堆排序

说白了，也就是大堆，或者小堆，通过删掉堆顶点，然后存入数组，来实现排序：

第一阶段：构建堆最多用2N次比较

第二阶段：第i次deleteMax最多用到2【logi】次比较，

总数最多2NlogN-O(N)次比较

代码：

 1 #include <iostream>
 2 #include <vector>
 3 using namespace std;
 4 template <typename Comparable>
 5 void heapsort(vector<Comparable> & a)
 6 {
 7     for(int i = a.size()/2; i>= 0 ;i--)
 8         percDown(a,i,a.size());
 9     for(int j=a.size()-1; j>0 ; j--)
10     {
11         swap(a[0],a[j]);
12         percDown(a,0,j);
13     }
14 }    
15 inline int leftChild(int i )
16 {
17     return 2*i;
18 }
19 template <typename Comparable>
20 void percDown(vector<Comparable> & a,int i,int n)
21 {
22     int child;
23     Comparable tmp;
24 
25     for(tmp = a[i] ; leftChild(i)<n ; i=child)
26     {
27         child = leftChild(i);
28         if(child != n-1 && a[child] < a[child+1])
29             child++;
30         if(tmp<a[child])
31             a[i]=a[child];
32         else
33             break;
34     }
35     a[i]=tmp;
36 }
37 int main()
38 {
39     vector<int> ivec;
40     ivec.push_back(1);
41     ivec.push_back(9);
42     ivec.push_back(2);
43     ivec.push_back(10);
44     ivec.push_back(3);
45     ivec.push_back(11);
46     ivec.push_back(4);
47     ivec.push_back(12);
48     ivec.push_back(5);
49     ivec.push_back(13);
50     ivec.push_back(6);
51     ivec.push_back(14);
52     ivec.push_back(7);
53     ivec.push_back(15);
54     ivec.push_back(8);
55     ivec.push_back(16);
56     heapsort(ivec);
57     for(int i =0;i<ivec.size();i++)
58         cout<<ivec[i]<<endl;
59     return 0;
60 }

结果如下：