Linux静态链接库使用类模板的快速排序算法
<p>快速排序的本质是从数组中选一个参考值ref，比该参考值的大的，将其放在ref的右边，比ref小的放在左边，然后不断的对两边重复执行该动作</p>
<p>
我们先列出来快速排序的步骤：</p>
<p>
1.从数组中选一个参考值ref，比该参考值的大的，将其放在ref的右边，</p>
<p>
上面的动作将数组划分为两部分:</p>
<p>
A ref B</p>
<p>
A是比ref小的数组元素集合，它仍然是数组，B是比ref大的元素集合，它也仍然是数组</p>
<p>
2.在对ref左右两边的元素重复上述动作，直到A和B都只剩下一个元素，那么排序就算完成了。</p>
<p>
</p>
<p>
重点是如何分别选出来两个集合A和B。算法导论里面把这个步骤叫做partition动作。</p>
<p>
先把算法导论里面的伪代码贴出来，大家先看一下：</p>
<p>
先看第一种ref的选择方法，即ref = a</p>
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<code class="xhtml plain">partition(a[], p, r)</code>
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<code class="xhtml plain">{</code>
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<code class="xhtml plain">i = p</code>
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<code class="xhtml plain">j = p-1</code>
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<code class="xhtml plain">ref = a</code>
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<code class="xhtml plain">for(; i<r; i++)</code>
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<code class="xhtml plain">{ </code>
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<code class="xhtml plain">if(a<ref)</code>
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<code class="xhtml plain">{</code>
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<code class="xhtml plain">j++</code>
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<code class="xhtml plain">exchange(a, a)</code>
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<code class="xhtml plain">}</code>
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<code class="xhtml plain">}</code>
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<code class="xhtml plain">exchange(a, a)</code>
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<code class="xhtml plain">return j+1;</code>
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<code class="xhtml plain">}</code>
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<p>
首先找一个参考值，ref = a，为了简单起见，这里取最后一个作为参考值，实际上可以去任意一个值作为参考值。这个我们一会再说。</p>
<p>
然后找定义两个游标，分别是i 和j。i=p， j=p-1。为什么要这么定义呢？原因是我们既然选的是第一个，也就是a，同时表示是从数组的第一个元素开始遍历的。</p>
<p>
选取j的目的是，我们要时刻知道当前最近一次比ref小的值的位置。由于我们选取的是a，作为参考值，且从第一个元素开始遍历，为了跟踪最近一次比ref小的数的游标，暂时j=p-1。大家可以仔细体会一下这个做的意义。</p>
<p>
观察上述代码可以看到，j总是记录着最近一次比ref小的数的游标，因此最后return j+1，所有比ref小的数的游标均小于j+1，所有比ref大的数的游标均大于j+2。</p>
<p>
总之我们执行partition的目的就是为了得到A，B，以及中间数的游标，这样我们就可以分别对A和B重复执行上述动作。</p>
<p>
</p>
<p>
接下来我们考虑另外两种选取ref的方法。从上面选取最后一个值a，作为参考值，并且在最后，将a和a交换的动作可以知道，我们总是希望知道我们选取参考值在partition过程中的位置，以便我们可以在最后一步，将a 和 a的值交换。这里的refId表示选取ref值在a[]中的游标。</p>
<p>
如果我们选取ref为最后一个值，那么在所有的partition过程中，这个值的位置是固定的。但是，假如我们选取的ref的refId是p到r范围内的一个随机数呢？</p>
<p>
显然，假如我们随机选取ref的值，那么在partition过程中，refId对于的ref就有可能和其他值交换。这时候我们就需要更新ref对应的游标。</p>
<p>
这样一来，思路就很清晰了。</p>
<p>
先给出partition的伪代码：</p>
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<code class="xhtml plain">partition(a[], p, r){</code>
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<code class="xhtml plain">refId = random(p,r)</code>
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<code class="xhtml plain">i = p</code>
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<code class="xhtml plain">j = p-1</code>
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<code class="xhtml plain">for(; i<=r; i++)</code>
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<code class="xhtml plain">{</code>
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<code class="xhtml plain">if(a<ref)</code>
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<code class="xhtml plain">{</code>
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<code class="xhtml plain">j++ if(j == refId)//此时j刚好等refId，并且要和a交换，则更新refId { refId = i }</code>
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<code class="xhtml plain">exchange(a, a)</code>
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<code class="xhtml plain">}</code>
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<code class="xhtml plain">}</code>
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<code class="xhtml plain">exchange(a, a)</code>
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<code class="xhtml plain">return j+1</code>
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<code class="xhtml plain">}</code>
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<p>
从三种选择ref的方法可以看到本质上都是一样的，都为用一个游标j记录最近一次遍历到的比ref小的数据的游标，然后将ref和a交换，返回j+1。</p>
<p>
下面给出C++的代码实现</p>
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<code class="xhtml plain">#include <</code><code class="xhtml keyword">iostream</code><code class="xhtml plain">></code>
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<code class="xhtml plain">#include <</code><code class="xhtml keyword">stack</code><code class="xhtml plain">></code>
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<code class="xhtml plain">#include"stdlib.h"</code>
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<code class="xhtml plain">#include <</code><code class="xhtml keyword">time.h</code><code class="xhtml plain">></code>
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<code class="xhtml plain">using namespace std;</code>
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<code class="xhtml plain">template<</code><code class="xhtml keyword">class</code> <code class="xhtml plain">T></code>
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<code class="xhtml plain">class SORT</code>
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<code class="xhtml plain">{</code>
