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📜  排序算法-堆排序

📅  最后修改于: 2020-10-15 01:23:29             🧑  作者: Mango

堆排序

堆排序通过使用给定数组的元素创建最小堆或最大堆来处理元素。最小堆或最大堆表示数组的顺序，其中根元素表示数组的最小或最大元素。在每个步骤中，堆的根元素都将被删除并存储到排序后的数组中，并且堆将再次被堆化。

堆排序基本上以递归方式执行两个主要操作。

  • 使用ARR的元素构建堆H。
  • 重复删除阶段1中形成的堆的根元素。

复杂

Complexity Best Case Average Case Worst case
Time Complexity Ω(n log (n)) θ(n log (n)) O(n log (n))
Space Complexity O(1)

算法

HEAP_SORT(ARR，N)

  • 步骤1 ：[Build H堆]重复i = 0到N-1 CALL INSERT_HEAP(ARR，N，ARR [i])[结束循环]
  • 步骤2 ：重复删除根元素在N> 0时重复CALL Delete_Heap(ARR，N，VAL)SET N = N + 1 [LOOP结束]
  • 步骤3 ：结束

C程序

#include
int temp;

void heapify(int arr[], int size, int i)
{
int largest = i;  
int left = 2*i + 1;  
int right = 2*i + 2;  

if (left < size && arr[left] >arr[largest])
largest = left;

if (right < size && arr[right] > arr[largest])
largest = right;

if (largest != i)
{
temp = arr[i];
    arr[i]= arr[largest]; 
    arr[largest] = temp;
heapify(arr, size, largest);
}
}

void heapSort(int arr[], int size)
{
int i;
for (i = size / 2 - 1; i >= 0; i--)
heapify(arr, size, i);
for (i=size-1; i>=0; i--)
{
temp = arr[0];
    arr[0]= arr[i]; 
    arr[i] = temp;
heapify(arr, i, 0);
}
}

void main()
{
int arr[] = {1, 10, 2, 3, 4, 1, 2, 100,23, 2};
int i;
int size = sizeof(arr)/sizeof(arr[0]);

heapSort(arr, size);

printf("printing sorted elements\n");
for (i=0; i

输出：

printing sorted elements 

1
1
2
2
2
3
4
10
23
100

Java程序

#include
int temp;

void heapify(int arr[], int size, int i)
{
int largest = i;  
int left = 2*i + 1;  
int right = 2*i + 2;  

if (left < size && arr[left] >arr[largest])
largest = left;

if (right < size && arr[right] > arr[largest])
largest = right;

if (largest != i)
{
temp = arr[i];
    arr[i]= arr[largest]; 
    arr[largest] = temp;
heapify(arr, size, largest);
}
}

void heapSort(int arr[], int size)
{
int i;
for (i = size / 2 - 1; i >= 0; i--)
heapify(arr, size, i);
for (i=size-1; i>=0; i--)
{
temp = arr[0];
    arr[0]= arr[i]; 
    arr[i] = temp;
heapify(arr, i, 0);
}
}

void main()
{
int arr[] = {1, 10, 2, 3, 4, 1, 2, 100, 23, 2};
int i;
int size = sizeof(arr)/sizeof(arr[0]);

heapSort(arr, size);

printf("printing sorted elements\n");
for (i=0; i

输出：

printing sorted elements 

1
1
2
2
2
3
4
10
23
100

C＃程序

using System;
public class HeapSorting {
static void heapify(int[] arr, int size, int i)
{
int largest = i;  
int left = 2*i + 1;  
int right = 2*i + 2;  
int temp;
if (left < size && arr[left] > arr[largest])
largest = left;

if (right < size && arr[right] > arr[largest])
largest = right;

if (largest != i)
{
temp = arr[i];
    arr[i]= arr[largest]; 
    arr[largest] = temp;
heapify(arr, size, largest);
}
}

static void heapSort(int[] arr, int size)
{
int i;
int temp;
for (i = size / 2 - 1; i >= 0; i--)
heapify(arr, size, i);
for (i=size-1; i>=0; i--)
{
temp = arr[0];
    arr[0]= arr[i]; 
    arr[i] = temp;
heapify(arr, i, 0);
}
}

public void Main()
{
int[] arr = {1, 10, 2, 3, 4, 1, 2, 100, 23, 2};
int i;
heapSort(arr, 10); 
Console.WriteLine("printing sorted elements");
for (i=0; i<10; ++i)
Console.WriteLine(arr[i]);
}
}

输出：

printing sorted elements 

1
1
2
2
2
3
4
10
23
100