AVLTree AVL_Insertion(ElementType x, AVLTree T)
{
if(!T)
{
T = (AVLTree)malloc(sizeof(AVLTreeNode));
T->Data = x;
T->Height = 0;
T->Left = T->Right = NULL;
}
else if(x < T->Data)
{
T->Left = AVL_Insertion(x, T->Left);
if(GetHeight(T->Left) - GetHeight(T->Right) == 2)
{
if(x < T->Left->Data)
T = SingleLeftRotation(T);
else
T = DoubleLeftRightRotation(T);
}
}
else if(x > T->Data)
{
T->Right = AVL_Insertion(x, T->Right);
if(GetHeight(T->Right) - GetHeight(T->Left) == 2)
{
if(x > T->Right->Data)
T = SingRightRotation(T);
else
T = DoubleRightLeftRotation(T);
}
}
T->Height = Max(GetHeight(T->Left), GetHeight(T->Right)) + 1;
return T;
}
avltree insert(int data, avltree T){
if(!T){
T=(avltree)malloc(sizeof(struct avltreeNode));
T->data=data;
T->height=0;
T->left=T->right=NULL;
// printf("%d\n",T->data);
}
else if(data < T->data){
T->left=insert(data,T->left);
if(GetHeight(T->left)-GetHeight(T->right)==2)
if(data < T->left->data)
T=SingleLeftRotation(T);
else
T=DoubleLeftRightRotation(T);
// printf("%d\n",T->data);
}
else if(data > T->data){
T->right=insert(data,T->right);
if(GetHeight(T->left)-GetHeight(T->right)==-2)
if(data > T->right->data)
T=SingleRightRotation(T);
else
T=DoubleRightLeftRotation(T);
// printf("%d\n",T->data);
}
T->height=Max(GetHeight(T->left),GetHeight(T->right))+1;
// printf("height:%d\n",T->height);
return T;
}
/*******************************************************************************
Função que faz o reequilíbrio do nó pretendido da AVL.
Function that balances the tree if necessary in each node that does not respect
the equilibrium rule, after insertion and deletion operations.
*******************************************************************************/
static void Balance (PtAVLNode *proot)
{
unsigned int LeftH, RightH;
if (*proot == NULL) return; /* subárvore vazia - empty tree */
LeftH = AVLHeight ((*proot)->PtLeft); /* altura subárvore esquerda - left subtree height */
RightH = AVLHeight ((*proot)->PtRight); /* altura subárvore direita - right subtree height */
if (LeftH - RightH == 2) /* subárvore esquerda desequilibrada? - left subtree unbalanced? */
{
LeftH = AVLHeight ((*proot)->PtLeft->PtLeft);
RightH = AVLHeight ((*proot)->PtLeft->PtRight);
if (LeftH >= RightH) SingleRightRotation (proot);
else DoubleLeftRightRotation (proot);
}
else if (RightH - LeftH == 2) /* subárvore direita desequilibrada? - right subtree unbalanced? */
{
RightH = AVLHeight ((*proot)->PtRight->PtRight);
LeftH = AVLHeight ((*proot)->PtRight->PtLeft);
if (RightH >= LeftH) SingleLeftRotation (proot);
else DoubleRightLeftRotation (proot);
}
else (*proot)->Height = LeftH > RightH ? LeftH + 1 : RightH + 1;
/* atualizar a altura do nó - updationg the node height */
}
AVLTree Insert( AVLTree T, ElementType X )
{ /* 将X插入AVL树T中，并且返回调整后的AVL树 */
if ( !T ) { /* 若插入空树，则新建包含一个结点的树 */
T = (AVLTree)malloc(sizeof(struct AVLNode));
T->Data = X;
T->Height = 0;
T->Left = T->Right = NULL;
} /* if (插入空树) 结束 */
else if ( X < T->Data ) {
/* 插入T的左子树 */
T->Left = Insert( T->Left, X);
/* 如果需要左旋 */
if ( GetHeight(T->Left)-GetHeight(T->Right) == 2 )
if ( X < T->Left->Data )
T = SingleLeftRotation(T); /* 左单旋 */
else
T = DoubleLeftRightRotation(T); /* 左-右双旋 */
} /* else if (插入左子树) 结束 */
else if ( X > T->Data ) {
/* 插入T的右子树 */
T->Right = Insert( T->Right, X );
/* 如果需要右旋 */
if ( GetHeight(T->Left)-GetHeight(T->Right) == -2 )
if ( X > T->Right->Data )
T = SingleRightRotation(T); /* 右单旋 */
else
T = DoubleRightLeftRotation(T); /* 右-左双旋 */
} /* else if (插入右子树) 结束 */
/* else X == T->Data，无须插入 */
/* 别忘了更新树高 */
T->Height = Max( GetHeight(T->Left), GetHeight(T->Right) ) + 1;
return T;
}