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algo_num_sort.html
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<meta name="description" content="十种常用排序算法的Python实现 冒泡排序 插入排序 选择排序 希尔排序 快速排序 归并排序 堆排序 桶排序 基数排序 计数排序 交换操作 # 交换 def swap(arr, i, j): arr[i], arr[j] = arr[j], arr[i] 冒泡排序 # 冒泡排序 def bubble_sort(arr): n = len(arr) for i in range(n):...">
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<h1 class="header-title">【算法总结】十种常用排序算法的Python实现</h1>
<p class="header-date">By <a href="./author/rivarrl.html">Rivarrl</a>, 2019-09-10 21:40:00, modified 2019-09-10 21:40:00, in category <a href="./category/algorithm.html">Algorithm</a></p>
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<h3>十种常用排序算法的Python实现</h3>
<ul>
<li>冒泡排序</li>
<li>插入排序</li>
<li>选择排序</li>
<li>希尔排序</li>
<li>快速排序</li>
<li>归并排序</li>
<li>堆排序</li>
<li>桶排序</li>
<li>基数排序</li>
<li>计数排序</li>
</ul>
<p>交换操作</p>
<div class="highlight"><pre><span></span><span class="c1"># 交换</span>
<span class="k">def</span> <span class="nf">swap</span><span class="p">(</span><span class="n">arr</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">):</span>
<span class="n">arr</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">arr</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">arr</span><span class="p">[</span><span class="n">j</span><span class="p">],</span> <span class="n">arr</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
</pre></div>
<p>冒泡排序</p>
<div class="highlight"><pre><span></span><span class="c1"># 冒泡排序</span>
<span class="k">def</span> <span class="nf">bubble_sort</span><span class="p">(</span><span class="n">arr</span><span class="p">):</span>
<span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
<span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span><span class="p">):</span>
<span class="k">if</span> <span class="n">arr</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">></span> <span class="n">arr</span><span class="p">[</span><span class="n">j</span><span class="p">]:</span>
<span class="n">swap</span><span class="p">(</span><span class="n">arr</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">)</span>
<span class="k">return</span> <span class="n">arr</span>
</pre></div>
<p>选择排序</p>
<div class="highlight"><pre><span></span><span class="c1"># 选择排序</span>
<span class="k">def</span> <span class="nf">selection_sort</span><span class="p">(</span><span class="n">arr</span><span class="p">):</span>
<span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
<span class="n">k</span> <span class="o">=</span> <span class="n">i</span>
<span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span><span class="p">):</span>
<span class="k">if</span> <span class="n">arr</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o"><</span> <span class="n">arr</span><span class="p">[</span><span class="n">k</span><span class="p">]:</span>
<span class="n">k</span> <span class="o">=</span> <span class="n">j</span>
<span class="n">swap</span><span class="p">(</span><span class="n">arr</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">k</span><span class="p">)</span>
<span class="k">return</span> <span class="n">arr</span>
</pre></div>
<p>插入排序</p>
<div class="highlight"><pre><span></span><span class="c1"># 插入排序1</span>
<span class="k">def</span> <span class="nf">insertion_sort</span><span class="p">(</span><span class="n">arr</span><span class="p">):</span>
<span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span><span class="p">):</span>
<span class="n">j</span><span class="p">,</span> <span class="n">base</span> <span class="o">=</span> <span class="n">i</span><span class="p">,</span> <span class="n">arr</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
<span class="k">while</span> <span class="n">j</span> <span class="o">></span> <span class="mi">0</span> <span class="ow">and</span> <span class="n">base</span> <span class="o"><</span> <span class="n">arr</span><span class="p">[</span><span class="n">j</span><span class="o">-</span><span class="mi">1</span><span class="p">]:</span>
<span class="n">arr</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">arr</span><span class="p">[</span><span class="n">j</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
<span class="n">j</span> <span class="o">-=</span> <span class="mi">1</span>
<span class="n">arr</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">base</span>
<span class="k">return</span> <span class="n">arr</span>
<span class="c1"># 插入排序2</span>
<span class="c1"># 1的简化版</span>
<span class="k">def</span> <span class="nf">insertion_sort2</span><span class="p">(</span><span class="n">arr</span><span class="p">):</span>
