#include<stdio.h>
#include<stdlib.h>
typedef struct AvlNode *Position;
typedef struct AvlNode *AvlTree;
typedef int ElementType;
struct AvlNode{
ElementType Element;
AvlTree Left;
AvlTree Right;
int Height;
}AvlNode;
//Avl函数的声明
AvlTree CreateTree(); //创建Avl树
Position Find(ElementType Element, AvlTree T); //查找
Position FindMax(AvlTree T);
Position FindMin(AvlTree T);
AvlTree Insert(ElementType Element, AvlTree T); //插入
AvlTree Delete(ElementType Element, AvlTree T); //删除
//插入结点到AVL树所需的函数声明
int Height(AvlTree T); //返回树的高
int Max(ElementType A, ElementType B); //比较树高
Position SingleRotateWithLeft(Position K2); //左单旋
Position SingleRotateWithRight(Position K2); //右单旋
Position DoubleRotateWithLeft(Position K3); //左右双旋
Position DoubleRotateWithRight(Position K3); //右左双旋
void PreOrder_1(AvlTree T); //先序遍历(递归)
int main()
{
AvlTree T;
ElementType Element;
int flag = 1, i;
printf(" 本程序实现Avl树的基本操作。 \n");
printf("| |\n");
printf("|**********************************************************************|\n");
printf("| Avl树的基本操作如下: |\n");
printf("| 0.创建Avl树 |\n");
printf("| 1.查找 |\n");
printf("| 2.插入 |\n");
printf("| 3.删除 |\n");
printf("| 4.将Avl树遍历 |\n");
printf("|**********************************************************************|\n");
while(flag){
printf("| 请选择功能: |\n");
scanf("%d", &i);
//输入需要选择的功能
switch(i){
case 0:
printf("请输入Avl树的根结点(0代表NULL):");
T = CreateTree();
break;
case 1:
if(T){
printf("请输入要查找的元素:");
scanf("%d", &Element);
if( Find(Element, T))
printf("该元素存在!\n");
else
printf("该元素不存在!\n");
}else
printf(" Avl树为空!\n");
break;
case 2:
if(T){
printf("请输入要插入的元素:");
scanf("%d", &Element);
T = Insert(Element, T);
}else
printf(" Avl树为空!\n");
break;
case 3:
if(T){
printf("请输入要删除的元素:");
scanf("%d", &Element);
T = Delete(Element, T);
}else
printf(" Avl树为空!\n");
break;
case 4:
if(T){
printf("(先序)遍历的结果为:");
PreOrder_1(T);
printf("\n");
}else
printf(" Avl树为空!\n");
break;
default:
flag = 0;
printf("程序运行结束,按任意键退出!\n");
}
}
return 0;
}
//Avl树的函数
AvlTree CreateTree() //创建Avl树
{
ElementType ch;
AvlTree T;
scanf("\n%d", &ch);
if(ch == 0)
T = NULL;
else{
if(!(T = (AvlTree)malloc(sizeof(AvlNode))))
exit(-1);
T->Element = ch;
printf("%d的左儿子为:", T->Element );
T->Left = CreateTree();
printf("%d的右儿子为:", T->Element );
T->Right = CreateTree();
}
return T;
}
Position Find(ElementType Element, AvlTree T) //Avl树的查找
{
if(T == NULL)
return NULL;
if(Element < T->Element) //向左找
return Find(Element, T->Left);
else if(Element > T->Element) //向右找
return Find(Element, T->Right);
else
return T;
}
Position FindMax(AvlTree T) //找最大值(非递归)
{
if(T != NULL){
while(T->Right != NULL ) //一直向右找
T = T->Right;
}
return T;
}
// Position FindMax(AvlTree T) //找最大值(递归)
//{
// if(T == NULL)
// return NULL;
// else if(T->Right == NULL)
// return T;
// else
// return FindMax(T->Right);
// }
