排序算法的研究

谁借莪１个温暖的怀抱￠ 2022-09-24 08:25 139阅读 0赞

[排序算法的研究][Link 1]  2006-03-24 23:38:31

分类： 项目管理

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           <h2 style="word-wrap:break-word; margin:0px; padding:0px"><span style="font-size:12px; word-wrap:break-word">排序算法是一种基本并且常用的算法。由于实际工作中处理的数量巨大，所以排序算法&nbsp;<br style="word-wrap:break-word"> 对算法本身的速度要求很高。&nbsp;<br style="word-wrap:break-word"> 而一般我们所谓的算法的性能主要是指算法的复杂度，一般用O方法来表示。在后面我将&nbsp;<br style="word-wrap:break-word"> 给出详细的说明。</span></h2> 
           <div style="word-wrap:break-word">
             对于排序的算法我想先做一点简单的介绍，也是给这篇文章理一个提纲。&nbsp; 
            <br style="word-wrap:break-word"> 我将按照算法的复杂度，从简单到难来分析算法。&nbsp; 
            <br style="word-wrap:break-word"> 第一部分是简单排序算法，后面你将看到他们的共同点是算法复杂度为O(N*N)（因为没有&nbsp; 
            <br style="word-wrap:break-word"> 使用word,所以无法打出上标和下标）。&nbsp; 
            <br style="word-wrap:break-word"> 第二部分是高级排序算法，复杂度为O(Log2(N))。这里我们只介绍一种算法。另外还有几种&nbsp; 
            <br style="word-wrap:break-word"> 算法因为涉及树与堆的概念，所以这里不于讨论。&nbsp; 
            <br style="word-wrap:break-word"> 第三部分类似动脑筋。这里的两种算法并不是最好的（甚至有最慢的），但是算法本身比较&nbsp; 
            <br style="word-wrap:break-word"> 奇特，值得参考（编程的角度）。同时也可以让我们从另外的角度来认识这个问题。&nbsp; 
            <br style="word-wrap:break-word"> 第四部分是我送给大家的一个餐后的甜点——一个基于模板的通用快速排序。由于是模板函数&nbsp; 
            <br style="word-wrap:break-word"> 可以对任何数据类型排序（抱歉，里面使用了一些论坛专家的呢称）。 
           </div> 
           <div style="word-wrap:break-word">
             现在，让我们开始吧： 
           </div> 
           <div style="word-wrap:break-word">
             一、简单排序算法&nbsp; 
            <br style="word-wrap:break-word"> 由于程序比较简单，所以没有加什么注释。所有的程序都给出了完整的运行代码，并在我的VC环境&nbsp; 
            <br style="word-wrap:break-word"> 下运行通过。因为没有涉及MFC和WINDOWS的内容，所以在BORLAND C++的平台上应该也不会有什么&nbsp; 
            <br style="word-wrap:break-word"> 问题的。在代码的后面给出了运行过程示意，希望对理解有帮助。 
           </div> 
           <div style="word-wrap:break-word"> 
            <span style="color:#ff0000; word-wrap:break-word">1.冒泡法：</span>&nbsp; 
            <br style="word-wrap:break-word"> 这是最原始，也是众所周知的最慢的算法了。他的名字的由来因为它的工作看来象是冒泡：&nbsp; 
            <br style="word-wrap:break-word"> #include 
           </div> 
           <div style="word-wrap:break-word">
             void BubbleSort(int* pData,int Count)&nbsp; 
            <br style="word-wrap:break-word"> {&nbsp; 
            <br style="word-wrap:break-word"> int iTemp;&nbsp; 
            <br style="word-wrap:break-word"> for(int i=1;i&lt;count;i++) 
            <br style="word-wrap:break-word"> {&nbsp; 
            <br style="word-wrap:break-word"> for(int j=Count-1;j&gt;=i;j--)&nbsp; 
            <br style="word-wrap:break-word"> {&nbsp; 
            <br style="word-wrap:break-word"> if(pData[j]&lt;pdata[j-1]) 
            <br style="word-wrap:break-word"> {&nbsp; 
            <br style="word-wrap:break-word"> iTemp = pData[j-1];&nbsp; 
            <br style="word-wrap:break-word"> pData[j-1] = pData[j];&nbsp; 
            <br style="word-wrap:break-word"> pData[j] = iTemp;&nbsp; 
            <br style="word-wrap:break-word"> }&nbsp; 
            <br style="word-wrap:break-word"> }&nbsp; 
            <br style="word-wrap:break-word"> }&nbsp; 
            <br style="word-wrap:break-word"> } 
           </div> 
           <div style="word-wrap:break-word">
             void main()&nbsp; 
            <br style="word-wrap:break-word"> {&nbsp; 
            <br style="word-wrap:break-word"> int data[] = ;&nbsp; 
            <br style="word-wrap:break-word"> BubbleSort(data,7);&nbsp; 
            <br style="word-wrap:break-word"> for (int i=0;i&lt;7;i++)&nbsp; 
            <br style="word-wrap:break-word"> cout&lt;&lt;data&lt;&lt;" ";="" 
            <br style="word-wrap:break-word"> cout&lt;&lt;"\n";&nbsp; 
            <br style="word-wrap:break-word"> } 
           </div> 
           <div style="word-wrap:break-word">
             倒序(最糟情况)&nbsp; 
            <br style="word-wrap:break-word"> 第一轮：10,9,8,7-&gt;10,9,7,8-&gt;10,7,9,8-&gt;7,10,9,8(交换3次)&nbsp; 
            <br style="word-wrap:break-word"> 第二轮：7,10,9,8-&gt;7,10,8,9-&gt;7,8,10,9(交换2次)&nbsp; 
            <br style="word-wrap:break-word"> 第一轮：7,8,10,9-&gt;7,8,9,10(交换1次)&nbsp; 
            <br style="word-wrap:break-word"> 循环次数：6次&nbsp; 
            <br style="word-wrap:break-word"> 交换次数：6次 
           </div> 
           <div style="word-wrap:break-word">
             其他：&nbsp; 
            <br style="word-wrap:break-word"> 第一轮：8,10,7,9-&gt;8,10,7,9-&gt;8,7,10,9-&gt;7,8,10,9(交换2次)&nbsp; 
            <br style="word-wrap:break-word"> 第二轮：7,8,10,9-&gt;7,8,10,9-&gt;7,8,10,9(交换0次)&nbsp; 
            <br style="word-wrap:break-word"> 第一轮：7,8,10,9-&gt;7,8,9,10(交换1次)&nbsp; 
            <br style="word-wrap:break-word"> 循环次数：6次&nbsp; 
