">rightEnd</span><span class="w"> </span><span class="o">=</span><span class="w"> </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="p">;</span>
-<a id="__codelineno-13-17" name="__codelineno-13-17" href="#__codelineno-13-17"></a><span class="w">    </span><span class="c1">// i, j 分别指向左子数组、右子数组的首元素</span>
-<a id="__codelineno-13-18" name="__codelineno-13-18" href="#__codelineno-13-18"></a><span class="w">    </span><span class="kr">var</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">leftStart</span><span class="p">;</span>
-<a id="__codelineno-13-19" name="__codelineno-13-19" href="#__codelineno-13-19"></a><span class="w">    </span><span class="kr">var</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rightStart</span><span class="p">;</span>
-<a id="__codelineno-13-20" name="__codelineno-13-20" href="#__codelineno-13-20"></a><span class="w">    </span><span class="c1">// 通过覆盖原数组 nums 来合并左子数组和右子数组</span>
-<a id="__codelineno-13-21" name="__codelineno-13-21" href="#__codelineno-13-21"></a><span class="w">    </span><span class="kr">var</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>
-<a id="__codelineno-13-22" name="__codelineno-13-22" href="#__codelineno-13-22"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">k</span><span class="w"> </span><span class="o">&lt;=</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="p">(</span><span class="n">k</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="p">{</span>
-<a id="__codelineno-13-23" name="__codelineno-13-23" href="#__codelineno-13-23"></a><span class="w">        </span><span class="c1">// 若“左子数组已全部合并完”，则选取右子数组元素，并且 j++</span>
-<a id="__codelineno-13-24" name="__codelineno-13-24" href="#__codelineno-13-24"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">leftEnd</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-13-25" name="__codelineno-13-25" href="#__codelineno-13-25"></a><span class="w">            </span><span class="n">nums</span><span class="p">[</span><span class="n">k</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">[</span><span class="n">j</span><span class="p">];</span>
-<a id="__codelineno-13-26" name="__codelineno-13-26" href="#__codelineno-13-26"></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><span class="p">;</span>
-<a id="__codelineno-13-27" name="__codelineno-13-27" href="#__codelineno-13-27"></a><span class="w">        </span><span class="c1">// 否则，若“右子数组已全部合并完”或“左子数组元素 &lt;= 右子数组元素”，则选取左子数组元素，并且 i++</span>
-<a id="__codelineno-13-28" name="__codelineno-13-28" href="#__codelineno-13-28"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w">  </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">rightEnd</span><span class="w"> </span><span class="k">or</span><span class="w"> </span><span class="n">tmp</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">tmp</span><span class="p">[</span><span class="n">j</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-13-29" name="__codelineno-13-29" href="#__codelineno-13-29"></a><span class="w">            </span><span class="n">nums</span><span class="p">[</span><span class="n">k</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
-<a id="__codelineno-13-30" name="__codelineno-13-30" href="#__codelineno-13-30"></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><span class="p">;</span>
-<a id="__codelineno-13-31" name="__codelineno-13-31" href="#__codelineno-13-31"></a><span class="w">        </span><span class="c1">// 否则，若“左右子数组都未全部合并完”且“左子数组元素 &gt; 右子数组元素”，则选取右子数组元素，并且 j++</span>
-<a id="__codelineno-13-32" name="__codelineno-13-32" href="#__codelineno-13-32"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-13-33" name="__codelineno-13-33" href="#__codelineno-13-33"></a><span class="w">            </span><span class="n">nums</span><span class="p">[</span><span class="n">k</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">[</span><span class="n">j</span><span class="p">];</span>
-<a id="__codelineno-13-34" name="__codelineno-13-34" href="#__codelineno-13-34"></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><span class="p">;</span>
-<a id="__codelineno-13-35" name="__codelineno-13-35" href="#__codelineno-13-35"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-13-36" name="__codelineno-13-36" href="#__codelineno-13-36"></a><span class="w">    </span><span class="p">}</span>
-<a id="__codelineno-13-37" name="__codelineno-13-37" href="#__codelineno-13-37"></a><span class="p">}</span>
-<a id="__codelineno-13-38" name="__codelineno-13-38" href="#__codelineno-13-38"></a>
-<a id="__codelineno-13-39" name="__codelineno-13-39" href="#__codelineno-13-39"></a><span class="c1">// 归并排序</span>
-<a id="__codelineno-13-40" name="__codelineno-13-40" href="#__codelineno-13-40"></a><span class="k">fn</span><span class="w"> </span><span class="n">mergeSort</span><span class="p">(</span><span class="n">nums</span><span class="o">:</span><span class="w"> </span><span class="p">[]</span><span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="o">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="o">:</span><span class="w"> </span><span class="kt">usize</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-13-41" name="__codelineno-13-41" href="#__codelineno-13-41"></a><span class="w">    </span><span class="c1">// 终止条件</span>
-<a id="__codelineno-13-42" name="__codelineno-13-42" href="#__codelineno-13-42"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">left</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span><span class="w">              </span><span class="c1">// 当子数组长度为 1 时终止递归</span>
-<a id="__codelineno-13-43" name="__codelineno-13-43" href="#__codelineno-13-43"></a><span class="w">    </span><span class="c1">// 划分阶段</span>
-<a id="__codelineno-13-44" name="__codelineno-13-44" href="#__codelineno-13-44"></a><span class="w">    </span><span class="kr">var</span><span class="w"> </span><span class="n">mid</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="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="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w">    </span><span class="c1">// 计算中点</span>
-<a id="__codelineno-13-45" name="__codelineno-13-45" href="#__codelineno-13-45"></a><span class="w">    </span><span class="k">try</span><span class="w"> </span><span class="n">mergeSort</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-13-46" name="__codelineno-13-46" href="#__codelineno-13-46"></a><span class="w">    </span><span class="k">try</span><span class="w"> </span><span class="n">mergeSort</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-13-47" name="__codelineno-13-47" href="#__codelineno-13-47"></a><span class="w">    </span><span class="c1">// 合并阶段</span>
-<a id="__codelineno-13-48" name="__codelineno-13-48" href="#__codelineno-13-48"></a><span class="w">    </span><span class="k">try</span><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-13-49" name="__codelineno-13-49" href="#__codelineno-13-49"></a><span class="p">}</span>
-</code></pre></div>
-</div>
 </div>
 </div>
 <details class="pythontutor">