Position FindMin(AvlTree T) //找最小值(非递归)
{
if(T != NULL){ //一直向左找
while(T->Left != NULL )
T = T->Left;
}
return T;
}
// Position FindMin(AvlTree T) //找最小值(递归)
//{
// if(T == NULL)
// return NULL;
// else if(T->Left == NULL)
// return T;
// else
// return FindMax(T->Left);
// }
AvlTree Insert(ElementType Element, AvlTree T) //插入元素到AVL树中
{
if(T == NULL){ //如果是空树,则初始化之
if(!(T = (AvlTree)malloc(sizeof(AvlNode))))
exit(-1);
else{
T->Element = Element;
T->Height = 0;
T->Left = T->Right = NULL;
}
}else if(Element < T->Element ){ //向左找
T->Left = Insert(Element, T->Left);
if(Height(T->Left ) - Height(T->Right ) == 2) //破坏了Avl树的平衡
if(Element < T->Left->Element )
T = SingleRotateWithLeft(T); //左 单旋(可以理解为此时树向左下沉(即天平偏向左边,需要向右挪树))
else
T = DoubleRotateWithLeft(T); //左右双旋 (先执行右单旋,再执行左单旋,一共旋转2次)
}else if(Element > T->Element ){
T->Right = Insert(Element, T->Right);
if(Height(T->Right ) - Height(T->Left ) == 2)
if(Element > T->Right->Element )
T = SingleRotateWithRight(T); //右单旋
else
T = DoubleRotateWithRight(T); //右左双旋
}
T->Height = Max(Height(T->Left ), Height(T->Right )) + 1; //平衡后新树的高度
return T;
}
AvlTree Delete(ElementType Element, AvlTree T) //删除元素 (与搜索二叉树的删除类似)
{
Position TmpCell;
if(T == NULL) //空树
printf("没找到该元素,无法删除!\n");
else if(Element < T->Element)
T->Left = Delete(Element, T->Left);
else if(Element > T->Element)
T->Right = Delete(Element, T->Right);
else if(T->Left && T->Right){ //要删除的树左右都有儿子
TmpCell = FindMin(T->Right); //用该结点右儿子上最小结点替换该结点,然后与只有一个儿子的操作方法相同
T->Element = TmpCell->Element;
T->Right = Delete(T->Element, T->Right);
}else{
TmpCell = T; //要删除的结点只有一个儿子
if(T->Left == NULL)
T = T->Right;
else if(T->Right == NULL)
T = T->Left;
free(TmpCell);
}
return T;
}
void PreOrder_1(AvlTree T) //先序遍历(递归)
{
if(T){
printf("%d ", T->Element);
PreOrder_1(T->Left);
PreOrder_1(T->Right);
}
}
int Height(AvlTree T) //返回的高
{
if(T == NULL)
return -1;
else
return 1 + Max(Height(T->Left ), Height(T->Right ));
}
int Max(ElementType A, ElementType B) //比较树高
{
if(A > B)
return A;
else
return B;
}
Position SingleRotateWithLeft(Position K2) //左单旋
{
Position K1;
K1 = K2->Left ;
K2->Left = K1->Right ;
K1->Right = K2;
K2->Height = Max(Height(K2->Left ), Height(K2->Right )) + 1;
K1->Height = Max(Height(K1->Left ), Height(K1->Right )) + 1;
return K1;
}
Position SingleRotateWithRight(Position K2) //右单旋
{
Position K1;
K1 = K2->Right ;
K2->Right = K1->Left ;
K1->Left = K2;
K2->Height = Max(Height(K2->Left ), Height(K2->Right )) + 1;
K1->Height = Max(Height(K1->Left ), Height(K1->Right )) + 1;
return K1;
}
Position DoubleRotateWithLeft(Position K3) //左右双旋
{
K3->Left = SingleRotateWithRight(K3->Left );
return SingleRotateWithLeft(K3);
}
Position DoubleRotateWithRight(Position K3) //右左双旋
{
K3->Right = SingleRotateWithLeft(K3->Right );
return SingleRotateWithRight(K3);
}