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顺序表的结构与实现
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Python中的顺序表
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链表
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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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<b>6.3.</b>
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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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="希尔排序">希尔排序</h1>
<p>希尔排序(Shell Sort)是插入排序的一种。也称缩小增量排序，是直接插入排序算法的一种更高效的改进版本。希尔排序是非稳定排序算法。该方法因DL．Shell于1959年提出而得名。 希尔排序是把记录按下标的一定增量分组，对每组使用直接插入排序算法排序；随着增量逐渐减少，每组包含的关键词越来越多，当增量减至1时，整个文件恰被分成一组，算法便终止。</p>
<h2 id="希尔排序过程">希尔排序过程</h2>
<p>希尔排序的基本思想是：将数组列在一个表中并对列分别进行插入排序，重复这过程，不过每次用更长的列（步长更长了，列数更少了）来进行。最后整个表就只有一列了。将数组转换至表是为了更好地理解这算法，算法本身还是使用数组进行排序。</p>
<p>例如，假设有这样一组数[ 13 14 94 33 82 25 59 94 65 23 45 27 73 25 39 10 ]，如果我们以步长为5开始进行排序，我们可以通过将这列表放在有5列的表中来更好地描述算法，这样他们就应该看起来是这样(竖着的元素是步长组成)：</p>
<pre><code>13 14 94 33 82
25 59 94 65 23
45 27 73 25 39
10
</code></pre><p>然后我们对每列进行排序：</p>
<pre><code>10 14 73 25 23
13 27 94 33 39
25 59 94 65 82
45
</code></pre><p>将上述四行数字，依序接在一起时我们得到：[ 10 14 73 25 23 13 27 94 33 39 25 59 94 65 82 45 ]。这时10已经移至正确位置了，然后再以3为步长进行排序：</p>
<pre><code>10 14 73
25 23 13
27 94 33
39 25 59
94 65 82
45
</code></pre><p>排序之后变为：</p>
<pre><code>10 14 13
25 23 33
27 25 59
39 65 73
45 94 82
94
</code></pre><p>最后以1步长进行排序（此时就是简单的插入排序了）</p>
<h2 id="希尔排序的分析">希尔排序的分析</h2>
<p><img src="../images/shellsort.png" alt="shellsort"></p>
<pre><code class="lang-python"><span class="hljs-function"><span class="hljs-keyword">def</span> <span class="hljs-title">shell_sort</span><span class="hljs-params">(alist)</span>:</span>
n = len(alist)
<span class="hljs-comment"># 初始步长</span>
gap = n / <span class="hljs-number">2</span>
<span class="hljs-keyword">while</span> gap > <span class="hljs-number">0</span>:
<span class="hljs-comment"># 按步长进行插入排序</span>
<span class="hljs-keyword">for</span> i <span class="hljs-keyword">in</span> range(gap, n):
j = i
<span class="hljs-comment"># 插入排序</span>
<span class="hljs-keyword">while</span> j>=gap <span class="hljs-keyword">and</span> alist[j-gap] > alist[j]:
alist[j-gap], alist[j] = alist[j], alist[j-gap]
j -= gap
<span class="hljs-comment"># 得到新的步长</span>
gap = gap / <span class="hljs-number">2</span>
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>]
shell_sort(alist)
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：根据步长序列的不同而不同</li>
<li>最坏时间复杂度：O(n<sup>2</sup>)</li>
<li>稳定想：不稳定</li>
</ul>
<h2 id="希尔排序演示">希尔排序演示</h2>
<p><img src="../images/shellsort.gif" alt="shellsort"></p>
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<script>
require(["gitbook"], function(gitbook) {
var config = {"highlight":{},"search":{"maxIndexSize":1000000},"sharing":{"facebook":true,"twitter":true,"google":false,"weibo":false,"instapaper":false,"vk":false,"all":["facebook","google","twitter","weibo","instapaper"]},"fontsettings":{"theme":"white","family":"sans","size":2}};
gitbook.start(config);
});
</script>
</body>
</html>