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11.1.1. 评价维度
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稳定性
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就地性
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自适应性
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比较类
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11.1.1. 评价维度
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就地性
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@ -1817,13 +1749,9 @@
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<p align="center"> Fig. 排序中不同的元素类型和判断规则 </p>
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<h2 id="1111">11.1.1. 评价维度<a class="headerlink" href="#1111" title="Permanent link">¶</a></h2>
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<p>排序算法主要可根据 <strong>稳定性 、就地性 、自适应性 、比较类</strong> 来分类。</p>
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<h3 id="_1">稳定性<a class="headerlink" href="#_1" title="Permanent link">¶</a></h3>
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<ul>
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<li>「稳定排序」在完成排序后，<strong>不改变</strong> 相等元素在数组中的相对顺序。</li>
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<li>「非稳定排序」在完成排序后，相等元素在数组中的相对位置 <strong>可能被改变</strong>。</li>
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</ul>
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<p>假设我们有一个存储学生信息的表格，第 1, 2 列分别是姓名和年龄。那么在以下示例中，「非稳定排序」会导致输入数据的有序性丢失。因此「稳定排序」是很好的特性，<strong>在多级排序中是必须的</strong>。</p>
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<p><strong>运行效率</strong>：我们希望排序算法的时间复杂度尽可能低，并且总体操作数量更少（即时间复杂度中的常数项更低）。在大数据量下，运行效率尤为重要。</p>
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<p><strong>就地性</strong>：顾名思义，「原地排序」直接在原数组上操作实现排序，而不用借助额外辅助数组，节约内存；并且一般情况下，原地排序的数据搬运操作较少，运行速度也更快。</p>
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<p><strong>稳定性</strong>：「稳定排序」在完成排序后，相等元素在数组中的相对顺序 <strong>不会发生改变</strong>。假设我们有一个存储学生信息的表格，第 1, 2 列分别是姓名和年龄。那么在以下示例中，「非稳定排序」会导致输入数据的有序性丢失。稳定性是排序算法很好的特性，<strong>在多级排序中是必须的</strong>。</p>
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<div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="c1"># 输入数据是按照姓名排序好的</span>
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<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="c1"># (name, age)</span>
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<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a><span class="w"> </span><span class="o">(</span><span class="s1">'A'</span>,<span class="w"> </span><span class="m">19</span><span class="o">)</span>
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@ -1841,32 +1769,11 @@
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<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a><span class="w"> </span><span class="o">(</span><span class="s1">'C'</span>,<span class="w"> </span><span class="m">21</span><span class="o">)</span>
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<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a><span class="w"> </span><span class="o">(</span><span class="s1">'E'</span>,<span class="w"> </span><span class="m">23</span><span class="o">)</span>
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</code></pre></div>
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<h3 id="_2">就地性<a class="headerlink" href="#_2" title="Permanent link">¶</a></h3>
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<ul>
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<li>「原地排序」无需辅助数据，不使用额外空间；</li>
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<li>「非原地排序」需要借助辅助数据，使用额外空间；</li>
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</ul>
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<p>「原地排序」不使用额外空间，可以节约内存；并且一般情况下，由于数据操作减少，原地排序的运行效率也更高。</p>
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<h3 id="_3">自适应性<a class="headerlink" href="#_3" title="Permanent link">¶</a></h3>
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<ul>
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<li>「自适应排序」的时间复杂度受输入数据影响，即最佳 / 最差 / 平均时间复杂度不相等。</li>
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<li>「非自适应排序」的时间复杂度恒定，与输入数据无关。</li>
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</ul>
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<p>我们希望 <strong>最差 = 平均</strong>，即不希望排序算法的运行效率在某些输入数据下发生劣化。</p>
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<h3 id="_4">比较类<a class="headerlink" href="#_4" title="Permanent link">¶</a></h3>
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<ul>
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<li>「比较类排序」基于元素之间的比较算子（小于、相等、大于）来决定元素的相对顺序。</li>
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<li>「非比较类排序」不基于元素之间的比较算子来决定元素的相对顺序。</li>
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</ul>
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<p>「比较类排序」的时间复杂度最优为 <span class="arithmatex">\(O(n \log n)\)</span> ；而「非比较类排序」可以达到 <span class="arithmatex">\(O(n)\)</span> 的时间复杂度，但通用性较差。</p>
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<p><strong>自适应性</strong>：「自适应排序」的时间复杂度受输入数据影响，即最佳、最差、平均时间复杂度不全部相等。自适应性也要分情况对待，若最差时间复杂度差于平均时间复杂度，代表排序算法会在某些数据下发生劣化，因此是负面性质；而若最佳时间复杂度优于平均时间复杂度，则是正面性质。</p>