            <br style="word-wrap:break-word"> 交换次数：3次 
           </div> 
           <div style="word-wrap:break-word">
             上面我们给出了程序段，现在我们分析它：这里，影响我们算法性能的主要部分是循环和交换，&nbsp; 
            <br style="word-wrap:break-word"> 显然，次数越多，性能就越差。从上面的程序我们可以看出循环的次数是固定的，为1+2+...+n-1。&nbsp; 
            <br style="word-wrap:break-word"> 写成公式就是1/2*(n-1)*n。&nbsp; 
            <br style="word-wrap:break-word"> 现在注意，我们给出O方法的定义： 
           </div> 
           <div style="word-wrap:break-word">
             若存在一常量K和起点n0，使当n&gt;=n0时，有f(n)&lt;=K*g(n),则f(n) = O(g(n))。（呵呵，不要说没&nbsp; 
            <br style="word-wrap:break-word"> 学好数学呀，对于编程数学是非常重要的！！！） 
           </div> 
           <div style="word-wrap:break-word">
             现在我们来看1/2*(n-1)*n，当K=1/2，n0=1，g(n)=n*n时，1/2*(n-1)*n&lt;=1/2*n*n=K*g(n)。所以f(n)&nbsp; 
            <br style="word-wrap:break-word"> =O(g(n))=O(n*n)。所以我们程序循环的复杂度为O(n*n)。&nbsp; 
            <br style="word-wrap:break-word"> 再看交换。从程序后面所跟的表可以看到，两种情况的循环相同，交换不同。其实交换本身同数据源的&nbsp; 
            <br style="word-wrap:break-word"> 有序程度有极大的关系，当数据处于倒序的情况时，交换次数同循环一样（每次循环判断都会交换），&nbsp; 
            <br style="word-wrap:break-word"> 复杂度为O(n*n)。当数据为正序，将不会有交换。复杂度为O(0)。乱序时处于中间状态。正是由于这样的 
            <br style="word-wrap:break-word"> 原因，我们通常都是通过循环次数来对比算法。 
           </div> 
           <div style="word-wrap:break-word"> 
            <br style="word-wrap:break-word"> 
            <span style="color:#ff0000; word-wrap:break-word">2.交换法：</span>&nbsp; 
            <br style="word-wrap:break-word"> 交换法的程序最清晰简单，每次用当前的元素一一的同其后的元素比较并交换。&nbsp; 
            <br style="word-wrap:break-word"> #include&nbsp; 
            <br style="word-wrap:break-word"> void ExchangeSort(int* pData,int Count)&nbsp; 
            <br style="word-wrap:break-word"> {&nbsp; 
            <br style="word-wrap:break-word"> int iTemp;&nbsp; 
            <br style="word-wrap:break-word"> for(int i=0;i&lt;count-1;i++) 
            <br style="word-wrap:break-word"> {&nbsp; 
            <br style="word-wrap:break-word"> for(int j=i+1;j&lt;count;j++) 
            <br style="word-wrap:break-word"> {&nbsp; 
            <br style="word-wrap:break-word"> if(pData[j]&lt;pdata) 
            <br style="word-wrap:break-word"> {&nbsp; 
            <br style="word-wrap:break-word"> iTemp = pData;&nbsp; 
            <br style="word-wrap:break-word"> pData = pData[j];&nbsp; 
            <br style="word-wrap:break-word"> pData[j] = iTemp;&nbsp; 
            <br style="word-wrap:break-word"> }&nbsp; 
            <br style="word-wrap:break-word"> }&nbsp; 
            <br style="word-wrap:break-word"> }&nbsp; 
            <br style="word-wrap:break-word"> } 
           </div> 
           <div style="word-wrap:break-word">
             void main()&nbsp; 
            <br style="word-wrap:break-word"> {&nbsp; 
            <br style="word-wrap:break-word"> int data[] = ;&nbsp; 
            <br style="word-wrap:break-word"> ExchangeSort(data,7);&nbsp; 
            <br style="word-wrap:break-word"> for (int i=0;i&lt;7;i++)&nbsp; 
            <br style="word-wrap:break-word"> cout&lt;&lt;data&lt;&lt;" ";="" 
            <br style="word-wrap:break-word"> cout&lt;&lt;"\n";&nbsp; 
            <br style="word-wrap:break-word"> }&nbsp; 
            <br style="word-wrap:break-word"> 倒序(最糟情况)&nbsp; 
            <br style="word-wrap:break-word"> 第一轮：10,9,8,7-&gt;9,10,8,7-&gt;8,10,9,7-&gt;7,10,9,8(交换3次)&nbsp; 
            <br style="word-wrap:break-word"> 第二轮：7,10,9,8-&gt;7,9,10,8-&gt;7,8,10,9(交换2次)&nbsp; 
            <br style="word-wrap:break-word"> 第一轮：7,8,10,9-&gt;7,8,9,10(交换1次)&nbsp; 
            <br style="word-wrap:break-word"> 循环次数：6次&nbsp; 
            <br style="word-wrap:break-word"> 交换次数：6次 
           </div> 
           <div style="word-wrap:break-word">
             其他：&nbsp; 
            <br style="word-wrap:break-word"> 第一轮：8,10,7,9-&gt;8,10,7,9-&gt;7,10,8,9-&gt;7,10,8,9(交换1次)&nbsp; 
            <br style="word-wrap:break-word"> 第二轮：7,10,8,9-&gt;7,8,10,9-&gt;7,8,10,9(交换1次)&nbsp; 
            <br style="word-wrap:break-word"> 第一轮：7,8,10,9-&gt;7,8,9,10(交换1次)&nbsp; 
            <br style="word-wrap:break-word"> 循环次数：6次&nbsp; 
            <br style="word-wrap:break-word"> 交换次数：3次 
           </div> 
           <div style="word-wrap:break-word">
             从运行的表格来看，交换几乎和冒泡一样糟。事实确实如此。循环次数和冒泡一样&nbsp; 
            <br style="word-wrap:break-word"> 也是1/2*(n-1)*n，所以算法的复杂度仍然是O(n*n)。由于我们无法给出所有的情况，所以&nbsp; 
            <br style="word-wrap:break-word"> 只能直接告诉大家他们在交换上面也是一样的糟糕（在某些情况下稍好，在某些情况下稍差）。 
           </div> 
           <div style="word-wrap:break-word"> 
            <span style="color:#ff0000; word-wrap:break-word">3.选择法：</span>&nbsp; 
