C语言：平衡二叉树的实现（AVL)

// AVL(二叉平衡树）树的实现.cpp : 定义控制台应用程序的入口点。//#include "stdafx.h"#include<iostream>#include<stdio.h>#include<math.h>#define ElementType charusing namespace std;typedef struct AVLNode *Position;typedef Position AVLTree; //AVL树类型 typedef struct AVLNode{ElementType Data;AVLTree Left;AVLTree Right;int Height;}AVLNode;//函数声明int GetHeight(AVLTree A);          //得到树的高度void InorderTraversal(AVLTree BT); //递归中序遍历void PreorderTraversal(AVLTree A); //递归前序遍历树void PostorderTraversal(AVLTree BT);//递归后序遍历void GetOrderPrintLeaves(AVLTree BT);//递归求叶子节点AVLTree SingleLeftRotation(AVLTree A);//将A与B做左旋转，更新A.B的高度，返回根节点BAVLTree SingleRightRotation(AVLTree A);//将A与B做右旋转，更新A.B的高度，返回根节点BAVLTree DoubleLeftRightRotation(AVLTree A);AVLTree DoubleRightLeftRotation(AVLTree A);AVLTree Insert(AVLTree T, ElementType X);//将X插入到AVL树中，并且返回调整后的AVL树int Max(int a, int b); //返回a与b的最大值//函数定义int GetHeight(AVLTree A)   //求树的高度{int AL, AR, MAX;while (A){AL = GetHeight(A->Left);AR = GetHeight(A->Right);MAX = (AL>AR) ? AL : AR;return (MAX + 1);}return 0;}void InorderTraversal(AVLTree BT){if (BT){InorderTraversal(BT->Left);/* 此处假设对BT结点的访问就是打印数据 */cout << BT->Data;/* 假设数据为整型 */InorderTraversal(BT->Right);}}void PreorderTraversal(AVLTree A) //递归前序遍历树{if (A){cout << A->Data;PreorderTraversal(A->Left);PreorderTraversal(A->Right);}}void PostorderTraversal(AVLTree BT){if (BT){PostorderTraversal(BT->Left);PostorderTraversal(BT->Right);cout << BT->Data;}}void GetOrderPrintLeaves(AVLTree BT){if (BT){if (!BT->Left&&!BT->Right){cout << BT->Data;}GetOrderPrintLeaves(BT->Left);GetOrderPrintLeaves(BT->Right);}}int Max(int a, int b){return a>b ? a : b;}//LL型平衡调整，又称单向右旋平衡处理AVLTree SingleLeftRotation(AVLTree A)//将A与B做左旋转，更新A.B的高度，返回根节点B{//A必须有一个左子树结点BAVLTree B = A->Left;A->Left = B->Right;B->Right = A;A->Height = Max(GetHeight(A->Left), GetHeight(A->Right)) + 1;B->Height = Max(GetHeight(B->Left), A->Height) + 1;return B;}//RR型平衡调整，又称单向左旋平衡处理AVLTree SingleRightRotation(AVLTree A)//将A与B做右旋转，更新A.B的高度，返回根节点B{//A必须有一个右子树结点BAVLTree B = A->Right;A->Right = B->Left;B->Left = A;A->Height = Max(GetHeight(A->Left), GetHeight(A->Right)) + 1;B->Height = Max(A->Height, GetHeight(B->Right)) + 1;return B;}//LR型平衡调整，又称双向旋转（先左后右）平衡处理AVLTree DoubleLeftRightRotation(AVLTree A){//A必须有一个左子结点B，且B必须有一个右子结点C,将A、B与C做两次单旋，返回新的根结点C// 将B与C做右单旋，C被返回 A->Left = SingleRightRotation(A->Left);//将A与C做左单旋，C被返回 return SingleLeftRotation(A);}//RL型平衡调整，又称双向旋转（向右后左）平衡处理AVLTree DoubleRightLeftRotation(AVLTree A){//A必须有一个左子结点B，且B必须有一个右子结点C,将A、B与C做两次单旋，返回新的根结点C// 将B与C做左单旋，C被返回 A->Right = SingleLeftRotation(A->Right);//将A与C做右单旋，C被返回 return SingleRightRotation(A);}AVLTree Insert(AVLTree T, ElementType X)//将X插入到AVL树中，并且返回调整后的AVL树{if (!T)  //若插入空树，则新建包含一个结点的树{T = (AVLTree)malloc(sizeof(struct AVLNode));T->Data = X;T->Height = 0;T->Left = T->Right = NULL;}else if (X<T->Data)    //插入T的左子树 {T->Left = Insert(T->Left, X);if (GetHeight(T->Left) - GetHeight(T->Right) == 2)  //如果需要左旋if (X<T->Left->Data)T = SingleLeftRotation(T); //左单旋elseT = DoubleLeftRightRotation(T);//左右双旋}else if (X>T->Data)    //插入T的左子树 {T->Right = Insert(T->Right, X);if (GetHeight(T->Right) - GetHeight(T->Left) == 2)//如果需要左旋if (X>T->Right->Data)T = SingleRightRotation(T);//左单旋elseT = DoubleRightLeftRotation(T);//左右双旋}T->Height = Max(GetHeight(T->Left), GetHeight(T->Right)) + 1;//更新树高return T;}int _tmain(int argc, _TCHAR* argv[]){AVLTree AVL = NULL;int e = 0;char ch;cout << "请输入要创建的AVL树的结点个数：";cin >> e;for (int i = 0; i < e; i++){cin >> ch;AVL = Insert(AVL, ch);}cout << "递归先序遍历：";PreorderTraversal(AVL);cout << endl;cout << "递归中序遍历：";InorderTraversal(AVL);cout << endl;cout << "递归后序遍历：";PostorderTraversal(AVL);cout << endl;cout << "递归输出叶子结点：";GetOrderPrintLeaves(AVL);cout << endl;cout << "请输入要插入的结点：";cin >> ch;AVL = Insert(AVL, ch);cout << "递归先序遍历：";PreorderTraversal(AVL);cout << endl;cout << "递归中序遍历：";InorderTraversal(AVL);cout << endl;cout << "递归后序遍历：";PostorderTraversal(AVL);cout << endl;cout << "递归输出叶子结点：";GetOrderPrintLeaves(AVL);cout << endl;return 0;}