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<code class="xhtml plain">public:</code>
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<code class="xhtml plain">static void myQsort(T a[], int p, int r);</code>
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<code class="xhtml plain">static void myQsortNoRecur(T a[], int p, int r);</code>
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<code class="xhtml plain">private:</code>
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<code class="xhtml plain">static int partition(T a[], int p, int r);</code>
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<code class="xhtml plain">static void exchange(T a[], int i, int j);</code>
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<code class="xhtml plain">};</code>
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<code class="xhtml plain">template<</code><code class="xhtml keyword">class</code> <code class="xhtml plain">T></code>
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<code class="xhtml plain">void SORT<</code><code class="xhtml keyword">T</code><code class="xhtml plain">>::exchange(T a[], int i, int j)</code>
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<code class="xhtml plain">{</code>
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<code class="xhtml plain">T temp = a;</code>
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<code class="xhtml plain">a = a;</code>
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<code class="xhtml plain">a = temp;</code>
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<code class="xhtml plain">return;</code>
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<code class="xhtml plain">}</code>
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<code class="xhtml plain">template<</code><code class="xhtml keyword">class</code> <code class="xhtml plain">T></code>
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<code class="xhtml plain">int SORT<</code><code class="xhtml keyword">T</code><code class="xhtml plain">>::partition(T a[],int p,int r)</code>
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<code class="xhtml plain">{</code>
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<code class="xhtml plain">int i = p;</code>
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<code class="xhtml plain">int j = p-1;</code>
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<code class="xhtml plain">T ref = a;</code>
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<code class="xhtml plain">int refId = p;</code>
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<code class="xhtml plain">srand((unsigned)time(NULL));</code>
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<code class="xhtml plain">refId = (rand() % (r-p+1))+ p;</code>
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<code class="xhtml plain">//cout<<</code><code class="xhtml keyword">refId</code><code class="xhtml plain"><<endl;</code>
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<code class="xhtml color1">ref</code> <code class="xhtml plain">= </code><code class="xhtml string">a</code><code class="xhtml plain">;</code>
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<code class="xhtml plain">for(; i<=r; i++)</code>
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<code class="xhtml plain">{</code>
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<code class="xhtml plain">if(a < ref)</code>
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<code class="xhtml plain">{</code>
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<code class="xhtml plain">j++;</code>
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<code class="xhtml plain">exchange(a, i, j);</code>
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<code class="xhtml plain">if(j == refId)</code>
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<code class="xhtml plain">{</code>
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<code class="xhtml color1">refId</code> <code class="xhtml plain">= </code><code class="xhtml string">i</code><code class="xhtml plain">;</code>
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<code class="xhtml plain">}</code>
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<code class="xhtml plain">}</code>
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<code class="xhtml plain">}</code>
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<code class="xhtml plain">exchange(a, j+1, refId);</code>
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<code class="xhtml plain">return j+1;</code>
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<code class="xhtml plain">}</code>
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<code class="xhtml plain">template<class T></code>
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<code class="xhtml plain">void SORT<</code><code class="xhtml keyword">T</code><code class="xhtml plain">>::myQsort(T a[],int p,int r)</code>
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<code class="xhtml plain">{</code>
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<code class="xhtml plain">int q = 0;</code>
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<code class="xhtml color1">q</code> <code class="xhtml plain">= </code><code class="xhtml string">partition</code><code class="xhtml plain">(a, p, r);</code>
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<code class="xhtml plain">myQsort(a, p, q-1);</code>