<span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span><span class="p">):</span>
<span class="n">j</span> <span class="o">=</span> <span class="n">i</span>
<span class="k">while</span> <span class="n">j</span> <span class="o">></span> <span class="mi">0</span> <span class="ow">and</span> <span class="n">arr</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o"><</span> <span class="n">arr</span><span class="p">[</span><span class="n">j</span><span class="o">-</span><span class="mi">1</span><span class="p">]:</span>
<span class="n">swap</span><span class="p">(</span><span class="n">arr</span><span class="p">,</span> <span class="n">j</span><span class="p">,</span> <span class="n">j</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>
<span class="n">j</span> <span class="o">-=</span> <span class="mi">1</span>
<span class="k">return</span> <span class="n">arr</span>
</pre></div>
<p>希尔排序</p>
<div class="highlight"><pre><span></span><span class="c1"># 希尔排序</span>
<span class="c1"># 带步长的插入排序, 对比插入排序2</span>
<span class="k">def</span> <span class="nf">shell_sort</span><span class="p">(</span><span class="n">arr</span><span class="p">):</span>
<span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span>
<span class="n">h</span> <span class="o">=</span> <span class="mi">1</span>
<span class="k">while</span> <span class="n">h</span> <span class="o"><</span> <span class="n">n</span><span class="o">//</span><span class="mi">3</span><span class="p">:</span> <span class="n">h</span> <span class="o">=</span> <span class="n">h</span> <span class="o">*</span> <span class="mi">3</span> <span class="o">+</span> <span class="mi">1</span>
<span class="k">while</span> <span class="n">h</span> <span class="o">>=</span> <span class="mi">1</span><span class="p">:</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span><span class="p">):</span>
<span class="n">j</span> <span class="o">=</span> <span class="n">i</span>
<span class="k">while</span> <span class="n">j</span> <span class="o">>=</span> <span class="n">h</span> <span class="ow">and</span> <span class="n">arr</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o"><</span> <span class="n">arr</span><span class="p">[</span><span class="n">j</span><span class="o">-</span><span class="n">h</span><span class="p">]:</span>
<span class="n">swap</span><span class="p">(</span><span class="n">arr</span><span class="p">,</span> <span class="n">j</span><span class="p">,</span> <span class="n">j</span><span class="o">-</span><span class="n">h</span><span class="p">)</span>
<span class="n">j</span> <span class="o">-=</span> <span class="n">h</span>
<span class="n">h</span> <span class="o">//=</span> <span class="mi">3</span>
<span class="k">return</span> <span class="n">arr</span>
</pre></div>
<p>快速排序</p>
<div class="highlight"><pre><span></span><span class="c1"># 快速排序</span>
<span class="k">def</span> <span class="nf">quick_sort</span><span class="p">(</span><span class="n">arr</span><span class="p">):</span>
<span class="k">def</span> <span class="nf">_quick_sort</span><span class="p">(</span><span class="n">arr</span><span class="p">,</span> <span class="n">l</span><span class="p">,</span> <span class="n">r</span><span class="p">):</span>
<span class="k">if</span> <span class="n">l</span> <span class="o">>=</span> <span class="n">r</span><span class="p">:</span> <span class="k">return</span>
<span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">,</span> <span class="n">base</span> <span class="o">=</span> <span class="n">l</span><span class="p">,</span> <span class="n">r</span><span class="p">,</span> <span class="n">arr</span><span class="p">[</span><span class="n">l</span><span class="p">]</span>
<span class="k">while</span> <span class="n">i</span> <span class="o"><</span> <span class="n">j</span><span class="p">:</span>
<span class="k">while</span> <span class="n">i</span> <span class="o"><</span> <span class="n">j</span> <span class="ow">and</span> <span class="n">arr</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">>=</span> <span class="n">base</span><span class="p">:</span>
<span class="n">j</span> <span class="o">-=</span> <span class="mi">1</span>
<span class="k">while</span> <span class="n">i</span> <span class="o"><</span> <span class="n">j</span> <span class="ow">and</span> <span class="n">arr</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o"><=</span> <span class="n">base</span><span class="p">:</span>
<span class="n">i</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="n">swap</span><span class="p">(</span><span class="n">arr</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">)</span>
