AVL树

///////////Avl树//////////////
struct AvlNode;
typedef struct AvlNode* AvlTree;
typedef struct AvlNode* Position;

struct AvlNode{
ElementType element;
AvlTree left;
AvlTree right;
int height;  //存储高度信息
}

//返回高度信息
int get_height(Position P){
if(P==NULL){
return -1;
}
else{
return P->height;
}
}

//插入元素到AVL树的例程  重难点
AvlTree Insert(ElementType x,AvlTree T){
if(T==NULL){
AvlTree T=malloc(sizeof(struct AvlNode));
T->element=x;
T->left=NULL;
T->right=NULL;
T->height=0;
//return T;
}
else if(x < T->element){
T->left=Insert(x,T->left);
//处理左平衡条件
if((get_height(T->left)-get_height(T->right))==2 /* >1 */){
if(x < T->left->element){  //左左
T=SingleRorateWithLeft(T);
}
else{  //左右
T=DoubleRotateWithLeft(T);
}
}
}
else if(x > T->element){
T->right=Insert(x,T->right);
//同理，处理右平衡条件
if((get_height(T->right) - get_height(T->left))==2){
if(x > T->right->element){  //右右
T=SingleRorateWithRight(T);
}
else{  //右左
T=DoubleRotateWithRight(T);
}
}

}
else{
//x is already exists,do nothing
}

//高度信息修改
T->height=max(get_height(T->left),get_height(T->right))+1;
return T;
}

//单旋转例程  左左
Position SingleRorateWithLeft(Position K2){
//初始化
Position K1;
K1=K2->left;

//旋转
K2->left=K1->right;
K1->right=K2;

//更新高度信息
K2->height=max(get_height(K2->left),get_height(K2->right))+1;
K1->height=max(get_height(K1->left),get_height(K1->right)/*K2->height*/)+1;

//返回新节点
return K1;
}

//右右
Position SingleRorateWithRight(Position K2){
Position K1;
K1=K2->right;

K2->right=K1->left;
K1->left=K2;

K2->height=max(get_height(K2->left),get_height(K2->right))+1;
K1->height=max(get_height(K1->left),get_height(K1->right))+1;

return K1;
}

//双旋转例程 左右
Position DoubleRotateWithLeft(Position K3){

K3->left=SingleRorateWithRight(K3->left);

return SingleRorateWithLeft(K3);
}

//双旋转例程 右左
Position DoubleRotateWithRight(Position K3){

K3->right=SingleRorateWithLeft(K3->right);

return SingleRorateWithRight(K3);
}