二叉树的旋转操作

二叉树的旋转操作是针对AVL平衡二叉树或RBT红黑树而言的，为了优化查找，当发现树不平衡时，使用旋转操作。旋转方式分为3类：

• 左旋
• 右旋
• 双旋转：对于不平衡情况LR , 下方先左旋然后整体右旋；不平衡情况RL类似。

代码如下：

#include <stdlib.h>
#include <stdio.h>

typedef struct tree
{
	int nValue;
	struct tree *pLeft;
	struct tree *pRight;
	struct tree *pFat;
}BinaryTree;

BinaryTree *CreateBinaryTree()
{
	BinaryTree *pRoot = NULL;
	pRoot = (BinaryTree*)malloc(sizeof(BinaryTree));
	pRoot->nValue = 10;
	pRoot->pFat = NULL;

	pRoot->pLeft = (BinaryTree*)malloc(sizeof(BinaryTree));
	pRoot->pLeft->nValue = 5;
	pRoot->pLeft->pFat = pRoot;
	
	pRoot->pLeft->pLeft = (BinaryTree*)malloc(sizeof(BinaryTree));
	pRoot->pLeft->pLeft->nValue = 4;
	pRoot->pLeft->pLeft->pRight = NULL;
	pRoot->pLeft->pLeft->pFat = pRoot->pLeft;

	pRoot->pLeft->pLeft->pLeft = (BinaryTree*)malloc(sizeof(BinaryTree));
	pRoot->pLeft->pLeft->pLeft->nValue = 1;
	pRoot->pLeft->pLeft->pLeft->pLeft = NULL;
	pRoot->pLeft->pLeft->pLeft->pRight = NULL;
	pRoot->pLeft->pLeft->pLeft->pFat = pRoot->pLeft->pLeft;


	pRoot->pLeft->pRight = (BinaryTree*)malloc(sizeof(BinaryTree));
	pRoot->pLeft->pRight->nValue = 7;
	pRoot->pLeft->pRight->pLeft = NULL;
	pRoot->pLeft->pRight->pRight = NULL;
	pRoot->pLeft->pRight->pFat = pRoot->pLeft;

	pRoot->pRight = (BinaryTree*)malloc(sizeof(BinaryTree));
	pRoot->pRight->nValue = 19;
	pRoot->pRight->pLeft = NULL;
	pRoot->pRight->pRight = NULL;
	pRoot->pRight->pFat = pRoot;

	return pRoot;
}

void PreOrderTraversal(BinaryTree *pRoot)
{
	//前序
	if(pRoot == NULL) return;
	printf("%d ", pRoot->nValue);
	PreOrderTraversal(pRoot->pLeft);
	PreOrderTraversal(pRoot->pRight);
}
//旋转操作实质：至多改变4个节点3对父子关系
//右旋
void RightRotate(BinaryTree **pTree)
{
	if(*pTree == NULL || (*pTree)->pLeft == NULL) return;
	BinaryTree *pNode = (*pTree); // A
	BinaryTree *pMark = (*pTree)->pLeft; //B
	pNode->pLeft = pMark->pRight;
	pMark->pRight = pNode;

	if(pNode->pFat != NULL)
	{
		if(pNode->pFat->pLeft == pNode)
		{
			pNode->pFat->pLeft = pMark;
		}
		else
		{
			pNode->pFat->pRight = pMark;
		}
		
	}
	else
	{
		(*pTree) = pMark;
	}
	if(pNode->pLeft != NULL) //E
	{
		pNode->pLeft->pFat = pNode;
	}
	pMark->pFat = pNode->pFat;
	pNode->pFat = pMark;
}
//左旋
void LeftRotate(BinaryTree **pTree)
{
	if(*pTree == NULL || (*pTree)->pRight == NULL) return;
	BinaryTree *pNode = (*pTree); // A
	BinaryTree *pMark = (*pTree)->pRight; //B
	pNode->pRight = pMark->pLeft;
	pMark->pLeft = pNode;

	if(pNode->pFat != NULL)
	{
		if(pNode->pFat->pLeft == pNode)
		{
			pNode->pFat->pLeft = pMark;
		}
		else
		{
			pNode->pFat->pRight = pMark;
		}
		
	}
	else
	{
		(*pTree) = pMark;
	}
	if(pNode->pRight != NULL) //E
	{
		pNode->pRight->pFat = pNode;
	}
	pMark->pFat = pNode->pFat;
	pNode->pFat = pMark;
}

int main()
{
	BinaryTree *pRoot = NULL;
	pRoot = CreateBinaryTree();
	PreOrderTraversal(pRoot);
	printf("\n");
	RightRotate(&pRoot);
	PreOrderTraversal(pRoot);
	printf("\n");
	LeftRotate(&pRoot);
	PreOrderTraversal(pRoot);
	printf("\n");
	return 0;
}