<span class="n">swap</span><span class="p">(</span><span class="n">arr</span><span class="p">,</span> <span class="n">l</span><span class="p">,</span> <span class="n">j</span><span class="p">)</span>
<span class="n">_quick_sort</span><span class="p">(</span><span class="n">arr</span><span class="p">,</span> <span class="n">l</span><span class="p">,</span> <span class="n">i</span><span class="p">)</span>
<span class="n">_quick_sort</span><span class="p">(</span><span class="n">arr</span><span class="p">,</span> <span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">,</span> <span class="n">r</span><span class="p">)</span>
<span class="n">_quick_sort</span><span class="p">(</span><span class="n">arr</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
<span class="k">return</span> <span class="n">arr</span>
</pre></div>
<p>归并排序</p>
<div class="highlight"><pre><span></span><span class="c1"># 归并排序</span>
<span class="c1"># 1: 自顶向下 2:自底向上</span>
<span class="k">def</span> <span class="nf">merge_sort</span><span class="p">(</span><span class="n">arr</span><span class="p">,</span> <span class="nb">type</span><span class="o">=</span><span class="mi">1</span><span class="p">):</span>
<span class="k">def</span> <span class="nf">_merge</span><span class="p">(</span><span class="n">arr</span><span class="p">,</span> <span class="n">l</span><span class="p">,</span> <span class="n">mid</span><span class="p">,</span> <span class="n">r</span><span class="p">):</span>
<span class="n">i</span><span class="p">,</span> <span class="n">j</span> <span class="o">=</span> <span class="n">l</span><span class="p">,</span> <span class="n">mid</span> <span class="o">+</span> <span class="mi">1</span>
<span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">l</span><span class="p">,</span> <span class="n">r</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
<span class="n">tmp</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="o">=</span> <span class="n">arr</span><span class="p">[</span><span class="n">k</span><span class="p">]</span>
<span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">l</span><span class="p">,</span> <span class="n">r</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
<span class="k">if</span> <span class="n">i</span> <span class="o">></span> <span class="n">mid</span><span class="p">:</span>
<span class="n">arr</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="o">=</span> <span class="n">tmp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span>
<span class="n">j</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="k">elif</span> <span class="n">j</span> <span class="o">></span> <span class="n">r</span><span class="p">:</span>
<span class="n">arr</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="o">=</span> <span class="n">tmp</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
<span class="n">i</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="k">elif</span> <span class="n">tmp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o"><</span> <span class="n">tmp</span><span class="p">[</span><span class="n">i</span><span class="p">]:</span>
<span class="n">arr</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="o">=</span> <span class="n">tmp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span>
<span class="n">j</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">arr</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="o">=</span> <span class="n">tmp</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
<span class="n">i</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="c1"># 自顶向下</span>
<span class="k">def</span> <span class="nf">_sort</span><span class="p">(</span><span class="n">arr</span><span class="p">,</span> <span class="n">l</span><span class="p">,</span> <span class="n">r</span><span class="p">):</span>
<span class="k">if</span> <span class="n">l</span> <span class="o">>=</span> <span class="n">r</span><span class="p">:</span> <span class="k">return</span>
<span class="n">mid</span> <span class="o">=</span> <span class="n">l</span> <span class="o">+</span> <span class="p">(</span><span class="n">r</span> <span class="o">-</span> <span class="n">l</span><span class="p">)</span> <span class="o">//</span> <span class="mi">2</span>
<span class="n">_sort</span><span class="p">(</span><span class="n">arr</span><span class="p">,</span> <span class="n">l</span><span class="p">,</span> <span class="n">mid</span><span class="p">)</span>
<span class="n">_sort</span><span class="p">(</span><span class="n">arr</span><span class="p">,</span> <span class="n">mid</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">r</span><span class="p">)</span>
