【算法学习】AVL平衡二叉搜索树原理及各项操作编程实现（C语言）

#include<stdio.h>
#include "fatal.h"

struct AvlNode;
typedef struct AvlNode *Position;
typedef struct AvlNode *AvlTree;

typedef int ElementType ;

AvlTree MakeEmpty(AvlTree T);
Position Find(ElementType X,AvlTree T);
Position FindMin(AvlTree T);
Position FindMax(AvlTree T);
AvlTree Insert(ElementType X,AvlTree T);
AvlTree Delete(ElementType X,AvlTree T);
ElementType Retrieve(Position P);

struct AvlNode
{
ElementType Element;
AvlTree left;
AvlTree right;
int height;
};

AvlTree MakeEmpty(AvlTree T)
{
if(T!=NULL)
{
MakeEmpty(T->left);
MakeEmpty(T->right);
free(T);
}
return NULL;
}

Position Find(ElementType X,AvlTree T)
{
if(T==NULL)
return NULL;
if(X<T->Element)
return Find(X,T->left);
else if(X>T->Element)
return Find(X,T->right);
else
return T;
}

Position FindMin(AvlTree T)
{
if(T==NULL)
return NULL;
if(T->left==NULL)
return T;
else
return FindMin(T->left);
}

Position FindMax(AvlTree T)
{
if(T==NULL)
return NULL;
if(T->right==NULL)
return T;
else
return FindMax(T->right);
}

static int Height(Position P)
{
if(P==NULL)
return -1;
else
return P->height;
}

static int Max(int Lhs,int Rhs)
{
return Lhs>Rhs?Lhs:Rhs;
}
//RR旋转
static Position SingleRotateWithLeft(Position K2)
{
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(K2->right))+1;
return K1;
}
//LL旋转
static Position SingleRotateWithRight(Position K1)
{
Position K2;
K2=K1->right;
K1->right=K2->left;
K2->left=K1;
K1->height=Max(Height(K1->left),Height(K1->right))+1;
K2->height=Max(Height(K2->right),Height(K1->left))+1;
return K2;
}
//LR旋转
static Position DoubleRotateWithLeft(Position K3)
{
K3->left=SingleRotateWithRight(K3->left);

return SingleRotateWithLeft(K3);
}

//RL旋转
static Position DoubleRotateWithRight(Position K3)
{
K3->right=SingleRotateWithLeft(K3->right);
return SingleRotateWithRight(K3);
}

AvlTree Insert(ElementType X,AvlTree T)
{
if(T==NULL)
{
T=malloc(sizeof(struct AvlNode));
if(T==NULL)
FatalError("out of space!!!");
else
{
T->Element=X;
T->right=T->left=NULL;
}
}
else if(X<T->Element)
{
T->left=Insert(X,T->left);
if(Height(T->left)-Height(T->right)==2)
{
if(X<T->left->Element)
T=SingleRotateWithLeft(T);
else
T=DoubleRotateWithLeft(T);
}
}
else if(X>T->Element)
{
T->right=Insert(X,T->right);
if(Height(T->right)-Height(T->left)==2)
{
if(X>T->right->Element)
T=SingleRotateWithRight(T);
else
T=DoubleRotateWithRight(T);
}
}
T->height=Max(Height(T->left),Height(T->right))+1;
return T;
}

AvlTree Delete(ElementType X,AvlTree T)
{
Position TmpCell;
if(T==NULL)
Error("Element not found");
else if(X<T->Element)
{
T->left=Delete(X,T->left);
if(Height(T->right)-Height(T->left)==2)
{
if(Height(T->right->left)>Height(T->right->right))
T=DoubleRotateWithRight(T);
else
T=SingleRotateWithRight(T);
}
}
else if(X>T->Element)
{
T->right=Delete(X,T->left);
if(Height(T->left)-Heighe(T->right)==2)
{
if(Heighe(T->left->right)>Height(T->left->left))
T=DoubleRotateWithLeft(T);
else
T=SingleRotateWithLeft(T);
}
}
//找到要删除的节点就是根节点，且根节点的左右子树都不为空
else if(T->left&&T->right)
{
if(Height(T->left)>Height(T->right))
{
T->Element=FindMax(T->left)->Element;
T->left=Delete(T->Element,T->left);
}
else
{
T->Element=FindMin(T->right)->Element;
T->right=Delete(T->Element,T->right);
}
}
//找到是根节点，但是根节点有一个或者没有子节点
else
{
TmpCell=T;
if(T->left==NULL)
T=T->right;
else if(T->right==NULL)
T=T->left;
free(TmpCell);
}
T->height=Max(Height(T->left),Height(T->right))+1;
return T;
}

ElementType Retrieve(Position P)
{
if(P==NULL)
return -1;
else
return P->Element;
}

#include <stdio.h>
#include <stdlib.h>

#define Error( Str )        FatalError( Str )
#define FatalError( Str )   fprintf( stderr, "%s\n", Str ), exit( 1 )