快速排序 （C语言）

快速排序是Hoare于1962年提出的一种二叉树的交换排序方法。其基本思想为：任取待排序元素序列中的某元素为基准值，按照该排序码将待排序集合分割成两个子序列，左子序列中所有元素均小于基准值，右子序列元素均大于基准值，然后最左右子序列重复该过程，直到所有元素都排列在相应位置上为止。

快速排序是一种不稳定的排序，其时间复杂度为o(nlogn)，空间复杂度为o(logn)

1.hoare版本

//hoare版本
int partition_1(int* ar, int left, int right)
{
	int low = left;
	int high = right - 1;
	int key = ar[low];
	while (low < high)
	{
		while (lowkey)
			high--;
		Swap(&ar[low], &ar[high]);
		while (low < high && ar[low] <= key)
			low++;
		Swap(&ar[low], &ar[high]);
	}
	return low;
}

void QuickSort_1(int* ar, int left, int right)
{
	if (left >= right)
		return;
	int pos = partition_1(ar, left, right);
	QuickSort_1(ar, left, pos);
	QuickSort_1(ar, pos + 1, right);

}

2.挖坑法

//挖坑法
int partition_2(int* ar, int left, int right)
{
	int low = left;
	int high = right - 1;
	int key = ar[low];
	while (low < high)
	{
		while (lowkey)
			high--;
		ar[low] = ar[high];
		while (low < high && ar[low] <= key)
			low++;
		ar[high] = ar[low];
	}
	ar[low] = key;
	return low;
}

void QuickSort_2(int* ar, int left, int right)
{
	if (left >= right)
		return;
	int pos = partition_2(ar, left, right);
	QuickSort_2(ar, left, pos);
	QuickSort_2(ar, pos + 1, right);

}

3.前后指针法

//前后指针法
int partition_3(int* ar, int left, int right)
{
	int key = ar[left];
	int next = left;
	for (int prev = next + 1; prev < right; prev++)
	{
		if (ar[prev] < key)
		{
			next++;
			if (next != prev)
			{
				Swap(&ar[next], &ar[prev]);
			}
		}
	}
	Swap(&ar[left], &ar[next]);
	return next;
}

void QuickSort_3(int* ar, int left, int right)
{
	if (left >= right)
		return;
	int pos = partition_3(ar, left, right);
	QuickSort_3(ar, left, pos);
	QuickSort_3(ar, pos + 1, right);

}

4.三者取中法

//三者取中法
int GetMinIndex(int* ar, int left, int right)
{
	int mid = (left + right - 1) / 2;
	if (ar[left] < ar[mid] && ar[mid] < ar[right - 1])
		return mid;
	if (ar[left] > ar[mid] && ar[left] < ar[right - 1])
		return left;
	return right - 1;
}

int partition_4(int* ar, int left, int right)
{
	int min_index = GetMinIndex(ar, left, right);
	if (min_index != left)
		Swap(&ar[left], &ar[min_index]);
	int key = ar[left];
	int next = left;
	for (int prev = next + 1; prev < right; prev++)
	{
		if (ar[prev] < key)
		{
			next++;
			if (next != prev)
			{
				Swap(&ar[next], &ar[prev]);
			}
		}
	}
	Swap(&ar[left], &ar[next]);
	return next;
}
#define M 20
void QuickSort_4(int* ar, int left, int right)
{
	if (left >= right)
		return;
	if (right - left <= M)
		InsertSort(ar, left, right);
	else
	{
		int pos = partition_4(ar, left, right);
		QuickSort_4(ar, left, pos);
		QuickSort_4(ar, pos + 1, right);
	}
}