            <br style="word-wrap:break-word"> 现在我们终于可以看到一点希望：选择法，这种方法提高了一点性能（某些情况下）&nbsp; 
            <br style="word-wrap:break-word"> 这种方法类似我们人为的排序习惯：从数据中选择最小的同第一个值交换，在从省下的部分中&nbsp; 
            <br style="word-wrap:break-word"> 选择最小的与第二个交换，这样往复下去。&nbsp; 
            <br style="word-wrap:break-word"> #include&nbsp; 
            <br style="word-wrap:break-word"> void SelectSort(int* pData,int Count)&nbsp; 
            <br style="word-wrap:break-word"> {&nbsp; 
            <br style="word-wrap:break-word"> int iTemp;&nbsp; 
            <br style="word-wrap:break-word"> int iPos;&nbsp; 
            <br style="word-wrap:break-word"> for(int i=0;i&lt;count-1;i++) 
            <br style="word-wrap:break-word"> {&nbsp; 
            <br style="word-wrap:break-word"> iTemp = pData;&nbsp; 
            <br style="word-wrap:break-word"> iPos = i;&nbsp; 
            <br style="word-wrap:break-word"> for(int j=i+1;j&lt;count;j++) 
            <br style="word-wrap:break-word"> {&nbsp; 
            <br style="word-wrap:break-word"> if(pData[j]&lt;itemp) 
            <br style="word-wrap:break-word"> {&nbsp; 
            <br style="word-wrap:break-word"> iTemp = pData[j];&nbsp; 
            <br style="word-wrap:break-word"> iPos = j;&nbsp; 
            <br style="word-wrap:break-word"> }&nbsp; 
            <br style="word-wrap:break-word"> }&nbsp; 
            <br style="word-wrap:break-word"> pData[iPos] = pData;&nbsp; 
            <br style="word-wrap:break-word"> pData = iTemp;&nbsp; 
            <br style="word-wrap:break-word"> }&nbsp; 
            <br style="word-wrap:break-word"> } 
           </div> 
           <div style="word-wrap:break-word">
             void main()&nbsp; 
            <br style="word-wrap:break-word"> {&nbsp; 
            <br style="word-wrap:break-word"> int data[] = ;&nbsp; 
            <br style="word-wrap:break-word"> SelectSort(data,7);&nbsp; 
            <br style="word-wrap:break-word"> for (int i=0;i&lt;7;i++)&nbsp; 
            <br style="word-wrap:break-word"> cout&lt;&lt;data&lt;&lt;" ";="" 
            <br style="word-wrap:break-word"> cout&lt;&lt;"\n";&nbsp; 
            <br style="word-wrap:break-word"> }&nbsp; 
            <br style="word-wrap:break-word"> 倒序(最糟情况)&nbsp; 
            <br style="word-wrap:break-word"> 第一轮：10,9,8,7-&gt;(iTemp=9)10,9,8,7-&gt;(iTemp=8)10,9,8,7-&gt;(iTemp=7)7,9,8,10(交换1次)&nbsp; 
            <br style="word-wrap:break-word"> 第二轮：7,9,8,10-&gt;7,9,8,10(iTemp=8)-&gt;(iTemp=8)7,8,9,10(交换1次)&nbsp; 
            <br style="word-wrap:break-word"> 第一轮：7,8,9,10-&gt;(iTemp=9)7,8,9,10(交换0次)&nbsp; 
            <br style="word-wrap:break-word"> 循环次数：6次&nbsp; 
            <br style="word-wrap:break-word"> 交换次数：2次 
           </div> 
           <div style="word-wrap:break-word">
             其他：&nbsp; 
            <br style="word-wrap:break-word"> 第一轮：8,10,7,9-&gt;(iTemp=8)8,10,7,9-&gt;(iTemp=7)8,10,7,9-&gt;(iTemp=7)7,10,8,9(交换1次)&nbsp; 
            <br style="word-wrap:break-word"> 第二轮：7,10,8,9-&gt;(iTemp=8)7,10,8,9-&gt;(iTemp=8)7,8,10,9(交换1次)&nbsp; 
            <br style="word-wrap:break-word"> 第一轮：7,8,10,9-&gt;(iTemp=9)7,8,9,10(交换1次)&nbsp; 
            <br style="word-wrap:break-word"> 循环次数：6次&nbsp; 
            <br style="word-wrap:break-word"> 交换次数：3次&nbsp; 
            <br style="word-wrap:break-word"> 遗憾的是算法需要的循环次数依然是1/2*(n-1)*n。所以算法复杂度为O(n*n)。&nbsp; 
            <br style="word-wrap:break-word"> 我们来看他的交换。由于每次外层循环只产生一次交换（只有一个最小值）。所以f(n)&lt;=n&nbsp; 
            <br style="word-wrap:break-word"> 所以我们有f(n)=O(n)。所以，在数据较乱的时候，可以减少一定的交换次数。 
           </div> 
           <div style="word-wrap:break-word"> 
            <br style="word-wrap:break-word"> 
            <span style="color:#ff0000; word-wrap:break-word">4.插入法：</span>&nbsp; 
            <br style="word-wrap:break-word"> 插入法较为复杂，它的基本工作原理是抽出牌，在前面的牌中寻找相应的位置插入，然后继续下一张&nbsp; 
            <br style="word-wrap:break-word"> #include&nbsp; 
            <br style="word-wrap:break-word"> void InsertSort(int* pData,int Count)&nbsp; 
            <br style="word-wrap:break-word"> {&nbsp; 
            <br style="word-wrap:break-word"> int iTemp;&nbsp; 
            <br style="word-wrap:break-word"> int iPos;&nbsp; 
            <br style="word-wrap:break-word"> for(int i=1;i&lt;count;i++) 
            <br style="word-wrap:break-word"> {&nbsp; 
            <br style="word-wrap:break-word"> iTemp = pData;&nbsp; 
            <br style="word-wrap:break-word"> iPos = i-1;&nbsp; 
            <br style="word-wrap:break-word"> while((iPos&gt;=0) &amp;&amp; (iTemp&lt;pdata[ipos])) 
            <br style="word-wrap:break-word"> {&nbsp; 
            <br style="word-wrap:break-word"> pData[iPos+1] = pData[iPos];&nbsp; 
            <br style="word-wrap:break-word"> iPos--;&nbsp; 
