中国大学MOOC-陈越、何钦铭-数据结构
跳过概念，直接看代码（不知道怎么做页内跳转，逃ε=ε=ε
-
RR旋转（右单旋）
破坏节点在发现节点的右子树的右子树上
破坏节点：插入此节点之后开始不平衡。
发现节点：插入节点后，离破坏节点路径最短的不平衡结点。
RR旋转 -
LL旋转（左单旋）
LL旋转 -
LR旋转
LR旋转
-
RL旋转
RL旋转
代码在此
#include <stdio.h>
#include <stdlib.h>
typedef int DataType;
typedef struct AVLTreeNode *AVLTree;
typedef struct AVLTreeNode *SubTree;
typedef struct AVLTreeNode
{
int height; /* to calculate balance factor */
DataType data;
AVLTree left;
AVLTree right;
};
AVLTree CreatAVLTree(DataType node);
AVLTree InsertIntoAVL(AVLTree T, DataType node);
int GetHeight(SubTree T);
int Max(int a, int b);
SubTree LLRotate(SubTree T);
SubTree RRRotate(SubTree T);
SubTree LRRotate(SubTree T);
SubTree RLRotate(SubTree T);
int main(int argc, char const *argv[])
{
int n, i;
AVLTree T;
DataType tempNode;
scanf("%d", &n);
scanf("%d", &tempNode);
T = CreatAVLTree(tempNode); /* creat an empty tree */
/* insert sequence to build a AVL tree */
for (i = 1; i < n; i++) {
scanf("%d", &tempNode);
if (T) {
T = InsertIntoAVL(T, tempNode);
}
else break;
/* judge the balance of the tree after insertion by the balance factor */
/* check from the node to root */
}
if (T)
printf("%d", T->data);
else
printf("Input Error! You enter a same number \n"); /* it's not necessary */
return 0;
}
AVLTree CreatAVLTree(DataType node)
{
AVLTree T;
T = (AVLTree)malloc(sizeof(struct AVLTreeNode));
T->height = 1;
T->data = node;
T->left = NULL;
T->right = NULL;
return T;
}
AVLTree InsertIntoAVL(AVLTree T, DataType node)
{
if (!T)
T = CreatAVLTree(node);
else {
if (node < T->data) {
T->left = InsertIntoAVL(T->left, node);
/* it will judge the balance factor from bottom to the top */
if (GetHeight(T->left) - GetHeight(T->right) == 2) {
if (node < T->left->data)
T = LLRotate(T);
/* it means the node on the current subtree's left subtree 'left */
else
T = LRRotate(T);
}
}
else if (node > T->data) {
T->right = InsertIntoAVL(T->right, node);
if (GetHeight(T->right) - GetHeight(T->left) == 2) {
if (node > T->right->data)
T = RRRotate(T);
else
T = RLRotate(T);
}
}
else /* considering the equal situation, but in this case, it's not necessary */
return NULL;
}
/* updata the height of AVLTree from the leaf node to the root after every insert */
T->height = Max(GetHeight(T->left), GetHeight(T->right)) + 1;
return T;
}
int GetHeight(SubTree T)
{
if (!T)
return 0;
else
return T->height;
}
int Max(int a, int b)
{
return (a > b) ? a : b;
}
SubTree LLRotate(SubTree T)
{
SubTree Tmp;
Tmp = T;
T = T->left;
Tmp->left = T->right;
T->right = Tmp;
Tmp->height = Max(GetHeight(Tmp->left), GetHeight(Tmp->right)) + 1;
T->height = Max(GetHeight(T->left), GetHeight(T->right)) + 1;
return T;
}
SubTree RRRotate(SubTree T)
{
SubTree Tmp;
Tmp = T;
T = T->right;
Tmp->right = T->left;
T->left = Tmp;
Tmp->height = Max(GetHeight(Tmp->left), GetHeight(Tmp->right)) + 1;
T->height = Max(GetHeight(T->left), GetHeight(T->right)) + 1;
return T;
}
SubTree LRRotate(SubTree T)
{
T->left = RRRotate(T->left);
T = LLRotate(T);
return T;
}
SubTree RLRotate(SubTree T)
{
T->right = LLRotate(T->right);
T = RRRotate(T);
return T;
}
/*SubTree LRRotate(SubTree T)
{
SubTree Tmp;
Tmp = T;
T = T->left->right;
Tmp->left->right = T->left;
T->left = Tmp->left;
Tmp->left = T->right;
T->right = Tmp;
Tmp->height = Max(GetHeight(Tmp->left), GetHeight(Tmp->right)) + 1;
T->height = Max(GetHeight(T->left), GetHeight(T->right)) + 1;
return T;
}*/
- LR旋转可以转换成发现者的左子树 T->left 先做 RR旋转，然后发现者再做LL旋转。
下面即为一个例子
8为发现者，4为破坏者。
LR旋转例子 -
发现者的左子树 T->left 先做 RR旋转
T->left做LL旋转 - 发现者再做LL旋转
发现者做LL旋转
本文完
