判断是否是平衡二叉树

本文有两种方法判断一棵树是否为AVL树#include <iostream>#include<math.h>   //abs#include<queue>#include <string>using namespace std;typedef struct TreeNode{    string data;    struct TreeNode* lchild;    struct TreeNode* rchild;}TreeNode;void levelTraver(TreeNode* T)  //层次遍历{    if (!T)        return;    queue<TreeNode*> Q;    TreeNode* cur = T;    Q.push(cur);    while (!Q.empty())    {        cout << Q.front()->data << " ";        cur = Q.front();        Q.pop();        if (cur->lchild)            Q.push(cur->lchild);        if (cur->rchild)            Q.push(cur->rchild);    }}TreeNode* NodebyString(string s)  //根据s的值{    if (s == "#") //若str[i]的值为#，则不创建节点        return NULL;    else  //否则，创建节点并返回    {        TreeNode* node = new TreeNode;        node->data = s;        return node;    }}TreeNode* levelDeSerialize(string str[])  //层序反序列化{    int index1 = 0;    TreeNode* T = NodebyString(str[index1++]);    queue<TreeNode*> Q;    if (T != NULL)        Q.push(T);    TreeNode* cur;    while (!Q.empty())    {        cur = Q.front();        Q.pop();        cur->lchild = NodebyString(str[index1++]);        cur->rchild = NodebyString(str[index1++]);        if (cur->lchild)            Q.push(cur->lchild);        if (cur->rchild)            Q.push(cur->rchild);    }    return T;}int height(TreeNode* T)  //求树的高度{    if (!T)        return 0;    //后序遍历求树的高度    int LH = height(T->lchild);    int RH = height(T->rchild);    return (LH > RH) ? (1 + LH) : (1 + RH);}//方法一：bool isAVLTree1(TreeNode* T)  //是否为平衡二叉树{    if (!T)  //求以T为根的二叉树是否为AVL树        return true;    int LH = height(T->lchild); //求左子树的高度    int RH = height(T->rchild); //求右子树的高度    if (abs(LH - RH) > 1)        return false;    //再判断T的左子树和右子树是否为AVL树    return isAVLTree1(T->lchild) && isAVLTree1(T->rchild);  }//方法二：//二叉树的层序遍历，顺便记录每一个节点的高度depth、平衡性bool isAVLTree2(TreeNode* T,int &depth)  //传入的必须是引用{    if (!T)    {        depth = 0;        return true;    }    int LH = 0;    int RH = 0;    if (isAVLTree2(T->lchild, LH) && isAVLTree2(T->rchild, RH))    {        if (abs(LH - RH) <= 1)        {            depth = 1 + (LH > RH ? LH : RH);            return true;        }    }    return false;}int main(){    string str[] = { "1", "2", "3", "#", "4", "5", "#", "6", "#", "#", "#", "#","#" };    TreeNode* T = levelDeSerialize(str); //反序列化    cout << "层序遍历" << endl;    levelTraver(T);    cout << "\n高度 = ";    int H = height(T);    cout << H << endl;    int depth = 0;    bool isAVL = isAVLTree2(T, depth);    cout <<"是否为平衡二叉树"<<isAVL << endl;    return 0;}