[置顶] AVL树及C实现代码

一、图解旋转（理清旋转方向、旋转点、旋转轴，而旋转点才是理解旋转的关键，旋转轴可以辅助理解）。

【LL型，右顺旋转A，旋转轴是A-B】

【RR型，左逆旋转A，旋转轴是A-B】

【LR型，先左逆旋转B，旋转轴是BC, 再右顺旋转A，旋转轴是A-C】

【RL型，先右顺旋转B，旋转轴是B-C，再左逆旋转A，旋转轴是AC】

二、C实现代码

void R_Rotate(BSTree *T)
{
	BSTree lc;

	lc = (*T)->lchild;
	(*T)->lchild = lc->rchild;
	lc->rchild = (*T);
	(*T) = lc;

	return;
}

void L_Rotate(BSTree *T)
{
	BSTree rc;

	rc = (*T)->rchild;
	(*T)->rchild = rc->lchild;
	rc->lchild = (*T);
	(*T) = rc;

	return;
}	

void LeftBalance(BSTree *T) 
{
	BSTree lc;
	BSTree rd;

	lc = (*T)->lchild;	
	switch (lc->bf)
	{
		case 1:
			(*T)->bf = lc->bf = 0;
			R_Rotate(T);
			break;
		case -1:
			rd	= lc->rchild;
			switch (rd->bf)
			{
				case 1:
					lc->bf = 0;	
					(*T)->bf = -1;
					break;
				case 0: /* 此处比较特殊，如果ABC构成LR图形，A没有右子树，就会造成这里rd的平衡因子为0的情况，RightBalance类似 */
					lc->bf = (*T)->bf = 0;
					break;
				case -1:
					lc->bf = 1;
					(*T)->bf = 0;
					break;
				default:
					break;
			}

			rd->bf = 0;

			L_Rotate(&lc);
			R_Rotate(T);
		default:
			break;
	}
	
}

void RightBalance(BSTree *T)
{
	BSTree rc;
	BSTree ld;

	rc = (*T)->rchild;
	switch (rc->bf)
	{
		case -1:
			(*T)->bf = rc->bf = 0;
			L_Rotate(T);
			break;
		case 1:
			ld = rc->lchild;
			switch (ld->bf)
			{
				case 1:
					rc->bf = -1;
					(*T)->bf = 0;
					break;
				case 0:
					rc->bf = (*T)->bf = 0;
					break;
				case -1:
					rc->bf = 0;
					(*T)->bf = 1;
					break;
				default:
					break;
			}	

			ld->bf = 0;

			R_Rotate(&rc);
			L_Rotate(T);
		default:
			break;
	}
}


Status InsertAVL(BSTree *T, ElemType e, Boolean *taller)
{
	if (!*T)	
	{
		(*T) = (BSTree)malloc(sizeof(BSTNode));
		if (!(*T))
		{
			printf("%s: malloc fail\n", __FUNCTION__);
			return ERROR;
		}

		(*T)->data = e;
		(*T)->lchild = (*T)->rchild = NULL;
		(*T)->bf = 0;
		*taller = TRUE;
	}
	else
	{
		if (e == (*T)->data)
		{
			printf("%s: AVL exits the node with key=%d\n", __FUNCTION__, e);
			return FAIL;
		}
		else if (e < (*T)->data)
		{
			if (SUCCESS != InsertAVL(&(*T)->lchild, e, taller))	
			{
				return FAIL;
			}

			if (*taller) /* 此处和上个if不是if else关系 */	
			{
				switch ((*T)->bf)	
				{
					case 1:
						LeftBalance(T);
						*taller = FALSE;
						break;
					case 0:
						(*T)->bf = 1;
						*taller = TRUE;
						break;
					case -1:
						(*T)->bf = 0;
						*taller = FALSE;
						break;
					default:
						break;
				}
			}
		}
		else
		{
			if (SUCCESS != InsertAVL(&(*T)->rchild, e, taller))	
			{
				return FAIL;
			}

			if (*taller)	
			{
				switch ((*T)->bf)	
				{
					case -1:
						RightBalance(T);
						*taller = FALSE;
						break;
					case 0:
						(*T)->bf = -1;
						*taller = TRUE;
						break;
					case 1:
						(*T)->bf = 0;
						*taller = FALSE;
						break;
					default:
						break;
				}
			}
			
		}
	}

	return SUCCESS; /* 一定要有返回值 */
}