            <br style="word-wrap:break-word"> }&nbsp; 
            <br style="word-wrap:break-word"> pData[iPos+1] = iTemp;&nbsp; 
            <br style="word-wrap:break-word"> }&nbsp; 
            <br style="word-wrap:break-word"> } 
           </div> 
           <div style="word-wrap:break-word">
             void main()&nbsp; 
            <br style="word-wrap:break-word"> {&nbsp; 
            <br style="word-wrap:break-word"> int data[] = ;&nbsp; 
            <br style="word-wrap:break-word"> InsertSort(data,7);&nbsp; 
            <br style="word-wrap:break-word"> for (int i=0;i&lt;7;i++)&nbsp; 
            <br style="word-wrap:break-word"> cout&lt;&lt;data&lt;&lt;" ";="" 
            <br style="word-wrap:break-word"> cout&lt;&lt;"\n";&nbsp; 
            <br style="word-wrap:break-word"> } 
           </div> 
           <div style="word-wrap:break-word">
             倒序(最糟情况)&nbsp; 
            <br style="word-wrap:break-word"> 第一轮：10,9,8,7-&gt;9,10,8,7(交换1次)(循环1次)&nbsp; 
            <br style="word-wrap:break-word"> 第二轮：9,10,8,7-&gt;8,9,10,7(交换1次)(循环2次)&nbsp; 
            <br style="word-wrap:break-word"> 第一轮：8,9,10,7-&gt;7,8,9,10(交换1次)(循环3次)&nbsp; 
            <br style="word-wrap:break-word"> 循环次数：6次&nbsp; 
            <br style="word-wrap:break-word"> 交换次数：3次 
           </div> 
           <div style="word-wrap:break-word">
             其他：&nbsp; 
            <br style="word-wrap:break-word"> 第一轮：8,10,7,9-&gt;8,10,7,9(交换0次)(循环1次)&nbsp; 
            <br style="word-wrap:break-word"> 第二轮：8,10,7,9-&gt;7,8,10,9(交换1次)(循环2次)&nbsp; 
            <br style="word-wrap:break-word"> 第一轮：7,8,10,9-&gt;7,8,9,10(交换1次)(循环1次)&nbsp; 
            <br style="word-wrap:break-word"> 循环次数：4次&nbsp; 
            <br style="word-wrap:break-word"> 交换次数：2次 
           </div> 
           <div style="word-wrap:break-word">
             上面结尾的行为分析事实上造成了一种假象，让我们认为这种算法是简单算法中最好的，其实不是，&nbsp; 
            <br style="word-wrap:break-word"> 因为其循环次数虽然并不固定，我们仍可以使用O方法。从上面的结果可以看出，循环的次数f(n)&lt;=&nbsp; 
            <br style="word-wrap:break-word"> 1/2*n*(n-1)&lt;=1/2*n*n。所以其复杂度仍为O(n*n)（这里说明一下，其实如果不是为了展示这些简单&nbsp; 
            <br style="word-wrap:break-word"> 排序的不同，交换次数仍然可以这样推导）。现在看交换，从外观上看，交换次数是O(n)（推导类似&nbsp; 
            <br style="word-wrap:break-word"> 选择法），但我们每次要进行与内层循环相同次数的‘=’操作。正常的一次交换我们需要三次‘=’&nbsp; 
            <br style="word-wrap:break-word"> 而这里显然多了一些，所以我们浪费了时间。 
           </div> 
           <div style="word-wrap:break-word">
             最终，我个人认为，在简单排序算法中，选择法是最好的。 
           </div> 
           <div style="word-wrap:break-word"> 
            <br style="word-wrap:break-word"> 二、高级排序算法：&nbsp; 
            <br style="word-wrap:break-word"> 高级排序算法中我们将只介绍这一种，同时也是目前我所知道（我看过的资料中）的最快的。&nbsp; 
            <br style="word-wrap:break-word"> 它的工作看起来仍然象一个二叉树。首先我们选择一个中间值middle程序中我们使用数组中间值，然后&nbsp; 
            <br style="word-wrap:break-word"> 把比它小的放在左边，大的放在右边（具体的实现是从两边找，找到一对后交换）。然后对两边分别使&nbsp; 
            <br style="word-wrap:break-word"> 用这个过程（最容易的方法——递归）。 
           </div> 
           <div style="word-wrap:break-word"> 
            <span style="color:#ff0000; word-wrap:break-word">1.快速排序：&nbsp;<br style="word-wrap:break-word"> </span>#include 
           </div> 
           <div style="word-wrap:break-word">
             void run(int* pData,int left,int right)&nbsp; 
            <br style="word-wrap:break-word"> {&nbsp; 
            <br style="word-wrap:break-word"> int i,j;&nbsp; 
            <br style="word-wrap:break-word"> int middle,iTemp;&nbsp; 
            <br style="word-wrap:break-word"> i = left;&nbsp; 
            <br style="word-wrap:break-word"> j = right;&nbsp; 
            <br style="word-wrap:break-word"> middle = pData[(left+right)/2]; //求中间值&nbsp; 
            <br style="word-wrap:break-word"> do{&nbsp; 
            <br style="word-wrap:break-word"> while((pData&lt;middle) &amp;&amp;="" (i&lt;right))="" 从左扫描大于中值的数="" 
            <br style="word-wrap:break-word"> i++;&nbsp; 
            <br style="word-wrap:break-word"> while((pData[j]&gt;middle) &amp;&amp; (j&gt;left))//从右扫描大于中值的数&nbsp; 
            <br style="word-wrap:break-word"> j--;&nbsp; 
            <br style="word-wrap:break-word"> if(i&lt;=j)//找到了一对值&nbsp; 
            <br style="word-wrap:break-word"> {&nbsp; 
            <br style="word-wrap:break-word"> //交换&nbsp; 
            <br style="word-wrap:break-word"> iTemp = pData;&nbsp; 
            <br style="word-wrap:break-word"> pData = pData[j];&nbsp; 
            <br style="word-wrap:break-word"> pData[j] = iTemp;&nbsp; 
            <br style="word-wrap:break-word"> i++;&nbsp; 
            <br style="word-wrap:break-word"> j--;&nbsp; 
            <br style="word-wrap:break-word"> }&nbsp; 
            <br style="word-wrap:break-word"> }while(i&lt;=j);//如果两边扫描的下标交错，就停止（完成一次） 
