/********************************************************************
created: 2007/08/28
filename: avltree.c
author: Lichuang
purpose: AVL樹的實現代碼,
參考資料<<數據結構與算法分析-C語言描述>>, 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) // 插入到左子樹中
{
pNode->pLeft = Insert(nData, pNode->pLeft);
if (Height(pNode->pLeft) - Height(pNode->pRight) == 2) // AVL樹不平衡
{
if (nData < pNode->pLeft->nData)
{
// 插入到了左子樹左邊, 做單旋轉
pNode = SingleRotateWithLeft(pNode);
}
else
{
// 插入到了左子樹右邊, 做雙旋轉
pNode = DoubleRotateWithLeft(pNode);
}
}
}
else if (nData > pNode->nData) // 插入到右子樹中
{
pNode->pRight = Insert(nData, pNode->pRight);
if (Height(pNode->pRight) - Height(pNode->pLeft) == 2) // AVL樹不平衡
{
if (nData > pNode->pRight->nData)
{
// 插入到了右子樹右邊, 做單旋轉
pNode = SingleRotateWithRight(pNode);
}
else
{
// 插入到了右子樹左邊, 做雙旋轉
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;
// 結點的位置變了, 要更新結點的高度值
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;
// 結點的位置變了, 要更新結點的高度值
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);
}
// 后序遍歷樹以刪除樹
void DeleteTree(AVLTree** ppRoot)
{
if (NULL == ppRoot || NULL == *ppRoot)
return;
DeleteTree(&((*ppRoot)->pLeft));
DeleteTree(&((*ppRoot)->pRight));
free(*ppRoot);
*ppRoot = NULL;
}
// 中序遍歷打印樹的所有結點, 因為左結點 < 父結點 < 右結點, 因此打印出來數據的大小是遞增的
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,關于AVL樹,chinaunix的win_hate有一段精彩的講述,在這個地址:
http://bbs.chinaunix.net/viewthread.php?tid=692071