/********************************************************************
created: 2007/08/28
filename: avltree.c
author: Lichuang
purpose: AVL树的实现代码,
参考资料<<数据结构与算法分析-C语言描述>>, 作者Allen Weiss
*********************************************************************/
#include <stdio.h>
#include <stdlib.h>
#include <time.h>
typedef struct AVLTree
{
int nData;
struct AVLTree* pLeft;
struct AVLTree* pRight;
int nHeight;
}AVLTree;
int Max(int a, int b);
int Height(AVLTree* pNode);
AVLTree* Insert(int nData, AVLTree* pNode);
AVLTree* SingleRotateWithLeft(AVLTree* pNode);
AVLTree* SingleRotateWithRight(AVLTree* pNode);
AVLTree* DoubleRotateWithLeft(AVLTree* pNode);
AVLTree* DoubleRotateWithRight(AVLTree* pNode);
void DeleteTree(AVLTree** ppRoot);
void PrintTree(AVLTree* pRoot);
int main()
{
int i;
AVLTree* pRoot = NULL;
srand((unsigned int)::time(NULL));
for (i = 0; i < 100000000; ++i)
{
pRoot = Insert(::rand(), pRoot);
}
//PrintTree(pRoot);
DeleteTree(&pRoot);
return 0;
}
int Max(int a, int b)
{
return (a > b ? a : b);
}
int Height(AVLTree* pNode)
{
if (NULL == pNode)
return -1;
return pNode->nHeight;
}
AVLTree* Insert(int nData, AVLTree* pNode)
{
if (NULL == pNode)
{
pNode = (AVLTree*)malloc(sizeof(AVLTree));
pNode->nData = nData;
pNode->nHeight = 0;
pNode->pLeft = pNode->pRight = NULL;
}
else if (nData < pNode->nData) // 插入到左子树中
{
pNode->pLeft = Insert(nData, pNode->pLeft);
if (Height(pNode->pLeft) - Height(pNode->pRight) == 2) // AVL树不平衡
{
if (nData < pNode->pLeft->nData)
{
// 插入到了左子树左边, 做单旋转
pNode = SingleRotateWithLeft(pNode);
}
else
{
// 插入到了左子树右边, 做双旋转
pNode = DoubleRotateWithLeft(pNode);
}
}
}
else if (nData > pNode->nData) // 插入到右子树中
{
pNode->pRight = Insert(nData, pNode->pRight);
if (Height(pNode->pRight) - Height(pNode->pLeft) == 2) // AVL树不平衡
{
if (nData > pNode->pRight->nData)
{
// 插入到了右子树右边, 做单旋转
pNode = SingleRotateWithRight(pNode);
}
else
{
// 插入到了右子树左边, 做双旋转
pNode = DoubleRotateWithRight(pNode);
}
}
}
pNode->nHeight = Max(Height(pNode->pLeft), Height(pNode->pRight)) + 1;
return pNode;
}
/********************************************************************
pNode pNode->pLeft
/ \
pNode->pLeft ==> pNode
\ /
pNode->pLeft->pRight pNode->pLeft->pRight
*********************************************************************/
AVLTree* SingleRotateWithLeft(AVLTree* pNode)
{
AVLTree* pNode1;
pNode1 = pNode->pLeft;
pNode->pLeft = pNode1->pRight;
pNode1->pRight = pNode;
// 结点的位置变了, 要更新结点的高度值
pNode->nHeight = Max(Height(pNode->pLeft), Height(pNode->pRight)) + 1;
pNode1->nHeight = Max(Height(pNode1->pLeft), pNode->nHeight) + 1;
return pNode1;
}
/********************************************************************
pNode pNode->pRight
\ /
pNode->pRight ==> pNode
/ \
pNode->pRight->pLeft pNode->pRight->pLeft
*********************************************************************/
AVLTree* SingleRotateWithRight(AVLTree* pNode)
{
AVLTree* pNode1;
pNode1 = pNode->pRight;
pNode->pRight = pNode1->pLeft;
pNode1->pLeft = pNode;
// 结点的位置变了, 要更新结点的高度值
pNode->nHeight = Max(Height(pNode->pLeft), Height(pNode->pRight)) + 1;
pNode1->nHeight = Max(Height(pNode1->pRight), pNode->nHeight) + 1;
return pNode1;
}
AVLTree* DoubleRotateWithLeft(AVLTree* pNode)
{
pNode->pLeft = SingleRotateWithRight(pNode->pLeft);
return SingleRotateWithLeft(pNode);
}
AVLTree* DoubleRotateWithRight(AVLTree* pNode)
{
pNode->pRight = SingleRotateWithLeft(pNode->pRight);
return SingleRotateWithRight(pNode);
}
// 后序遍历树以删除树
void DeleteTree(AVLTree** ppRoot)
{
if (NULL == ppRoot || NULL == *ppRoot)
return;
DeleteTree(&((*ppRoot)->pLeft));
DeleteTree(&((*ppRoot)->pRight));
free(*ppRoot);
*ppRoot = NULL;
}
// 中序遍历打印树的所有结点, 因为左结点 < 父结点 < 右结点, 因此打印出来数据的大小是递增的
void PrintTree(AVLTree* pRoot)
{
if (NULL == pRoot)
return;
static int n = 0;
PrintTree(pRoot->pLeft);
printf("[%d]nData = %d\n", ++n, pRoot->nData);
PrintTree(pRoot->pRight);
}
另外,关于AVL树,chinaunix的win_hate有一段精彩的讲述,在这个地址:
http://bbs.chinaunix.net/viewthread.php?tid=692071