本文详细介绍了多种排序算法，包括冒泡排序、选择排序、快速排序等，并对比了它们的稳定性、时间复杂度及辅助空间需求。提供了C#实现代码示例。
排序大全
1.稳定性比较
插入排序、冒泡排序、二叉树排序、归并排序及其他线形排序是稳定的
选择排序、希尔排序、快速排序、堆排序是不稳定的
2.时间复杂性比较
插入排序、冒泡排序、选择排序的时间复杂性为O(n2)
其它非线形排序的时间复杂性为O(nlog2n)
线形排序的时间复杂性为O(n);
3.辅助空间的比较
归并排序的辅助空间为O(n),其它排序的辅助空间为O(1);
4. C# Codes
4.1 冒泡排序
class Program
{
static void Main(string[] args)
{
int[] array = new int[] { 6, 6, 5, 4, 3, 2, 1, 0 };
array = Sort(array);
foreach (var item in array)
{
Console.WriteLine(item.ToString());
}
Console.ReadKey();
}
static int[] Sort(int[] array)
{
for (int i = 0; i < array.Length; i++)
{
for (int j = 0; j < array.Length - i -1; j++)
{
if (array[j+1] < array[j])
{
Swap(array, j, j+1);
}
}
}
return array;
}
static void Swap(int[] array, int firstIndex, int secondIndex)
{
int preserve = array[firstIndex];
array[firstIndex] = array[secondIndex];
array[secondIndex] = preserve;
}
}
4.2 简单选择排序
class Program
{
static void Main(string[] args)
{
int[] array = new int[] { 6, 6, 5, 4, 3, 2, 1, 0 };
array = SelectSort(array);
foreach (var item in array)
{
Console.WriteLine(item.ToString());
}
Console.ReadKey();
}
static int[] SelectSort(int[] array)
{
for (int i = 0; i < array.Length; i++)
{
for (int j = i; j < array.Length; j++)
{
if (array[j] < array[i])
{
Swap(array, j, i);
}
}
}
return array;
}
static void Swap(int[] array, int firstIndex, int secondIndex)
{
int preserve = array[firstIndex];
array[firstIndex] = array[secondIndex];
array[secondIndex] = preserve;
}
}
4.3 快速排序
class Program
{
static void Main(string[] args)
{
int[] array = new int[] { 6, 6, 5, 4, 3, 2, 1, 0 };
array = QuickSort(array, 0, array.Length - 1);
foreach (var item in array)
{
Console.WriteLine(item.ToString());
}
Console.ReadKey();
}
static int[] QuickSort(int[] array,int start, int end)
{
int low = start;
int high = end;
int mark = start;
while (low < high)
{
while (low < mark)
{
if (array[low] > array[mark])
{
Swap(array, low, mark);
mark = low;
continue;
}
else
low++;
}
while (mark < high)
{
if (array[mark] > array[high])
{
Swap(array, high, mark);
mark = high;
continue;
}
else
high--;
}
}
if (mark - start > 1)
{
QuickSort(array, start, mark-1);
}
if (end - mark > 1)
{
QuickSort(array, mark+1, end);
}
return array;
}
static void Swap(int[] array, int firstIndex, int secondIndex)
{
int preserve = array[firstIndex];
array[firstIndex] = array[secondIndex];
array[secondIndex] = preserve;
}
}
4.4 堆排序
class Program
{
static void Main(string[] args)
{
int[] array = new int[] {5,6,7,8,2,3,4,6,5,4,3,2 };
array = HeapSort(array);
foreach (var item in array)
{
Console.WriteLine(item.ToString());
}
Console.ReadKey();
}
public static void CreateHeap(int[] array, int lastIndex)
{
for (int i = lastIndex; i > 0; i--)
{
if (array[i] > array[i / 2])
{
Swap(array, i, i / 2);
}
}
}
public static int[] HeapSort(int[] array)
{
for (int i = array.Length - 1; i > 0; i--)
{
CreateHeap(array, i);
Swap(array, 0, i);
}
return array;
}
static void Swap(int[] array, int firstIndex, int secondIndex)
{
int preserve = array[firstIndex];
array[firstIndex] = array[secondIndex];
array[secondIndex] = preserve;