<span class="n">_merge</span><span class="p">(</span><span class="n">arr</span><span class="p">,</span> <span class="n">l</span><span class="p">,</span> <span class="n">mid</span><span class="p">,</span> <span class="n">r</span><span class="p">)</span>
<span class="c1"># 自底向上</span>
<span class="k">def</span> <span class="nf">_sort_bottom_up</span><span class="p">(</span><span class="n">arr</span><span class="p">):</span>
<span class="n">n</span><span class="p">,</span> <span class="n">step</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">arr</span><span class="p">),</span> <span class="mi">1</span>
<span class="k">while</span> <span class="n">step</span> <span class="o"><</span> <span class="n">n</span><span class="p">:</span>
<span class="n">l</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">while</span> <span class="n">l</span> <span class="o"><</span> <span class="n">n</span><span class="p">:</span>
<span class="n">_merge</span><span class="p">(</span><span class="n">arr</span><span class="p">,</span> <span class="n">l</span><span class="p">,</span> <span class="n">l</span> <span class="o">+</span> <span class="n">step</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="nb">min</span><span class="p">(</span><span class="n">l</span> <span class="o">+</span> <span class="n">step</span> <span class="o">+</span> <span class="n">step</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">n</span><span class="o">-</span><span class="mi">1</span><span class="p">))</span>
<span class="n">l</span> <span class="o">+=</span> <span class="n">step</span> <span class="o">+</span> <span class="n">step</span>
<span class="n">step</span> <span class="o">+=</span> <span class="n">step</span>
<span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span>
<span class="n">tmp</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">n</span>
<span class="k">if</span> <span class="nb">type</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
<span class="n">_sort</span><span class="p">(</span><span class="n">arr</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="n">n</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">_sort_bottom_up</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span>
<span class="k">return</span> <span class="n">arr</span>
</pre></div>
<p>堆排序</p>
<div class="highlight"><pre><span></span><span class="c1"># 堆排序</span>
<span class="c1"># 每次要将根节点与末尾交换, 所以正序排序建大顶堆, 逆序排序建小顶堆</span>
<span class="k">def</span> <span class="nf">heap_sort</span><span class="p">(</span><span class="n">arr</span><span class="p">):</span>
<span class="k">def</span> <span class="nf">_build_max_heap</span><span class="p">(</span><span class="n">arr</span><span class="p">):</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span><span class="o">//</span><span class="mi">2</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">):</span>
<span class="n">_heapify</span><span class="p">(</span><span class="n">arr</span><span class="p">,</span> <span class="n">i</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">_heapify</span><span class="p">(</span><span class="n">arr</span><span class="p">,</span> <span class="n">i</span><span class="p">):</span>
<span class="n">l</span> <span class="o">=</span> <span class="n">i</span> <span class="o">*</span> <span class="mi">2</span> <span class="o">+</span> <span class="mi">1</span>
<span class="n">r</span> <span class="o">=</span> <span class="n">l</span> <span class="o">+</span> <span class="mi">1</span>
<span class="n">p</span> <span class="o">=</span> <span class="n">i</span>
<span class="k">if</span> <span class="n">l</span> <span class="o"><</span> <span class="n">N</span> <span class="ow">and</span> <span class="n">arr</span><span class="p">[</span><span class="n">p</span><span class="p">]</span> <span class="o"><</span> <span class="n">arr</span><span class="p">[</span><span class="n">l</span><span class="p">]:</span>
<span class="n">p</span> <span class="o">=</span> <span class="n">l</span>
<span class="k">if</span> <span class="n">r</span> <span class="o"><</span> <span class="n">N</span> <span class="ow">and</span> <span class="n">arr</span><span class="p">[</span><span class="n">p</span><span class="p">]</span> <span class="o"><</span> <span class="n">arr</span><span class="p">[</span><span class="n">r</span><span class="p">]:</span>
<span class="n">p</span> <span class="o">=</span> <span class="n">r</span>
<span class="k">if</span> <span class="n">p</span> <span class="o">!=</span> <span class="n">i</span><span class="p">:</span>
<span class="n">swap</span><span class="p">(</span><span class="n">arr</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">p</span><span class="p">)</span>