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<code class="xhtml plain">myQsort(a, p+1, r);</code>
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<code class="xhtml plain">return;</code>
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<code class="xhtml plain">template<class T></code>
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<code class="xhtml plain">void SORT<</code><code class="xhtml keyword">T</code><code class="xhtml plain">>::myQsortNoRecur(T a[], int p, int r)</code>
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<code class="xhtml plain">int start = p;</code>
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<code class="xhtml plain">int end = r;</code>
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<code class="xhtml plain">int mid = 0;</code>
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<code class="xhtml plain">std::stack<</code><code class="xhtml keyword">int</code><code class="xhtml plain">> sortStk;</code>
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<code class="xhtml plain">sortStk.push(p);</code>
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<code class="xhtml plain">sortStk.push(r);</code>
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<code class="xhtml plain">while(!sortStk.empty())</code>
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<code class="xhtml plain">{</code>
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<code class="xhtml plain">end = sortStk.top();</code>
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<code class="xhtml plain">sortStk.pop();</code>
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<code class="xhtml plain">start = sortStk.top();</code>
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<code class="xhtml plain">sortStk.pop();</code>
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<code class="xhtml plain">if(start < </code><code class="xhtml keyword">end</code><code class="xhtml plain">)</code>
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<code class="xhtml plain">{</code>
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<code class="xhtml color1">mid</code> <code class="xhtml plain">= </code><code class="xhtml string">partition</code><code class="xhtml plain">(a, start, end);</code>
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<code class="xhtml plain">sortStk.push(start);</code>
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<code class="xhtml plain">sortStk.push(mid -1);</code>
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<code class="xhtml plain">sortStk.push(mid + 1);</code>
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<code class="xhtml plain">sortStk.push(end);</code>
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<code class="xhtml plain">}</code>
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<code class="xhtml plain">}</code>
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<code class="xhtml plain">int main(int argc, char** argv)</code>
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<code class="xhtml plain">int b;</code>
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<code class="xhtml plain">srand((unsigned)time(NULL));</code>
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<code class="xhtml plain">for(int </code><code class="xhtml color1">i</code><code class="xhtml plain">=</code><code class="xhtml string">0</code><code class="xhtml plain">; i<9; i++)</code>
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<code class="xhtml plain">a = rand();</code>
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<code class="xhtml plain">srand((unsigned)time(NULL));</code>
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<code class="xhtml plain">for(int </code><code class="xhtml color1">i</code><code class="xhtml plain">=</code><code class="xhtml string">0</code><code class="xhtml plain">; i<9; i++)</code>
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<code class="xhtml plain">{</code>
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<code class="xhtml plain">b = rand();</code>
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<code class="xhtml plain">}</code>
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<code class="xhtml plain">SORT<int>::myQsort(a,0, 9);</code>
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<code class="xhtml plain">SORT<</code><code class="xhtml keyword">int</code><code class="xhtml plain">>::myQsortNoRecur(b,0, 9);</code>
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<div class="line number109 index108 alt2">
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<div class="line number110 index109 alt1">
<code class="xhtml plain">for(int i=0; i<10; i++)</code>
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<code class="xhtml plain">{</code>
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<div class="line number112 index111 alt1">
<code class="xhtml plain">cout<<a<<" ";</code>
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<code class="xhtml plain">}</code>
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<code class="xhtml plain">cout<<endl;</code>
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<code class="xhtml plain">for(int i=0; i<10; i++)</code>
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<code class="xhtml plain">{</code>
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<code class="xhtml plain">cout<<b<<" ";</code>
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<code class="xhtml plain">}</code>
