一、快速排序递归法

1.快速排序思想

2.hoare版本实现快速排序

//快速排序
void QuickSort(int* a, int left, int right)
{
	if (left >= right)
	{
		return;
	}
	int begin = left;
	int end = right;
	int keyi = left;
	while (left < right)
	{
		//右边找小
		while (left < right && a[right] >= a[keyi])
		{
			right--;
		}
		//左边找大
		while (left < right && a[left] <= a[keyi])
		{
			left++;
		}
		Swap(&a[left], &a[right]);
	}
	Swap(&a[keyi], &a[left]);
	QuickSort(a, begin, left - 1);
	QuickSort(a, left + 1, end);

}

3.hoare版本的优化

1>使用随机值rand()函数

//快速排序
void QuickSort1(int* a, int left, int right)
{
	if (left >= right)
	{
		return;
	}
	int begin = left;
	int end = right;
	int keyi = left;
	int randi = left + rand() % (right - left);
	Swap(&a[randi], &a[left]);
	while (left < right)
	{
		//右边找小
		while (left < right && a[right] >= a[keyi])
		{
			right--;
		}
		//左边找大
		while (left < right && a[left] <= a[keyi])
		{
			left++;
		}
		Swap(&a[left], &a[right]);
	}
	Swap(&a[keyi], &a[left]);
	QuickSort1(a, begin, left - 1);
	QuickSort1(a, left + 1, end);

}

2>三数取中

int GetMidNumi(int* a, int left, int right)
{
	int mid = (left + right) / 2;
	if (a[left] < a[mid])
	{
		if (a[mid] < a[right])
		{
			return mid;
		}
		else if (a[left] < a[right])
		{
			return right;
		}
		else
		{
			return left;
		}
	}
	else
	{
		if (a[left] < a[right])
		{
			return left;
		}
		else if (a[mid] < a[right])
		{
			return right;
		}
		else
		{
			return mid;
		}
	}
}
//快速排序：三数取中
void QuickSort2(int* a, int left, int right)
{
	if (left >= right)
	{
		return;
	}
	int begin = left;
	int end = right;
	int keyi = left;
	
	int midi = GetMidNumi(a, left, right);
	Swap(&a[midi], &a[left]);
	while (left < right)
	{
		//右边找小
		while (left < right && a[right] >= a[keyi])
		{
			right--;
		}
		//左边找大
		while (left < right && a[left] <= a[keyi])
		{
			left++;
		}
		Swap(&a[left], &a[right]);
	}
	Swap(&a[keyi], &a[left]);
	QuickSort2(a, begin, left - 1);
	QuickSort2(a, left + 1, end);
}

3>三路划分

4.证明hoare版本的key在左边，必须让右边先走

5.挖坑法实现快速排序

//快速排序：挖坑法
void QuickSort3(int* a, int left, int right)
{
	if (left >= right)
	{
		return;
	}
	int begin = left;
	int end = right;
	int hole = left;

	int midi = GetMidNumi(a, left, right);
	Swap(&a[midi], &a[left]);
	int key = a[left];
	while (left < right)
	{
		//右边找小
		while (left < right && a[right] >= key)
		{
			right--;
		}
		a[hole] = a[right];
		hole = right;
		//左边找大
		while (left < right && a[left] <= key)
		{
			left++;
		}
		a[hole] = a[left];
		hole = left;
	}
	a[hole] = key;
	QuickSort3(a, begin, hole - 1);
	QuickSort3(a, hole + 1, end);
}

6.将前面快排的一趟排序给提取出来

int PartSort1(int* a, int left, int right)
{
	int keyi = left;
	int midi = GetMidNumi(a, left, right);
	Swap(&a[midi], &a[left]);
	while (left < right)
	{
		//右边找小
		while (left < right && a[right] >= a[keyi])
		{
			right--;
		}
		//左边找大
		while (left < right && a[left] <= a[keyi])
		{
			left++;
		}
		Swap(&a[left], &a[right]);
	}
	Swap(&a[keyi], &a[left]);
	return left;
}
int PartSort2(int* a, int left, int right)
{
	int hole = left;
	int midi = GetMidNumi(a, left, right);
	Swap(&a[midi], &a[left]);
	int key = a[left];
	while (left < right)
	{
		//右边找小
		while (left < right && a[right] >= key)
		{
			right--;
		}
		a[hole] = a[right];
		hole = right;
		//左边找大
		while (left < right && a[left] <= key)
		{
			left++;
		}
		a[hole] = a[left];
		hole = left;
	}
	a[hole] = key;
	return hole;
}
//快速排序
void QuickSort(int* a, int left, int right)
{
	if (left >= right)
	{
		return;
	}
	int keyi = PartSort2(a, left, right);
	QuickSort(a, left, keyi - 1);
	QuickSort(a, keyi + 1, right);
}

7.双指针法实现快速排序

int PartSort3(int* a, int left, int right)
{
	int midi = GetMidNumi(a, left, right);
	Swap(&a[midi], &a[left]);
	int prev = left;
	int cur = left + 1;
	int key = a[left];
	while (cur <= right)
	{
		if (a[cur] > key)
		{
			cur++;
		}
		else
		{
			prev++;
			Swap(&a[prev], &a[cur]);
			cur++;
		}
	}
	Swap(&a[prev], &a[left]);
	return prev;
}
//快速排序
void QuickSort(int* a, int left, int right)
{
	if (left >= right)
	{
		return;
	}
	int keyi = PartSort3(a, left, right);
	QuickSort(a, left, keyi - 1);
	QuickSort(a, keyi + 1, right);
}

int PartSort3(int* a, int left, int right)
{
	int midi = GetMidNumi(a, left, right);
	Swap(&a[midi], &a[left]);
	int prev = left;
	int cur = left + 1;
	int key = a[left];
	while (cur <= right)
	{
		if (a[cur] < key && ++prev != cur)
			Swap(&a[cur], &a[prev]);
		cur++;
	}
	Swap(&a[prev], &a[left]);
	return prev;
}
//快速排序
void QuickSort(int* a, int left, int right)
{
	if (left >= right)
	{
		return;
	}
	int keyi = PartSort3(a, left, right);
	QuickSort(a, left, keyi - 1);
	QuickSort(a, keyi + 1, right);
}

8.快速排序小区间优化

//快速排序
void QuickSort(int* a, int left, int right)
{
	if (left >= right)
	{
		return;
	}
	if ((right - left + 1) > 10)
	{
		int keyi = PartSort3(a, left, right);
		QuickSort(a, left, keyi - 1);
		QuickSort(a, keyi + 1, right);
	}
	else
	{
		InsertSort(a + left, right - left + 1);
	}
}

二、快速排序非递归

//快速排序非递归
void QuickSortNonR(int* a, int left, int right)
{
	if (left >= right)
	{
		return;
	}
	Stack st;
	StackInit(&st);
	StackPush(&st, right);
	StackPush(&st, left);

	while (!StackEmpty(&st))
	{
		int begin = StackTop(&st);
		StackPop(&st);
		int end = StackTop(&st);
		StackPop(&st);
		int keyi = PartSort3(a, begin, end);

		
		// [begin,keyi-1] keyi [keyi+1,end]
		if (keyi + 1 < end)
		{
			StackPush(&st, end);
			StackPush(&st, keyi + 1);
		}
		if (begin < keyi - 1)
		{
			StackPush(&st, keyi - 1);
			StackPush(&st, begin);
		}
	}
	StackDestroy(&st);
}