           </div> 
           <div style="word-wrap:break-word">
             //当左边部分有值(left&lt;j)，递归左半边 
            <br style="word-wrap:break-word"> if(left&lt;j) 
            <br style="word-wrap:break-word"> run(pData,left,j);&nbsp; 
            <br style="word-wrap:break-word"> //当右边部分有值(right&gt;i)，递归右半边&nbsp; 
            <br style="word-wrap:break-word"> if(right&gt;i)&nbsp; 
            <br style="word-wrap:break-word"> run(pData,i,right);&nbsp; 
            <br style="word-wrap:break-word"> } 
           </div> 
           <div style="word-wrap:break-word">
             void QuickSort(int* pData,int Count)&nbsp; 
            <br style="word-wrap:break-word"> {&nbsp; 
            <br style="word-wrap:break-word"> run(pData,0,Count-1);&nbsp; 
            <br style="word-wrap:break-word"> } 
           </div> 
           <div style="word-wrap:break-word">
             void main()&nbsp; 
            <br style="word-wrap:break-word"> {&nbsp; 
            <br style="word-wrap:break-word"> int data[] = ;&nbsp; 
            <br style="word-wrap:break-word"> QuickSort(data,7);&nbsp; 
            <br style="word-wrap:break-word"> for (int i=0;i&lt;7;i++)&nbsp; 
            <br style="word-wrap:break-word"> cout&lt;&lt;data&lt;&lt;" ";="" 
            <br style="word-wrap:break-word"> cout&lt;&lt;"\n";&nbsp; 
            <br style="word-wrap:break-word"> } 
           </div> 
           <div style="word-wrap:break-word">
             这里我没有给出行为的分析，因为这个很简单，我们直接来分析算法：首先我们考虑最理想的情况&nbsp; 
            <br style="word-wrap:break-word"> 1.数组的大小是2的幂，这样分下去始终可以被2整除。假设为2的k次方，即k=log2(n)。&nbsp; 
            <br style="word-wrap:break-word"> 2.每次我们选择的值刚好是中间值，这样，数组才可以被等分。&nbsp; 
            <br style="word-wrap:break-word"> 第一层递归，循环n次，第二层循环2*(n/2)......&nbsp; 
            <br style="word-wrap:break-word"> 所以共有n+2(n/2)+4(n/4)+...+n*(n/n) = n+n+n+...+n=k*n=log2(n)*n&nbsp; 
            <br style="word-wrap:break-word"> 所以算法复杂度为O(log2(n)*n)&nbsp; 
            <br style="word-wrap:break-word"> 其他的情况只会比这种情况差，最差的情况是每次选择到的middle都是最小值或最大值，那么他将变&nbsp; 
            <br style="word-wrap:break-word"> 成交换法（由于使用了递归，情况更糟）。但是你认为这种情况发生的几率有多大？？呵呵，你完全&nbsp; 
            <br style="word-wrap:break-word"> 不必担心这个问题。实践证明，大多数的情况，快速排序总是最好的。&nbsp; 
            <br style="word-wrap:break-word"> 如果你担心这个问题，你可以使用堆排序，这是一种稳定的O(log2(n)*n)算法，但是通常情况下速度要慢 
            <br style="word-wrap:break-word"> 于快速排序（因为要重组堆）。 
           </div> 
           <div style="word-wrap:break-word">
             三、其他排序&nbsp; 
            <br style="word-wrap:break-word"> 
            <span style="color:#ff0000; word-wrap:break-word">1.双向冒泡：</span>&nbsp; 
            <br style="word-wrap:break-word"> 通常的冒泡是单向的，而这里是双向的，也就是说还要进行反向的工作。&nbsp; 
            <br style="word-wrap:break-word"> 代码看起来复杂，仔细理一下就明白了，是一个来回震荡的方式。&nbsp; 
            <br style="word-wrap:break-word"> 写这段代码的作者认为这样可以在冒泡的基础上减少一些交换（我不这么认为，也许我错了）。&nbsp; 
            <br style="word-wrap:break-word"> 反正我认为这是一段有趣的代码，值得一看。&nbsp; 
            <br style="word-wrap:break-word"> #include&nbsp; 
            <br style="word-wrap:break-word"> void Bubble2Sort(int* pData,int Count)&nbsp; 
            <br style="word-wrap:break-word"> {&nbsp; 
            <br style="word-wrap:break-word"> int iTemp;&nbsp; 
            <br style="word-wrap:break-word"> int left = 1;&nbsp; 
            <br style="word-wrap:break-word"> int right =Count -1;&nbsp; 
            <br style="word-wrap:break-word"> int t;&nbsp; 
            <br style="word-wrap:break-word"> do&nbsp; 
            <br style="word-wrap:break-word"> {&nbsp; 
            <br style="word-wrap:break-word"> //正向的部分&nbsp; 
            <br style="word-wrap:break-word"> for(int i=right;i&gt;=left;i--)&nbsp; 
            <br style="word-wrap:break-word"> {&nbsp; 
            <br style="word-wrap:break-word"> if(pData&lt;pdata[i-1]) 
            <br style="word-wrap:break-word"> {&nbsp; 
            <br style="word-wrap:break-word"> iTemp = pData;&nbsp; 
            <br style="word-wrap:break-word"> pData = pData[i-1];&nbsp; 
            <br style="word-wrap:break-word"> pData[i-1] = iTemp;&nbsp; 
            <br style="word-wrap:break-word"> t = i;&nbsp; 
            <br style="word-wrap:break-word"> }&nbsp; 
            <br style="word-wrap:break-word"> }&nbsp; 
            <br style="word-wrap:break-word"> left = t+1; 
           </div> 
           <div style="word-wrap:break-word">
             //反向的部分&nbsp; 
            <br style="word-wrap:break-word"> for(i=left;i&lt;right+1;i++) 
            <br style="word-wrap:break-word"> {&nbsp; 
            <br style="word-wrap:break-word"> if(pData&lt;pdata[i-1]) 
            <br style="word-wrap:break-word"> {&nbsp; 
