堆排序【代码】

  1 // Heapsort.cpp: 定义控制台应用程序的入口点。
  2 //
  3 
  4 
  5 #include "stdafx.h"
  6 #include <iostream>
  7 
  8 using namespace std;
  9 
 10 int PARENT(int i)
 11 {
 12     return (i - 1) / 2;
 13 }
 14 
 15 int LEFT(int i)
 16 {
 17     return 2 * i + 1;
 18 }
 19 
 20 int RIGHT(int i)
 21 {
 22     return 2 * i + 2;
 23 }
 24 //维护最大堆，时间复杂度为O(lgn)
 25 int MAX_HEAPIFY(int *A,int i,int len)
 26 {
 27     int l, r, largest;//l为左孩子的下标，r为右孩子的下标，largest为三者中最大数的下标
 28     int temp;
 29     l = LEFT(i);
 30     r = RIGHT(i);
 31     if (l < len && A[l] > A[i])
 32         largest = l;
 33     else
 34         largest = i;
 35 
 36     if (r < len && A[r] > A[largest])
 37         largest = r;
 38     
 39     if (largest != i)
 40     {
 41         temp = A[i];
 42         A[i] = A[largest];
 43         A[largest] = temp;
 44         MAX_HEAPIFY(A, largest, len);
 45     }
 46     else
 47     {
 48         if (l >= len && r >= len)//到达了叶节点，停止递归
 49         {
 50             return 0;
 51         }
 52         MAX_HEAPIFY(A, l, len);
 53         MAX_HEAPIFY(A, r, len);
 54     }    
 55 }
 56 
 57 //从无序的输入数据数组中构造一个最大堆，时间复杂度为O(n)
 58 int BUILD_MAX_HEAP(int *A,int len)
 59 {
 60     int start = PARENT(len);
 61     for (int i = start; i >= 0; i--)
 62     {
 63         MAX_HEAPIFY(A, i, len);
 64     }
 65     return 0;
 66 }
 67 
 68 int HEAPSORT(int *A,int len)
 69 {
 70     int length = len;
 71     int *res = new int[len]{0};//记录排完序后的结果
 72     int ptr = len - 1;
 73     BUILD_MAX_HEAP(A, len);
 74 
 75     for (int i = 0; i < length; i++)
 76         cout << A[i] << ends;
 77     cout << endl << endl;
 78 
 79     for (int i = length; i >= 1; i--)
 80     {
 81         res[ptr--] = A[0];
 82         A[0] = A[len-1];
 83         len--;
 84         int *A_temp = new int[len];
 85         for (int i = 0; i < len; i++)//把删掉最后一个元素后的数组A复制到A_temp中
 86         {
 87             A_temp[i] = A[i];
 88         }
 89         MAX_HEAPIFY(A_temp, 0, len);//对A_temp重新维持为最大堆
 90         for (int i = 0; i < len; i++)//把A_temp的值复制给A
 91         {
 92             A[i] = A_temp[i];
 93         }
 94 
 95         for (int i = 0; i < len; i++)
 96             cout << A[i] << ends;
 97         cout << endl;
 98         delete A_temp;
 99     }
100 
101     cout << "排序后的数组为（升序）：" << endl;
102     for (int i = 0; i < length; i++)
103         cout << res[i] << ends;
104     cout << endl;
105     return 0;
106 }
107 
108 int main()
109 {
110     int A[] = {16,4,10,14,7,9,3,2,8,1};
111     cout << "排序前的数组为：" << endl;
112     for (auto c : A)
113         cout << c << ends;
114     cout << endl;
115     /*BUILD_MAX_HEAP(A,10);
116     for (auto c : A)
117         cout << c << ends;
118     cout << endl;*/
119     HEAPSORT(A,10);
120     return 0;
121 }