<span class="n">_heapify</span><span class="p">(</span><span class="n">arr</span><span class="p">,</span> <span class="n">p</span><span class="p">)</span>
<span class="n">N</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span>
<span class="n">_build_max_heap</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">):</span>
<span class="n">swap</span><span class="p">(</span><span class="n">arr</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="n">i</span><span class="p">)</span>
<span class="n">N</span> <span class="o">-=</span> <span class="mi">1</span>
<span class="n">_heapify</span><span class="p">(</span><span class="n">arr</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
<span class="k">return</span> <span class="n">arr</span>
</pre></div>
<p>桶排序</p>
<div class="highlight"><pre><span></span><span class="c1"># 桶排序</span>
<span class="c1"># 分配空间少的计数排序桶变为二维数组,每个桶存储多个元素.</span>
<span class="c1"># 计数排序也就是单桶大小为1时的桶排序</span>
<span class="k">def</span> <span class="nf">bucket_sort</span><span class="p">(</span><span class="n">arr</span><span class="p">):</span>
<span class="n">_MIN</span><span class="p">,</span> <span class="n">_MAX</span> <span class="o">=</span> <span class="n">get_min_max</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span>
<span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span>
<span class="n">k</span> <span class="o">=</span> <span class="p">(</span><span class="n">_MAX</span> <span class="o">-</span> <span class="n">_MIN</span><span class="p">)</span> <span class="o">//</span> <span class="mi">3</span> <span class="o">+</span> <span class="mi">1</span>
<span class="n">tmp</span> <span class="o">=</span> <span class="p">[[]</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">k</span><span class="p">)]</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
<span class="n">x</span> <span class="o">=</span> <span class="p">(</span><span class="n">arr</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">-</span> <span class="n">_MIN</span><span class="p">)</span> <span class="o">//</span> <span class="mi">3</span>
<span class="n">tmp</span><span class="p">[</span><span class="n">x</span><span class="p">]</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">arr</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
<span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">tmp</span><span class="p">[</span><span class="n">x</span><span class="p">])</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">):</span>
<span class="k">if</span> <span class="n">tmp</span><span class="p">[</span><span class="n">x</span><span class="p">][</span><span class="n">j</span><span class="p">]</span> <span class="o"><</span> <span class="n">tmp</span><span class="p">[</span><span class="n">x</span><span class="p">][</span><span class="n">j</span><span class="o">-</span><span class="mi">1</span><span class="p">]:</span>
<span class="n">swap</span><span class="p">(</span><span class="n">tmp</span><span class="p">[</span><span class="n">x</span><span class="p">],</span> <span class="n">j</span><span class="p">,</span> <span class="n">j</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">break</span>
<span class="n">i</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">tmp</span><span class="p">:</span>
<span class="k">for</span> <span class="n">e</span> <span class="ow">in</span> <span class="n">x</span><span class="p">:</span>
<span class="n">arr</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">e</span>
<span class="n">i</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="k">return</span> <span class="n">arr</span>
</pre></div>
<p>基数排序</p>
<div class="highlight"><pre><span></span><span class="c1"># 基数排序</span>
<span class="c1"># 基数排序适用于数组中的数值不大的非负整数情况, 原理是按数值的每一位排序装桶</span>
<span class="c1"># 可以分为低位优先(LSD)和高位优先(MSD)</span>
<span class="c1"># 代码中使用的LSD</span>
<span class="k">def</span> <span class="nf">radix_sort</span><span class="p">(</span><span class="n">arr</span><span class="p">):</span>
<span class="n">get_digit</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">x</span><span class="p">,</span> <span class="n">d</span><span class="p">:</span> <span class="p">(</span><span class="n">x</span><span class="o">//</span><span class="n">d</span><span class="p">)</span> <span class="o">%</span> <span class="mi">10</span>
<span class="n">max_num</span> <span class="o">=</span> <span class="nb">max</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span>
<span class="n">_MAX_DIGIT</span> <span class="o">=</span> <span class="mi">1</span>
<span class="k">while</span> <span class="n">max_num</span> <span class="o">>=</span> <span class="mi">10</span><span class="p">:</span>