}
}
4.5 二分插入排序
class Program
{
static void Main(string[] args)
{
int[] array = new int[] { 3,2,1,4,5,67,678678,234234,2,3,4,5,6,7,8,4 };
array = HalfInsertSort(array);
foreach (var item in array)
{
Console.WriteLine(item.ToString());
}
Console.ReadKey();
}
public static int[] HalfInsertSort(int[] array)
{
for (int i = 0; i < array.Length; i++)
{
int start = 0;
int end = i - 1;
while (start <= end)
{
int middle = (start + end) / 2;
if (array[middle] <= array[i])
start = middle + 1;
else
end = middle - 1;
}
int insertValue = array[i];
for (int j = i; j > start; j--)
{
array[j] = array[j - 1];
}
array[start] = insertValue;
}
return array;
}
}
4.6 直接插入排序
class Program
{
static void Main(string[] args)
{
int[] array = new int[] { 6, 6, 5, 4, 3, 2, 1, 0 };
array = InsertSort(array);
foreach (var item in array)
{
Console.WriteLine(item.ToString());
}
Console.ReadKey();
}
static int[] InsertSort(int[] array)
{
for (int i = 0; i < array.Length; i++)
{
for (int j = 0; j < i; j++)
{
if (array[j] > array[i])
{
Swap(array, j, i);
}
}
}
return array;
}
static void Swap(int[] array, int firstIndex, int secondIndex)
{
int preserve = array[firstIndex];
array[firstIndex] = array[secondIndex];
array[secondIndex] = preserve;
}
}
4.7 归并排序
class Program
{
static void Main(string[] args)
{
int[] array = new int[] {1,1,2,2,2,2,3,3,2,2,2,22222222,1,1,1,1,1,1,1,1,0,0,0,0,7};
array = MergeSort(array, 0, array.Length - 1);
foreach (var item in array)
{
Console.WriteLine(item.ToString());
}
Console.ReadKey();
}
public static int[] MergeSort(int[] array, int start, int end)
{
int middle = start;
if (start < end)
{
middle = (start + end) / 2;
MergeSort(array, start, middle);
MergeSort(array, middle + 1, end);
Merge(array, start, end);
}
return array;
}
public static void Merge(int[] array, int start, int end)
{
int middle = (start + end) / 2;
Queue<int> container = new Queue<int>();
int first = start;
int second = middle + 1;
while (first <= middle && second <= end)
{
if (array[first] < array[second])
{
container.Enqueue(array[first++]);
}
else
{
container.Enqueue(array[second++]);
}
}
while (first <= middle)
{
container.Enqueue(array[first++]);
}
while (second <= end)
{
container.Enqueue(array[second++]);
}
for (int i = start; i <= end; i++)
{
array[i] = container.Dequeue();
}
}
}
4.8 希尔排序
class Program
{
static void Main(string[] args)
{
int[] array = new int[] { 3,2,1,4,5,67,678678,234234,31231,1,3,3,3,3,3,3,3,3,2,2,2,1,1,1,1,1,1,12,3,3,3,3,32,3,4,5,6,7,8,4 };
foreach (var item in ShellSort(array))
{
Console.WriteLine(item.ToString());
}
Console.ReadKey();
}
public static int[] ShellSort(int[] array)
{
int point = array.Length / 2;
while (point > 0)
{
for (int i = 0; i < point; i ++)
{
for (int j = i; j < array.Length; j += point)
{
for (int k = i; k < j; k += point)
{
if (array[k] > array[j])
{
int insertValue=array[j];
for (int t = j; t > k; t -= point)
{
array[t] = array[t - point];
}
array[k] = insertValue;
}
continue;
}
}
}
point = point / 2;
}
return array;
}
}
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