二叉树学习三：AVL树

  1 #include "stdafx.h"
  2 #include<time.h>
  3 #include<stdlib.h>
  4 #include<iostream>
  5 using namespace std;
  6 
  7 typedef struct AVLTree{
  8     int ndata;
  9     AVLTree* pLchild;
 10     AVLTree* pRchild;
 11     int nheight;
 12 }AVLTree;
 13 
 14 AVLTree* LLRotate(AVLTree* pRoot);
 15 AVLTree* RRRotate(AVLTree* pRoot);
 16 AVLTree* LRRotate(AVLTree* pRoot);
 17 AVLTree* RLRotate(AVLTree* pRoot);
 18 
 19 int Compare(int a,int b){
 20     return(a > b ? a : b);
 21 }
 22 int Height(AVLTree* pRoot){
 23     if (NULL==pRoot)
 24     {
 25         return -1;
 26     }
 27     else
 28     {
 29         return(pRoot->nheight);
 30     }
 31 }
 32 
 33 AVLTree* Insert(AVLTree* pRoot, int nData){
 34     if (NULL==pRoot)
 35     {
 36         pRoot = new AVLTree;
 37         pRoot->ndata = nData;
 38         pRoot->nheight = 0;
 39         pRoot->pLchild = NULL;
 40         pRoot->pRchild = NULL;
 41     }
 42     else if (pRoot->ndata>nData)
 43     {
 44         pRoot->pLchild = Insert(pRoot->pLchild, nData);
 45         if (Height(pRoot->pLchild) - Height(pRoot->pRchild)==2)
 46         {
 47             if (pRoot->pLchild->ndata>nData)
 48             {
 49                 pRoot = LLRotate(pRoot);
 50             }
 51             else
 52             {
 53                 pRoot = LRRotate(pRoot);
 54             }
 55         }
 56     }
 57     else if (pRoot->ndata<nData)
 58     {
 59         pRoot->pRchild = Insert(pRoot->pRchild, nData);
 60         if (Height(pRoot->pRchild) - Height(pRoot->pLchild) == 2)
 61         {
 62             if (pRoot->pRchild->ndata<nData)
 63             {
 64                 pRoot = RRRotate(pRoot);
 65             }
 66             else
 67             {
 68                 pRoot = RLRotate(pRoot);
 69             }
 70         }
 71     }
 72     pRoot->nheight = Compare(Height(pRoot->pLchild), Height(pRoot->pRchild)) + 1;
 73     return pRoot;
 74 }
 75 
 76 //LL旋转
 77 AVLTree* LLRotate(AVLTree* pRoot){
 78     AVLTree* pTemp;
 79 
 80     pTemp = pRoot->pLchild;
 81     pRoot->pLchild = pTemp->pRchild;
 82     pTemp->pRchild = pRoot;
 83 
 84     pRoot->nheight = Compare(Height(pRoot->pLchild), Height(pRoot->pRchild)) + 1;
 85     pTemp->nheight = Compare(Height(pTemp->pLchild), pRoot->nheight) + 1;
 86     return pTemp;
 87 }
 88 
 89 //RR旋转
 90 AVLTree* RRRotate(AVLTree* pRoot){
 91     AVLTree* pTemp;
 92 
 93     pTemp = pRoot->pRchild;
 94     pRoot->pRchild = pTemp->pLchild;
 95     pTemp->pLchild = pRoot;
 96 
 97     pRoot->nheight = Compare(Height(pRoot->pLchild), Height(pRoot->pRchild)) + 1;
 98     pTemp->nheight = Compare(Height(pTemp->pRchild), pRoot->nheight) + 1;
 99     return pTemp;
100 }
101 
102 //LR旋转
103 AVLTree* LRRotate(AVLTree* pRoot){
104     pRoot->pLchild = RRRotate(pRoot->pLchild);
105     return LLRotate(pRoot);
106 }
107 
108 //RL旋转
109 AVLTree* RLRotate(AVLTree* pRoot){
110     pRoot->pRchild = LLRotate(pRoot->pRchild);
111     return RRRotate(pRoot);
112 }
113 
114 //输出树
115 void PrintTree(AVLTree* pRoot){
116     if (NULL==pRoot)
117     {
118         return;
119     }
120     static int n = 0;
121     PrintTree(pRoot->pLchild);
122     cout << ++n << "\t" << pRoot->ndata << "\t" << pRoot->nheight << "\n";
123     PrintTree(pRoot->pRchild);
124 }
125 
126 int main()
127 {
128     AVLTree* pRoot = NULL;
129     srand((unsigned int)time(NULL));
130     for (int i = 0; i < 10; i++)
131     {
132         pRoot = Insert(pRoot, rand() % 100);
133     }
134     PrintTree(pRoot);
135     return 0;
136 }