            <br style="word-wrap:break-word"> iTemp = pData;&nbsp; 
            <br style="word-wrap:break-word"> pData = pData[i-1];&nbsp; 
            <br style="word-wrap:break-word"> pData[i-1] = iTemp;&nbsp; 
            <br style="word-wrap:break-word"> t = i;&nbsp; 
            <br style="word-wrap:break-word"> }&nbsp; 
            <br style="word-wrap:break-word"> }&nbsp; 
            <br style="word-wrap:break-word"> right = t-1;&nbsp; 
            <br style="word-wrap:break-word"> }while(left&lt;=right);&nbsp; 
            <br style="word-wrap:break-word"> } 
           </div> 
           <div style="word-wrap:break-word">
             void main()&nbsp; 
            <br style="word-wrap:break-word"> {&nbsp; 
            <br style="word-wrap:break-word"> int data[] = ;&nbsp; 
            <br style="word-wrap:break-word"> Bubble2Sort(data,7);&nbsp; 
            <br style="word-wrap:break-word"> for (int i=0;i&lt;7;i++)&nbsp; 
            <br style="word-wrap:break-word"> cout&lt;&lt;data&lt;&lt;" ";="" 
            <br style="word-wrap:break-word"> cout&lt;&lt;"\n";&nbsp; 
            <br style="word-wrap:break-word"> } 
           </div> 
           <div style="word-wrap:break-word"> 
            <br style="word-wrap:break-word"> 
            <span style="color:#ff0000; word-wrap:break-word">2.SHELL排序&nbsp;<br style="word-wrap:break-word"> </span>这个排序非常复杂，看了程序就知道了。&nbsp; 
            <br style="word-wrap:break-word"> 首先需要一个递减的步长，这里我们使用的是9、5、3、1（最后的步长必须是1）。&nbsp; 
            <br style="word-wrap:break-word"> 工作原理是首先对相隔9-1个元素的所有内容排序，然后再使用同样的方法对相隔5-1个元素的排序&nbsp; 
            <br style="word-wrap:break-word"> 以次类推。&nbsp; 
            <br style="word-wrap:break-word"> #include&nbsp; 
            <br style="word-wrap:break-word"> void ShellSort(int* pData,int Count)&nbsp; 
            <br style="word-wrap:break-word"> {&nbsp; 
            <br style="word-wrap:break-word"> int step[4];&nbsp; 
            <br style="word-wrap:break-word"> step[0] = 9;&nbsp; 
            <br style="word-wrap:break-word"> step[1] = 5;&nbsp; 
            <br style="word-wrap:break-word"> step[2] = 3;&nbsp; 
            <br style="word-wrap:break-word"> step[3] = 1; 
           </div> 
           <div style="word-wrap:break-word">
             int iTemp;&nbsp; 
            <br style="word-wrap:break-word"> int k,s,w;&nbsp; 
            <br style="word-wrap:break-word"> for(int i=0;i&lt;4;i++)&nbsp; 
            <br style="word-wrap:break-word"> {&nbsp; 
            <br style="word-wrap:break-word"> k = step;&nbsp; 
            <br style="word-wrap:break-word"> s = -k;&nbsp; 
            <br style="word-wrap:break-word"> for(int j=k;j&lt;count;j++) 
            <br style="word-wrap:break-word"> {&nbsp; 
            <br style="word-wrap:break-word"> iTemp = pData[j];&nbsp; 
            <br style="word-wrap:break-word"> w = j-k;//求上step个元素的下标&nbsp; 
            <br style="word-wrap:break-word"> if(s ==0)&nbsp; 
            <br style="word-wrap:break-word"> {&nbsp; 
            <br style="word-wrap:break-word"> s = -k;&nbsp; 
            <br style="word-wrap:break-word"> s++;&nbsp; 
            <br style="word-wrap:break-word"> pData[s] = iTemp;&nbsp; 
            <br style="word-wrap:break-word"> }&nbsp; 
            <br style="word-wrap:break-word"> while((iTemp=0) &amp;&amp; (w&lt;=Count))&nbsp; 
            <br style="word-wrap:break-word"> {&nbsp; 
            <br style="word-wrap:break-word"> pData[w+k] = pData[w];&nbsp; 
            <br style="word-wrap:break-word"> w = w-k;&nbsp; 
            <br style="word-wrap:break-word"> }&nbsp; 
            <br style="word-wrap:break-word"> pData[w+k] = iTemp;&nbsp; 
            <br style="word-wrap:break-word"> }&nbsp; 
            <br style="word-wrap:break-word"> }&nbsp; 
            <br style="word-wrap:break-word"> } 
           </div> 
           <div style="word-wrap:break-word">
             void main()&nbsp; 
            <br style="word-wrap:break-word"> {&nbsp; 
            <br style="word-wrap:break-word"> int data[] = ;&nbsp; 
            <br style="word-wrap:break-word"> ShellSort(data,12);&nbsp; 
            <br style="word-wrap:break-word"> for (int i=0;i&lt;12;i++)&nbsp; 
            <br style="word-wrap:break-word"> cout&lt;&lt;data&lt;&lt;" ";="" 
            <br style="word-wrap:break-word"> cout&lt;&lt;"\n";&nbsp; 
            <br style="word-wrap:break-word"> }&nbsp; 
            <br style="word-wrap:break-word"> 呵呵，程序看起来有些头疼。不过也不是很难，把s==0的块去掉就轻松多了，这里是避免使用0&nbsp; 
            <br style="word-wrap:break-word"> 步长造成程序异常而写的代码。这个代码我认为很值得一看。&nbsp; 
            <br style="word-wrap:break-word"> 这个算法的得名是因为其发明者的名字D.L.SHELL。依照参考资料上的说法：“由于复杂的数学原因&nbsp; 