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<p><strong>是否基于比较</strong>：「比较排序」是根据比较算子（<span class="arithmatex">\(<\)</span> , <span class="arithmatex">\(=\)</span> , <span class="arithmatex">\(>\)</span>）来判断元素的相对顺序，进而排序整个数组，理论最优时间复杂度为 <span class="arithmatex">\(O(n \log n)\)</span> 。「非比较排序」不采用，时间复杂度可以达到 <span class="arithmatex">\(O(n)\)</span> ，但通用性相对较差。</p>
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<h2 id="1112">11.1.2. 理想排序算法<a class="headerlink" href="#1112" title="Permanent link">¶</a></h2>
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<ul>
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<li><strong>运行快</strong>，即时间复杂度低；</li>
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<li><strong>稳定排序</strong>，即排序后相等元素的相对位置不变化；</li>
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<li><strong>原地排序</strong>，即运行中不使用额外的辅助空间；</li>
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<li><strong>正向自适应性</strong>，即算法的运行效率不会在某些输入数据下发生劣化；</li>
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</ul>
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<p>然而，<strong>没有排序算法同时具备以上所有特性</strong>。排序算法的选型使用取决于具体的列表类型、列表长度、元素分布等因素。</p>
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<p><strong>运行快、原地、稳定、正向自适应、通用性好</strong>。显然，<strong>目前没有发现具备以上所有特性的排序算法</strong>，排序算法的选型使用取决于具体的数据特点与问题特征。</p>
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<p>接下来，我们将一起学习各种排序算法，并基于以上评价维度展开分析各个排序算法的优缺点。</p>
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|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_reference/</loc>
|
||||
<lastmod>2023-03-26</lastmod>
|
||||
<lastmod>2023-03-27</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_searching/binary_search/</loc>
|
||||
<lastmod>2023-03-26</lastmod>
|
||||
<lastmod>2023-03-27</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_searching/hashing_search/</loc>
|
||||
<lastmod>2023-03-26</lastmod>
|
||||
<lastmod>2023-03-27</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_searching/linear_search/</loc>
|
||||
<lastmod>2023-03-26</lastmod>
|
||||
<lastmod>2023-03-27</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_searching/summary/</loc>
|
||||
<lastmod>2023-03-26</lastmod>
|
||||
<lastmod>2023-03-27</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_sorting/bubble_sort/</loc>
|
||||
<lastmod>2023-03-26</lastmod>
|
||||
<lastmod>2023-03-27</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_sorting/bucket_sort/</loc>
|
||||
<lastmod>2023-03-26</lastmod>
|
||||
<lastmod>2023-03-27</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_sorting/counting_sort/</loc>
|
||||
<lastmod>2023-03-26</lastmod>
|
||||
<lastmod>2023-03-27</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_sorting/insertion_sort/</loc>
|
||||
<lastmod>2023-03-26</lastmod>
|
||||
<lastmod>2023-03-27</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_sorting/intro_to_sort/</loc>
|
||||
<lastmod>2023-03-26</lastmod>
|
||||
<lastmod>2023-03-27</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_sorting/merge_sort/</loc>
|
||||
<lastmod>2023-03-26</lastmod>
|
||||
<lastmod>2023-03-27</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_sorting/quick_sort/</loc>
|
||||
<lastmod>2023-03-26</lastmod>
|
||||
<lastmod>2023-03-27</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_sorting/radix_sort/</loc>
|
||||
<lastmod>2023-03-26</lastmod>
|
||||
<lastmod>2023-03-27</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_sorting/summary/</loc>
|
||||
<lastmod>2023-03-26</lastmod>
|
||||
<lastmod>2023-03-27</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_stack_and_queue/deque/</loc>
|
||||
<lastmod>2023-03-26</lastmod>
|
||||
<lastmod>2023-03-27</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_stack_and_queue/queue/</loc>
|
||||
<lastmod>2023-03-26</lastmod>
|
||||
<lastmod>2023-03-27</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_stack_and_queue/stack/</loc>
|
||||
<lastmod>2023-03-26</lastmod>
|
||||
<lastmod>2023-03-27</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_stack_and_queue/summary/</loc>
|
||||
<lastmod>2023-03-26</lastmod>
|
||||
<lastmod>2023-03-27</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_tree/avl_tree/</loc>
|
||||
<lastmod>2023-03-26</lastmod>
|
||||
<lastmod>2023-03-27</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_tree/binary_search_tree/</loc>
|
||||
<lastmod>2023-03-26</lastmod>
|
||||
<lastmod>2023-03-27</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_tree/binary_tree/</loc>
|
||||
<lastmod>2023-03-26</lastmod>
|
||||
<lastmod>2023-03-27</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_tree/binary_tree_traversal/</loc>
|
||||
<lastmod>2023-03-26</lastmod>
|
||||
<lastmod>2023-03-27</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
<url>
|
||||
<loc>https://www.hello-algo.com/chapter_tree/summary/</loc>
|
||||
<lastmod>2023-03-26</lastmod>
|
||||
<lastmod>2023-03-27</lastmod>
|
||||
<changefreq>daily</changefreq>
|
||||
</url>
|
||||
</urlset>
|
||||
BIN
sitemap.xml.gz
BIN
sitemap.xml.gz
Binary file not shown.
Loading…
Reference in New Issue
Block a user