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<code class="xhtml plain">return 0;</code>
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<div class="line number120 index119 alt1">
<code class="xhtml plain">}</code>
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</div>
</td>
</tr></tbody></table>
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<div class="code_n">
<textarea></textarea>
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<p>
上面的代码我直接给出了快速排序的递归和非递归实现。<br>
递归的实现方式很好理解，但是加入别人正在面试你快速排序算法的时候，多半会让你用非递归的方式实现给他看。下面我们就讨论一下。</p>
<p>
先观察一下递归算法的运行过程，即每次都去对一段更小的范围去调用partition函数。所以我们需要知道每一次调用partition函数的start和end游标，同时，每一次partition调用都会产生新的start和end游标。</p>
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<code class="xhtml plain">template<</code><code class="xhtml keyword">class</code> <code class="xhtml plain">T></code>
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<code class="xhtml plain">void SORT<</code><code class="xhtml keyword">T</code><code class="xhtml plain">>::myQsort(T a[],int p,int r)</code>
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<code class="xhtml plain">{</code>
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<code class="xhtml plain">int q = 0;</code>
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<code class="xhtml plain">if(p<r)</code>
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<code class="xhtml plain">{</code>
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<code class="xhtml plain">q = partition(a, p, r);</code>
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<code class="xhtml plain">myQsort(a, p, q-1);</code>
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<code class="xhtml plain">myQsort(a, p+1, r);</code>
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<code class="xhtml plain">}</code>
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<code class="xhtml plain">return;</code>
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<code class="xhtml plain">}</code>
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<div class="codetool" id="codetool">
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<p>
这样的话，我们就可以用一个通用容器去存放每次调用partition生成的start和end游标。知道虽有的合法的start和end游标都作为参数调用了partition函数。所谓合法的start和end就是start < end。。。。。</p>
<p>
关于递归算法的非递归实现，第一个想到的数据结构肯定是栈。其实别的数据结构，例如队列，也是可以实现。这里给出基于stl内的stack的实现方法。代码如下</p>
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<code class="xhtml plain">template<</code><code class="xhtml keyword">class</code> <code class="xhtml plain">T></code>
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<code class="xhtml plain">void SORT<</code><code class="xhtml keyword">T</code><code class="xhtml plain">>::myQsortNoRecur(T a[], int p, int r)</code>
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<div class="line number3 index2 alt2">
<code class="xhtml plain">{</code>
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<div class="line number4 index3 alt1">
<code class="xhtml plain">int start = p;</code>
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<code class="xhtml plain">int end = r;</code>
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<code class="xhtml plain">int mid = 0;</code>
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<code class="xhtml plain">std::stack<</code><code class="xhtml keyword">int</code><code class="xhtml plain">> sortStk;</code>
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<code class="xhtml plain">sortStk.push(p);</code>
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<code class="xhtml plain">sortStk.push(r);</code>
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<code class="xhtml plain">while(!sortStk.empty())</code>
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<code class="xhtml plain">{</code>
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<code class="xhtml plain">end = sortStk.top();</code>
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<code class="xhtml plain">sortStk.pop();</code>
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<code class="xhtml plain">start = sortStk.top();</code>
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<code class="xhtml plain">sortStk.pop();</code>
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<code class="xhtml plain">if(start < end)</code>
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<code class="xhtml plain">{</code>
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<code class="xhtml plain">mid = partition(a, start, end);</code>
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<code class="xhtml plain">sortStk.push(start);</code>
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<code class="xhtml plain">sortStk.push(mid -1);</code>
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<code class="xhtml plain">sortStk.push(mid + 1);</code>
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<code class="xhtml plain">sortStk.push(end);</code>
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<code class="xhtml plain">}</code>
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<code class="xhtml plain">}</code>
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<code class="xhtml plain">}</code>
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<p>
上面代码的运行过程就是每次循环，从容器内拿一个start和end，如果是合法的，就依次将他们再次放入容易，知道这个容器为空未知。</p>
<p>
给个运行实例吧，我在代码里面实现的是实现随机数排序，ref采用随机选取的方式。</p>
<p>
原文链接：http://www.cnblogs.com/real-madrid/p/7203618.html</p>
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