AVL树的简单实现

来源：互联网发布：福州数据分析培训编辑：程序博客网时间：2024/05/01 06:09

AVL树是在二叉查找树的基础上加了一个平衡条件，目的是为了防止二叉查找树在某一边的深度过大而使效率降低
AVL树的关键是两个单旋转：左旋转和右旋转
双旋转也就是这两个旋转的组合

旋转的话用图是最好解释的下面用从别人那里盗来的图来说明下吧
这里写图片描述

想搞明白的话，自己照着这个图里面的画一画就差不多了

那么下面我就上代码了：

头文件：

#ifndef AVLTREE_H_INCLUDED#define AVLTREE_H_INCLUDEDstruct AvlNode;typedef struct AvlNode *Position;typedef struct AvlNode *AvlTree;typedef double 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);   //如果是采用懒惰删除，则可以实现这个方法用以恢复#endif // AVLTREE_H_INCLUDED

实现：

#include "AVLTree.h"#include <stdio.h>#include <stdlib.h>struct AvlNode{    ElementType Element;    AvlTree Left;    AvlTree Right;    int Height;};static int Height(Position P){    if(P == NULL)        return -1;    else        return P->Height;}static int Max(int H1,int H2){    if(H1 > H2)        return H1;    else        return H2;}static void FatalError(char * s){}static void Error(char * s){}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),K2->Height)+1;    return K1;}static Position SingleRotateWithRight(Position K1){    Position K2;    K2 = K1->Right;    K1->Right = K2->Left;    K2->Left = K1;    K1->Height = Max(Height(K1->Right),Height(K1->Left))+1;    K2->Height = Max(Height(K2->Right),K1->Height)+1;    return K2;}static Position DoubleRotateWithLeft(Position K3){    K3->Left = SingleRotateWithLeft(K3->Left);    return SingleRotateWithRight(K3);}static Position DoubleRotateWithRight(Position K1){    K1->Right = SingleRotateWithRight(K1->Right);    return SingleRotateWithLeft(K1);}Position Find(ElementType X,AvlTree T){    if(T == NULL)        return NULL;    else if(X > T->Element)        return Find(X,T->Right);    else if(X < T->Element)        return Find(X,T->Left);    else        return T;}Position FindMax(AvlTree T){    if(T != NULL)        while(T->Right != NULL)            T = T->Right;    return T;}Position FindMin(AvlTree T){    if(T != NULL)        while(T->Left != NULL)            T = T->Left;    return T;}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->Height = 0;            T->Left = T->Right = NULL;        }      //  printf("%lf\n",T->Element);    }    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 = DoubleRotateWithRight(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)        Delete(X,T->Right);    else if(X < T->Element)        Delete(X,T->Left);    else if(T->Left && T->Right)    {        TmpCell = FindMin(T->Right);        T->Element = TmpCell->Element;        T->Right = Delete(T->Element,T->Right);        T->Height = Max(T->Left->Height,Height(T->Right))+1;        if(T->Left->Height - T->Right->Height == 2)        {            if(T->Left->Left->Height > T->Left->Right->Height)                SingleRotateWithLeft(T);            else                DoubleRotateWithLeft(T);        }    }    else    {        TmpCell = T;        ElementType Tmp;        if(T->Right == NULL)            T = T->Left;        else if(T->Left == NULL)            T = T->Right;        free(TmpCell);        T->Height = (Height(T->Left),Height(T->Right))+1;    }    return T;}AvlTree MakeEmpty(AvlTree T){}int main(){    AvlTree T = NULL;    AvlTree T2 = NULL;    T = Insert(1.01,T);    Insert(2,T);    printf("%lf\n",T->Element);    Position P = FindMax(T);    printf("%lf\n",P->Element);    return 0;}

同样在最后加了一个main函数用于测试，编译器是gcc

PS：代码改编自《数据结构与算法分析第二版》，因为自己在改了一些，所以不保证没有BUG（因为书上的代码是ANSI C，有些用gcc过不了）

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