            <br style="word-wrap:break-word"> 避免使用2的幂次步长，它能降低算法效率。”另外算法的复杂度为n的1.2次幂。同样因为非常复杂并&nbsp; 
            <br style="word-wrap:break-word"> “超出本书讨论范围”的原因（我也不知道过程），我们只有结果了。 
           </div> 
           <div style="word-wrap:break-word"> 
            <br style="word-wrap:break-word"> 四、基于模板的通用排序：&nbsp; 
            <br style="word-wrap:break-word"> 这个程序我想就没有分析的必要了，大家看一下就可以了。不明白可以在论坛上问。&nbsp; 
            <br style="word-wrap:break-word"> MyData.h文件&nbsp; 
            <br style="word-wrap:break-word"> ///&nbsp; 
            <br style="word-wrap:break-word"> class CMyData&nbsp; 
            <br style="word-wrap:break-word"> {&nbsp; 
            <br style="word-wrap:break-word"> public:&nbsp; 
            <br style="word-wrap:break-word"> CMyData(int Index,char* strData);&nbsp; 
            <br style="word-wrap:break-word"> CMyData();&nbsp; 
            <br style="word-wrap:break-word"> virtual ~CMyData(); 
           </div> 
           <div style="word-wrap:break-word">
             int m_iIndex;&nbsp; 
            <br style="word-wrap:break-word"> int GetDataSize(){ return m_iDataSize; };&nbsp; 
            <br style="word-wrap:break-word"> const char* GetData(){ return m_strDatamember; };&nbsp; 
            <br style="word-wrap:break-word"> //这里重载了操作符：&nbsp; 
            <br style="word-wrap:break-word"> CMyData&amp; operator =(CMyData &amp;SrcData);&nbsp; 
            <br style="word-wrap:break-word"> bool operator &lt;(CMyData&amp; data );&nbsp; 
            <br style="word-wrap:break-word"> bool operator &gt;(CMyData&amp; data ); 
           </div> 
           <div style="word-wrap:break-word">
             private:&nbsp; 
            <br style="word-wrap:break-word"> char* m_strDatamember;&nbsp; 
            <br style="word-wrap:break-word"> int m_iDataSize;&nbsp; 
            <br style="word-wrap:break-word"> };&nbsp; 
            <br style="word-wrap:break-word"> 
           </div> 
           <div style="word-wrap:break-word">
             MyData.cpp文件&nbsp; 
            <br style="word-wrap:break-word"> &nbsp; 
            <br style="word-wrap:break-word"> CMyData::CMyData():&nbsp; 
            <br style="word-wrap:break-word"> m_iIndex(0),&nbsp; 
            <br style="word-wrap:break-word"> m_iDataSize(0),&nbsp; 
            <br style="word-wrap:break-word"> m_strDatamember(NULL)&nbsp; 
            <br style="word-wrap:break-word"> {&nbsp; 
            <br style="word-wrap:break-word"> } 
           </div> 
           <div style="word-wrap:break-word">
             CMyData::~CMyData()&nbsp; 
            <br style="word-wrap:break-word"> {&nbsp; 
            <br style="word-wrap:break-word"> if(m_strDatamember != NULL)&nbsp; 
            <br style="word-wrap:break-word"> delete[] m_strDatamember;&nbsp; 
            <br style="word-wrap:break-word"> m_strDatamember = NULL;&nbsp; 
            <br style="word-wrap:break-word"> } 
           </div> 
           <div style="word-wrap:break-word">
             CMyData::CMyData(int Index,char* strData):&nbsp; 
            <br style="word-wrap:break-word"> m_iIndex(Index),&nbsp; 
            <br style="word-wrap:break-word"> m_iDataSize(0),&nbsp; 
            <br style="word-wrap:break-word"> m_strDatamember(NULL)&nbsp; 
            <br style="word-wrap:break-word"> {&nbsp; 
            <br style="word-wrap:break-word"> m_iDataSize = strlen(strData);&nbsp; 
            <br style="word-wrap:break-word"> m_strDatamember = new char[m_iDataSize+1];&nbsp; 
            <br style="word-wrap:break-word"> strcpy(m_strDatamember,strData);&nbsp; 
            <br style="word-wrap:break-word"> } 
           </div> 
           <div style="word-wrap:break-word">
             CMyData&amp; CMyData::operator =(CMyData &amp;SrcData)&nbsp; 
            <br style="word-wrap:break-word"> {&nbsp; 
            <br style="word-wrap:break-word"> m_iIndex = SrcData.m_iIndex;&nbsp; 
            <br style="word-wrap:break-word"> m_iDataSize = SrcData.GetDataSize();&nbsp; 
            <br style="word-wrap:break-word"> m_strDatamember = new char[m_iDataSize+1];&nbsp; 
            <br style="word-wrap:break-word"> strcpy(m_strDatamember,SrcData.GetData());&nbsp; 
            <br style="word-wrap:break-word"> return *this;&nbsp; 
            <br style="word-wrap:break-word"> } 
           </div> 
           <div style="word-wrap:break-word">
             bool CMyData::operator &lt;(CMyData&amp; data )&nbsp; 
            <br style="word-wrap:break-word"> {&nbsp; 
            <br style="word-wrap:break-word"> return m_iIndex&lt;data.m_iindex; 
            <br style="word-wrap:break-word"> } 
           </div> 
           <div style="word-wrap:break-word">
             bool CMyData::operator &gt;(CMyData&amp; data )&nbsp; 
            <br style="word-wrap:break-word"> {&nbsp; 
