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顺序表的结构与实现
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顺序表的操作
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Python中的顺序表
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单向链表
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单项循环链表
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双向链表
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栈
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栈结构实现
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队列
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队列的实现
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双端队列
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排序与搜索
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<b>6.1.</b>
冒泡排序
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<b>6.2.</b>
选择排序
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插入排序
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<b>6.4.</b>
快速排序
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<b>6.5.</b>
希尔排序
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<b>6.6.</b>
归并排序
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常见排序算法效率比较
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搜索
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二叉树
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<h1 id="快速排序">快速排序</h1>
<p>快速排序（英语：Quicksort），又称划分交换排序（partition-exchange sort），通过一趟排序将要排序的数据分割成独立的两部分，其中一部分的所有数据都比另外一部分的所有数据都要小，然后再按此方法对这两部分数据分别进行快速排序，整个排序过程可以递归进行，以此达到整个数据变成有序序列。</p>
<p>步骤为：</p>
<ol>
<li>从数列中挑出一个元素，称为"基准"（pivot），</li>
<li>重新排序数列，所有元素比基准值小的摆放在基准前面，所有元素比基准值大的摆在基准的后面（相同的数可以到任一边）。在这个分区结束之后，该基准就处于数列的中间位置。这个称为分区（partition）操作。</li>
<li>递归地（recursive）把小于基准值元素的子数列和大于基准值元素的子数列排序。</li>
</ol>
<p>递归的最底部情形，是数列的大小是零或一，也就是永远都已经被排序好了。虽然一直递归下去，但是这个算法总会结束，因为在每次的迭代（iteration）中，它至少会把一个元素摆到它最后的位置去。</p>
<h2 id="快速排序的分析">快速排序的分析</h2>
<p><img src="../images/快速排序.jpg" alt="quicksort1"></p>
<pre><code class="lang-python"><span class="hljs-function"><span class="hljs-keyword">def</span> <span class="hljs-title">quick_sort</span><span class="hljs-params">(alist, start, end)</span>:</span>
<span class="hljs-string">"""快速排序"""</span>
<span class="hljs-comment"># 递归的退出条件</span>
<span class="hljs-keyword">if</span> start >= end:
<span class="hljs-keyword">return</span>
<span class="hljs-comment"># 设定起始元素为要寻找位置的基准元素</span>
mid = alist[start]
<span class="hljs-comment"># low为序列左边的由左向右移动的游标</span>
low = start
<span class="hljs-comment"># high为序列右边的由右向左移动的游标</span>
high = end
<span class="hljs-keyword">while</span> low < high:
<span class="hljs-comment"># 如果low与high未重合，high指向的元素不比基准元素小，则high向左移动</span>
<span class="hljs-keyword">while</span> low < high <span class="hljs-keyword">and</span> alist[high] >= mid:
high -= <span class="hljs-number">1</span>
<span class="hljs-comment"># 将high指向的元素放到low的位置上</span>
alist[low] = alist[high]
<span class="hljs-comment"># 如果low与high未重合，low指向的元素比基准元素小，则low向右移动</span>
<span class="hljs-keyword">while</span> low < high <span class="hljs-keyword">and</span> alist[low] < mid:
low += <span class="hljs-number">1</span>
<span class="hljs-comment"># 将low指向的元素放到high的位置上</span>
alist[high] = alist[low]
<span class="hljs-comment"># 退出循环后，low与high重合，此时所指位置为基准元素的正确位置</span>
<span class="hljs-comment"># 将基准元素放到该位置</span>
alist[low] = mid
<span class="hljs-comment"># 对基准元素左边的子序列进行快速排序</span>
quick_sort(alist, start, low-<span class="hljs-number">1</span>)
<span class="hljs-comment"># 对基准元素右边的子序列进行快速排序</span>
quick_sort(alist, low+<span class="hljs-number">1</span>, end)
alist = [<span class="hljs-number">54</span>,<span class="hljs-number">26</span>,<span class="hljs-number">93</span>,<span class="hljs-number">17</span>,<span class="hljs-number">77</span>,<span class="hljs-number">31</span>,<span class="hljs-number">44</span>,<span class="hljs-number">55</span>,<span class="hljs-number">20</span>]
quick_sort(alist,<span class="hljs-number">0</span>,len(alist)-<span class="hljs-number">1</span>)
print(alist)
</code></pre>
<h2 id="时间复杂度">时间复杂度</h2>
<ul>
<li>最优时间复杂度：O(nlogn)</li>
<li>最坏时间复杂度：O(n<sup>2</sup>)</li>
<li>稳定性：不稳定</li>
</ul>
<p>从一开始快速排序平均需要花费O(n log n)时间的描述并不明显。但是不难观察到的是分区运算，数组的元素都会在每次循环中走访过一次，使用O(n)的时间。在使用结合（concatenation）的版本中，这项运算也是O(n)。</p>
<p>在最好的情况，每次我们运行一次分区，我们会把一个数列分为两个几近相等的片段。这个意思就是每次递归调用处理一半大小的数列。因此，在到达大小为一的数列前，我们只要作log n次嵌套的调用。这个意思就是调用树的深度是O(log n)。但是在同一层次结构的两个程序调用中，不会处理到原来数列的相同部分；因此，程序调用的每一层次结构总共全部仅需要O(n)的时间（每个调用有某些共同的额外耗费，但是因为在每一层次结构仅仅只有O(n)个调用，这些被归纳在O(n)系数中）。结果是这个算法仅需使用O(n log n)时间。</p>
<h2 id="快速排序演示">快速排序演示</h2>
<p><img src="../images/quicksort.gif" alt="quicksort"></p>
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