<span class="n">max_num</span> <span class="o">//=</span> <span class="mi">10</span>
<span class="n">_MAX_DIGIT</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span>
<span class="n">digit</span> <span class="o">=</span> <span class="mi">1</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">_MAX_DIGIT</span><span class="p">):</span>
<span class="n">pos</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="mi">10</span>
<span class="n">tmp</span> <span class="o">=</span> <span class="p">[</span><span class="n">x</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">arr</span><span class="p">]</span>
<span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">tmp</span><span class="p">:</span>
<span class="n">k</span> <span class="o">=</span> <span class="n">get_digit</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">digit</span><span class="p">)</span>
<span class="n">pos</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">10</span><span class="p">):</span>
<span class="n">pos</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">+=</span> <span class="n">pos</span><span class="p">[</span><span class="n">j</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">):</span>
<span class="n">base</span> <span class="o">=</span> <span class="n">tmp</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
<span class="n">k</span> <span class="o">=</span> <span class="n">get_digit</span><span class="p">(</span><span class="n">base</span><span class="p">,</span> <span class="n">digit</span><span class="p">)</span>
<span class="n">arr</span><span class="p">[</span><span class="n">pos</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">base</span>
<span class="n">pos</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="o">-=</span> <span class="mi">1</span>
<span class="n">digit</span> <span class="o">*=</span> <span class="mi">10</span>
<span class="k">return</span> <span class="n">arr</span>
</pre></div>
<p>计数排序</p>
<div class="highlight"><pre><span></span><span class="c1"># 计数排序</span>
<span class="c1"># 只能排整型数组</span>
<span class="k">def</span> <span class="nf">count_sort</span><span class="p">(</span><span class="n">arr</span><span class="p">):</span>
<span class="k">def</span> <span class="nf">get_min_max</span><span class="p">(</span><span class="n">arr</span><span class="p">):</span>
<span class="n">_MIN</span><span class="p">,</span> <span class="n">_MAX</span> <span class="o">=</span> <span class="nb">float</span><span class="p">(</span><span class="s2">"inf"</span><span class="p">),</span> <span class="o">-</span><span class="nb">float</span><span class="p">(</span><span class="s2">"inf"</span><span class="p">)</span>
<span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">arr</span><span class="p">:</span>
<span class="k">if</span> <span class="n">x</span> <span class="o"><</span> <span class="n">_MIN</span><span class="p">:</span>
<span class="n">_MIN</span> <span class="o">=</span> <span class="n">x</span>
<span class="k">if</span> <span class="n">x</span> <span class="o">></span> <span class="n">_MAX</span><span class="p">:</span>
<span class="n">_MAX</span> <span class="o">=</span> <span class="n">x</span>
<span class="k">return</span> <span class="n">_MIN</span><span class="p">,</span> <span class="n">_MAX</span>
<span class="n">_MIN</span><span class="p">,</span> <span class="n">_MAX</span> <span class="o">=</span> <span class="n">get_min_max</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span>
<span class="n">tmp</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="p">(</span><span class="n">_MAX</span> <span class="o">-</span> <span class="n">_MIN</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
<span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
<span class="n">tmp</span><span class="p">[</span><span class="n">arr</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">-</span> <span class="n">_MIN</span><span class="p">]</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="n">i</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">for</span> <span class="n">j</span><span class="p">,</span> <span class="n">x</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">tmp</span><span class="p">):</span>
<span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
<span class="n">arr</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">j</span> <span class="o">+</span> <span class="n">_MIN</span>
<span class="n">i</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="k">return</span> <span class="n">arr</span>
</pre></div>
<p>完整代码见<a href="https://github.com/Rivarrl/leetcode_python/blob/master/basic/num_sort.py">这里</a></p>
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