            <br style="word-wrap:break-word"> return m_iIndex&gt;data.m_iIndex;&nbsp; 
            <br style="word-wrap:break-word"> }&nbsp; 
            <br style="word-wrap:break-word"> /// 
           </div> 
           <div style="word-wrap:break-word">
             //&nbsp; 
            <br style="word-wrap:break-word"> //主程序部分&nbsp; 
            <br style="word-wrap:break-word"> #include&nbsp; 
            <br style="word-wrap:break-word"> #include "MyData.h" 
           </div> 
           <div style="word-wrap:break-word">
             template&nbsp; 
            <br style="word-wrap:break-word"> void run(T* pData,int left,int right)&nbsp; 
            <br style="word-wrap:break-word"> {&nbsp; 
            <br style="word-wrap:break-word"> int i,j;&nbsp; 
            <br style="word-wrap:break-word"> T middle,iTemp;&nbsp; 
            <br style="word-wrap:break-word"> i = left;&nbsp; 
            <br style="word-wrap:break-word"> j = right;&nbsp; 
            <br style="word-wrap:break-word"> //下面的比较都调用我们重载的操作符函数&nbsp; 
            <br style="word-wrap:break-word"> middle = pData[(left+right)/2]; //求中间值&nbsp; 
            <br style="word-wrap:break-word"> do{&nbsp; 
            <br style="word-wrap:break-word"> while((pData&lt;middle) &amp;&amp;="" (i&lt;right))="" 从左扫描大于中值的数="" 
            <br style="word-wrap:break-word"> i++;&nbsp; 
            <br style="word-wrap:break-word"> while((pData[j]&gt;middle) &amp;&amp; (j&gt;left))//从右扫描大于中值的数&nbsp; 
            <br style="word-wrap:break-word"> j--;&nbsp; 
            <br style="word-wrap:break-word"> if(i&lt;=j)//找到了一对值&nbsp; 
            <br style="word-wrap:break-word"> {&nbsp; 
            <br style="word-wrap:break-word"> //交换&nbsp; 
            <br style="word-wrap:break-word"> iTemp = pData;&nbsp; 
            <br style="word-wrap:break-word"> pData = pData[j];&nbsp; 
            <br style="word-wrap:break-word"> pData[j] = iTemp;&nbsp; 
            <br style="word-wrap:break-word"> i++;&nbsp; 
            <br style="word-wrap:break-word"> j--;&nbsp; 
            <br style="word-wrap:break-word"> }&nbsp; 
            <br style="word-wrap:break-word"> }while(i&lt;=j);//如果两边扫描的下标交错，就停止（完成一次） 
           </div> 
           <div style="word-wrap:break-word">
             //当左边部分有值(left&lt;j)，递归左半边 
            <br style="word-wrap:break-word"> if(left&lt;j) 
            <br style="word-wrap:break-word"> run(pData,left,j);&nbsp; 
            <br style="word-wrap:break-word"> //当右边部分有值(right&gt;i)，递归右半边&nbsp; 
            <br style="word-wrap:break-word"> if(right&gt;i)&nbsp; 
            <br style="word-wrap:break-word"> run(pData,i,right);&nbsp; 
            <br style="word-wrap:break-word"> } 
           </div> 
           <div style="word-wrap:break-word">
             template&nbsp; 
            <br style="word-wrap:break-word"> void QuickSort(T* pData,int Count)&nbsp; 
            <br style="word-wrap:break-word"> {&nbsp; 
            <br style="word-wrap:break-word"> run(pData,0,Count-1);&nbsp; 
            <br style="word-wrap:break-word"> } 
           </div> 
           <div style="word-wrap:break-word">
             void main()&nbsp; 
            <br style="word-wrap:break-word"> {&nbsp; 
            <br style="word-wrap:break-word"> CMyData data[] = {&nbsp; 
            <br style="word-wrap:break-word"> CMyData(8,"xulion"),&nbsp; 
            <br style="word-wrap:break-word"> CMyData(7,"sanzoo"),&nbsp; 
            <br style="word-wrap:break-word"> CMyData(6,"wangjun"),&nbsp; 
            <br style="word-wrap:break-word"> CMyData(5,"VCKBASE"),&nbsp; 
            <br style="word-wrap:break-word"> CMyData(4,"jacky2000"),&nbsp; 
            <br style="word-wrap:break-word"> CMyData(3,"cwally"),&nbsp; 
            <br style="word-wrap:break-word"> CMyData(2,"VCUSER"),&nbsp; 
            <br style="word-wrap:break-word"> CMyData(1,"isdong")&nbsp; 
            <br style="word-wrap:break-word"> };&nbsp; 
            <br style="word-wrap:break-word"> QuickSort(data,8);&nbsp; 
            <br style="word-wrap:break-word"> for (int i=0;i&lt;8;i++)&nbsp; 
            <br style="word-wrap:break-word"> cout&lt;&lt;data.m_iindex&lt;&lt;" "&lt;&lt;data.getdata()&lt;&lt;"\n";="" 
            <br style="word-wrap:break-word"> cout&lt;&lt;"\n";&nbsp; 
            <br style="word-wrap:break-word"> } 
            <br style="word-wrap:break-word"> ---------------------------------- 
            <br style="word-wrap:break-word"> 以上系转贴。 
           </div> 
          </div> 
         </div> 
        </div> </td> 
      </tr> 
     </tbody> 
    </table> </td> 
  </tr> 
 </tbody> 
</table>

[Link 1]: http://blog.chinaunix.net/uid-14022540-id-2849042.html